problem solving stage

What is Problem Solving? (Steps, Techniques, Examples)

By Status.net Editorial Team on May 7, 2023 — 5 minutes to read

What Is Problem Solving?

Definition and importance.

Problem solving is the process of finding solutions to obstacles or challenges you encounter in your life or work. It is a crucial skill that allows you to tackle complex situations, adapt to changes, and overcome difficulties with ease. Mastering this ability will contribute to both your personal and professional growth, leading to more successful outcomes and better decision-making.

Problem-Solving Steps

The problem-solving process typically includes the following steps:

Identify the issue : Recognize the problem that needs to be solved.
Analyze the situation : Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present.
Generate potential solutions : Brainstorm a list of possible solutions to the issue, without immediately judging or evaluating them.
Evaluate options : Weigh the pros and cons of each potential solution, considering factors such as feasibility, effectiveness, and potential risks.
Select the best solution : Choose the option that best addresses the problem and aligns with your objectives.
Implement the solution : Put the selected solution into action and monitor the results to ensure it resolves the issue.
Review and learn : Reflect on the problem-solving process, identify any improvements or adjustments that can be made, and apply these learnings to future situations.

Defining the Problem

To start tackling a problem, first, identify and understand it. Analyzing the issue thoroughly helps to clarify its scope and nature. Ask questions to gather information and consider the problem from various angles. Some strategies to define the problem include:

Brainstorming with others
Asking the 5 Ws and 1 H (Who, What, When, Where, Why, and How)
Analyzing cause and effect
Creating a problem statement

Generating Solutions

Once the problem is clearly understood, brainstorm possible solutions. Think creatively and keep an open mind, as well as considering lessons from past experiences. Consider:

Creating a list of potential ideas to solve the problem
Grouping and categorizing similar solutions
Prioritizing potential solutions based on feasibility, cost, and resources required
Involving others to share diverse opinions and inputs

Evaluating and Selecting Solutions

Evaluate each potential solution, weighing its pros and cons. To facilitate decision-making, use techniques such as:

SWOT analysis (Strengths, Weaknesses, Opportunities, Threats)
Decision-making matrices
Pros and cons lists
Risk assessments

After evaluating, choose the most suitable solution based on effectiveness, cost, and time constraints.

Implementing and Monitoring the Solution

Implement the chosen solution and monitor its progress. Key actions include:

Communicating the solution to relevant parties
Setting timelines and milestones
Assigning tasks and responsibilities
Monitoring the solution and making adjustments as necessary
Evaluating the effectiveness of the solution after implementation

Utilize feedback from stakeholders and consider potential improvements. Remember that problem-solving is an ongoing process that can always be refined and enhanced.

Problem-Solving Techniques

During each step, you may find it helpful to utilize various problem-solving techniques, such as:

Brainstorming : A free-flowing, open-minded session where ideas are generated and listed without judgment, to encourage creativity and innovative thinking.
Root cause analysis : A method that explores the underlying causes of a problem to find the most effective solution rather than addressing superficial symptoms.
SWOT analysis : A tool used to evaluate the strengths, weaknesses, opportunities, and threats related to a problem or decision, providing a comprehensive view of the situation.
Mind mapping : A visual technique that uses diagrams to organize and connect ideas, helping to identify patterns, relationships, and possible solutions.

Brainstorming

When facing a problem, start by conducting a brainstorming session. Gather your team and encourage an open discussion where everyone contributes ideas, no matter how outlandish they may seem. This helps you:

Generate a diverse range of solutions
Encourage all team members to participate
Foster creative thinking

When brainstorming, remember to:

Reserve judgment until the session is over
Encourage wild ideas
Combine and improve upon ideas

Root Cause Analysis

For effective problem-solving, identifying the root cause of the issue at hand is crucial. Try these methods:

5 Whys : Ask “why” five times to get to the underlying cause.
Fishbone Diagram : Create a diagram representing the problem and break it down into categories of potential causes.
Pareto Analysis : Determine the few most significant causes underlying the majority of problems.

SWOT Analysis

SWOT analysis helps you examine the Strengths, Weaknesses, Opportunities, and Threats related to your problem. To perform a SWOT analysis:

List your problem’s strengths, such as relevant resources or strong partnerships.
Identify its weaknesses, such as knowledge gaps or limited resources.
Explore opportunities, like trends or new technologies, that could help solve the problem.
Recognize potential threats, like competition or regulatory barriers.

SWOT analysis aids in understanding the internal and external factors affecting the problem, which can help guide your solution.

Mind Mapping

A mind map is a visual representation of your problem and potential solutions. It enables you to organize information in a structured and intuitive manner. To create a mind map:

Write the problem in the center of a blank page.
Draw branches from the central problem to related sub-problems or contributing factors.
Add more branches to represent potential solutions or further ideas.

Mind mapping allows you to visually see connections between ideas and promotes creativity in problem-solving.

Examples of Problem Solving in Various Contexts

In the business world, you might encounter problems related to finances, operations, or communication. Applying problem-solving skills in these situations could look like:

Identifying areas of improvement in your company’s financial performance and implementing cost-saving measures
Resolving internal conflicts among team members by listening and understanding different perspectives, then proposing and negotiating solutions
Streamlining a process for better productivity by removing redundancies, automating tasks, or re-allocating resources

In educational contexts, problem-solving can be seen in various aspects, such as:

Addressing a gap in students’ understanding by employing diverse teaching methods to cater to different learning styles
Developing a strategy for successful time management to balance academic responsibilities and extracurricular activities
Seeking resources and support to provide equal opportunities for learners with special needs or disabilities

Everyday life is full of challenges that require problem-solving skills. Some examples include:

Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
How to Resolve Employee Conflict at Work [Steps, Tips, Examples]
How to Write Inspiring Core Values? 5 Steps with Examples
30 Employee Feedback Examples (Positive & Negative)

Skip to main content
Skip to primary sidebar
Skip to footer

Psychology Spot

All About Psychology

The 5 phases of problem solving

Problem solving is a complex psychological process through which we try to find the best way to overcome an obstacle or face a challenge. Unfortunately, this process is not always linear, but can follow tortuous paths, plunging us into a situation of psychological anguish when we believe that there is no possible solution.

On the other hand, knowing the phases of problem solving will save us a lot of headaches. Providing a coherent structure to the situation that concerns us, and having a common thread that guides us along the way, will help us to put some order in the mental chaos that problems usually generate.

To Solve a Problem, Experience Does not Always Work in Our Favor

Experience can be a plus or, on the contrary, become an impediment to solving problems. Psychologists from the universities of Hong Kong and Princeton examined how we implement problem-solving strategies by asking a group of people to solve a series of problems with matches.

Participants were presented with a series of linked squares. Each square in the matrix was made up of separate pieces, and people had to remove a certain number of matches while keeping a specified number of squares intact. The interesting thing about these types of problems is that they generally have more than one solution, different strategies can be used and these must change according to the configuration of the matrix, just as it usually happens with life problems.

These researchers found that participants went through two major stages in problem solving. At first they let themselves be carried away by the perceptual characteristics of the problem and began to explore different strategies, some successful and others not.

In a second moment they used the accumulated experience to narrow their options of strategies, focusing on those that were more successful. The problem is that the more the participants trusted their strategic knowledge, the more difficulties they had in solving problems that demanded the application of novel strategies. In practice, they suffered from a kind of functional fixation.

These series of experiments show us that to solve a problem we must keep an open mind because along the way circumstances are likely to change and we need the mental flexibility necessary to change our problem-solving strategies.

The Stages of Problem Solving We Can All Apply

1. Identify the problem

It may seem like a truism, but the truth is that identifying the real problem is not as easy as it seems, especially when it comes to a situation that affects us emotionally. In fact, when the problem is too scary or we sense that we do not have the psychological tools to solve it, we usually put into practice defense mechanisms such as displacement that allow us to erase the problematic situation from our conscious mind.

Instead, being able to identify the problem is the first step in finding a solution. Many times that means stopping looking outside for the culprits and searching within, wondering why a situation is particularly bothering or hindering us.

2. Understand the problem

Many times the problem brings with it the seed of the solution. So one of the steps in solving a problem is making sure we understand it. It is not enough to identify the problem, we need to define it. For this we need to analyze it from different perspectives.

For example, if we are trying to carry out a professional project that does not finish taking off, we have to clarify the reasons. Do we need more training? Are we in an overly competitive sector? Do we have enough resources? We need to understand the source of the problem.

Organizing the information available is another crucial step in the problem-solving process. We have to ask ourselves both, what we know about the problem and everything we do not know. Ultimately, the accuracy of the solution will largely depend on the amount of information available.

3. Assume a psychological distance

Most of the major problems in life have the potential to generate an emotional tsunami. However, many times that affective involvement obfuscates and prevents us from thinking clearly. That is why on many occasions one of the most important but least known phases for solving problems consists of moving away from what concerns us. To assume a psychological distance , we can take a few days away from the problematic environment or try to stop thinking about what worries us for a while.

During that time the unconscious mind will continue to work and is likely to generate creative and perfectly valid insights that lead to the solution of the problem. That distance to allow us to overcome the functional fixations that prevent us from thinking outside the box, giving way to a mental restructuring that will allow us to see the problem from another perspective.

4. Find solutions and develop strategies

Each problem is different, so it will require a specific solution. A solution cannot always be reached by insight, so it will be necessary to think of possible alternatives to solve the problem. Synectics , for example, is a problem-solving method that uses creativity to find original solutions.

The next step is to develop a strategy, since solutions that do not materialize in concrete steps are very difficult to implement. Therefore, we must ask ourselves how we are going to implement our solution. In this phase of problem solving it is important to be honest with ourselves and “land” that strategy taking into account our resources and real availability. It is useless to develop a great strategy if we cannot apply it later.

5. Evaluation of progress

Very few problems are solved overnight. These are generally complex situations that we must patiently “unwind” over time. Therefore, another of the phases to solve a problem consists of monitoring the results that we are achieving. This way we make sure that we are on the right track and we are not wasting energy and time uselessly.

In this last stage of problem solving it is important to be able to adapt our expectations. It is difficult for a professional project to take off in the blink of an eye, so we must focus on the small steps that indicate that the solution is paying off. To do this, it is important to sit down and reflect on the impact of the solution from time to time.

We must also bear in mind that circumstances often change, so we may need to make adjustments to our initial solution. This requires great mental flexibility to change course when we realize that the strategy is not as effective as we would like.

Fedor, A. et. Al. (2015) Problem solving stages in the five square problem. Front. Psychol ; 6: 1050.

Louis Lee, N. Y. & Johnson-Laird, P. N. (2013) Strategic changes in problem solving. Journal of Cognitive Psychology ; 25: 165–173.

Gillen, G. (2009) Managing Executive Function Impairments to Optimize Function. Cognitive and Perceptual Rehabilitation ; 245-283.

Jennifer Delgado

I am a psychologist and I spent several years writing articles for scientific journals specialized in Health and Psychology. I want to help you create great experiences. Learn more about me .

Marriage wears out women more than men, according to science

26/04/2024 By Jennifer Delgado

How anxiety medications work?

The biggest mistake we all make when trying to persuade others

25/04/2024 By Jennifer Delgado

35 problem-solving techniques and methods for solving complex problems

Design your next session with SessionLab

Join the 150,000+ facilitators  using SessionLab.

How do you identify problems?

How do you identify the right solution.

Tips for more effective problem-solving

Complete problem-solving methods

Problem-solving techniques to identify and analyze problems
Problem-solving techniques for developing solutions

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve.

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward.

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.

Try different approaches

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

Six Thinking Hats
Lightning Decision Jam
Problem Definition Process
Discovery & Action Dialogue

Design Sprint 2.0

Open Space Technology

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on.

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages.

Lightning Decision Jam (LDJ) #action #decision making #problem solving #issue analysis #innovation #design #remote-friendly The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design.

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition #problem solving #idea generation #creativity #online #remote-friendly A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges.

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results.

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys #hyperisland #innovation This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold.

World Cafe #hyperisland #innovation #issue analysis World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD) #idea generation #liberating structures #action #issue analysis #remote-friendly DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology #action plan #idea generation #problem solving #issue analysis #large group #online #remote-friendly Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

The Creativity Dice
Fishbone Analysis
Problem Tree
SWOT Analysis
Agreement-Certainty Matrix
The Journalistic Six
LEGO Challenge
What, So What, Now What?
Journalists

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed.

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It! #gamestorming #problem solving #action Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed.

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable.

The Creativity Dice #creativity #problem solving #thiagi #issue analysis Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around.

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish.

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis #problem solving ##root cause analysis #decision making #online facilitation A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them.

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree #define intentions #create #design #issue analysis A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward.

SWOT analysis #gamestorming #problem solving #action #meeting facilitation The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results.

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause.

Agreement-Certainty Matrix #issue analysis #liberating structures #problem solving You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic . A problem is simple when it can be solved reliably with practices that are easy to duplicate. It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably. A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail. Chaotic is when the context is too turbulent to identify a path forward. A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.” The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process.

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID #gamestorming #project planning #issue analysis #problem solving When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!

Speed Boat #gamestorming #problem solving #action Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How #idea generation #issue analysis #problem solving #online #creative thinking #remote-friendly A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills.

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO!

LEGO Challenge #hyperisland #team A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems.

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken.

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What? #issue analysis #innovation #liberating structures You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists #vision #big picture #issue analysis #remote-friendly This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

Improved Solutions
Four-Step Sketch
15% Solutions
How-Now-Wow matrix
Impact Effort Matrix

21. Mindspin

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly.

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation.

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex.

MindSpin #teampedia #idea generation #problem solving #action A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result.

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution.

Improved Solutions #creativity #thiagi #problem solving #action #team You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged.

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch #design sprint #innovation #idea generation #remote-friendly The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper, Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change.

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change.

15% Solutions #action #liberating structures #remote-friendly You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference. 15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change. With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process.

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud.

How-Now-Wow Matrix #gamestorming #idea generation #remote-friendly When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice.

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them.

Impact and Effort Matrix #gamestorming #decision making #action #remote-friendly In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action?

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus.

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively.

Dotmocracy #action #decision making #group prioritization #hyperisland #remote-friendly Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

Check-in/Check-out
Doodling Together
Show and Tell
Constellations
Draw a Tree

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute.

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out #team #opening #closing #hyperisland #remote-friendly Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start.

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems.

Doodling Together #collaboration #creativity #teamwork #fun #team #visual methods #energiser #icebreaker #remote-friendly Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team!

Show and Tell #gamestorming #action #opening #meeting facilitation Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible.

Constellations #trust #connection #opening #coaching #patterns #system Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic.

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree #thiagi #opening #perspectives #remote-friendly With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

One Breath Feedback
Who What When Matrix
Response Cards

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space.

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round.

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them.

One breath feedback #closing #feedback #action This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward.

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved.

Who/What/When Matrix #gamestorming #action #project planning With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out!

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised.

Response Cards #debriefing #closing #structured sharing #questions and answers #thiagi #action It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Save time and effort discovering the right solutions

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks to build your agenda. When you make changes or update your agenda, your session timing adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore how to use SessionLab to design effective problem solving workshops or watch this five minute video to see the planner in action!

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you!

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

Design your next workshop with SessionLab

Join the 150,000 facilitators using SessionLab

The Art of Effective Problem Solving: A Step-by-Step Guide
Learn Lean Sigma
Problem Solving

Whether we realise it or not, problem solving skills are an important part of our daily lives. From resolving a minor annoyance at home to tackling complex business challenges at work, our ability to solve problems has a significant impact on our success and happiness. However, not everyone is naturally gifted at problem-solving, and even those who are can always improve their skills. In this blog post, we will go over the art of effective problem-solving step by step.

You will learn how to define a problem, gather information, assess alternatives, and implement a solution, all while honing your critical thinking and creative problem-solving skills. Whether you’re a seasoned problem solver or just getting started, this guide will arm you with the knowledge and tools you need to face any challenge with confidence. So let’s get started!

Problem solving methodologies.

Individuals and organisations can use a variety of problem-solving methodologies to address complex challenges. 8D and A3 problem solving techniques are two popular methodologies in the Lean Six Sigma framework.

Methodology of 8D (Eight Discipline) Problem Solving:

The 8D problem solving methodology is a systematic, team-based approach to problem solving. It is a method that guides a team through eight distinct steps to solve a problem in a systematic and comprehensive manner.

The 8D process consists of the following steps:

Form a team: Assemble a group of people who have the necessary expertise to work on the problem.
Define the issue: Clearly identify and define the problem, including the root cause and the customer impact.
Create a temporary containment plan: Put in place a plan to lessen the impact of the problem until a permanent solution can be found.
Identify the root cause: To identify the underlying causes of the problem, use root cause analysis techniques such as Fishbone diagrams and Pareto charts.
Create and test long-term corrective actions: Create and test a long-term solution to eliminate the root cause of the problem.
Implement and validate the permanent solution: Implement and validate the permanent solution’s effectiveness.
Prevent recurrence: Put in place measures to keep the problem from recurring.
Recognize and reward the team: Recognize and reward the team for its efforts.

Download the 8D Problem Solving Template

A3 Problem Solving Method:

The A3 problem solving technique is a visual, team-based problem-solving approach that is frequently used in Lean Six Sigma projects. The A3 report is a one-page document that clearly and concisely outlines the problem, root cause analysis, and proposed solution.

The A3 problem-solving procedure consists of the following steps:

Determine the issue: Define the issue clearly, including its impact on the customer.
Perform root cause analysis: Identify the underlying causes of the problem using root cause analysis techniques.
Create and implement a solution: Create and implement a solution that addresses the problem’s root cause.
Monitor and improve the solution: Keep an eye on the solution’s effectiveness and make any necessary changes.

Subsequently, in the Lean Six Sigma framework, the 8D and A3 problem solving methodologies are two popular approaches to problem solving. Both methodologies provide a structured, team-based problem-solving approach that guides individuals through a comprehensive and systematic process of identifying, analysing, and resolving problems in an effective and efficient manner.

Step 1 – Define the Problem

The definition of the problem is the first step in effective problem solving. This may appear to be a simple task, but it is actually quite difficult. This is because problems are frequently complex and multi-layered, making it easy to confuse symptoms with the underlying cause. To avoid this pitfall, it is critical to thoroughly understand the problem.

To begin, ask yourself some clarifying questions:

What exactly is the issue?
What are the problem’s symptoms or consequences?
Who or what is impacted by the issue?
When and where does the issue arise?

Answering these questions will assist you in determining the scope of the problem. However, simply describing the problem is not always sufficient; you must also identify the root cause. The root cause is the underlying cause of the problem and is usually the key to resolving it permanently.

Try asking “why” questions to find the root cause:

What causes the problem?
Why does it continue?
Why does it have the effects that it does?

By repeatedly asking “ why ,” you’ll eventually get to the bottom of the problem. This is an important step in the problem-solving process because it ensures that you’re dealing with the root cause rather than just the symptoms.

Once you have a firm grasp on the issue, it is time to divide it into smaller, more manageable chunks. This makes tackling the problem easier and reduces the risk of becoming overwhelmed. For example, if you’re attempting to solve a complex business problem, you might divide it into smaller components like market research, product development, and sales strategies.

To summarise step 1, defining the problem is an important first step in effective problem-solving. You will be able to identify the root cause and break it down into manageable parts if you take the time to thoroughly understand the problem. This will prepare you for the next step in the problem-solving process, which is gathering information and brainstorming ideas.

Step 2 – Gather Information and Brainstorm Ideas

Gathering information and brainstorming ideas is the next step in effective problem solving. This entails researching the problem and relevant information, collaborating with others, and coming up with a variety of potential solutions. This increases your chances of finding the best solution to the problem.

Begin by researching the problem and relevant information. This could include reading articles, conducting surveys, or consulting with experts. The goal is to collect as much information as possible in order to better understand the problem and possible solutions.

Next, work with others to gather a variety of perspectives. Brainstorming with others can be an excellent way to come up with new and creative ideas. Encourage everyone to share their thoughts and ideas when working in a group, and make an effort to actively listen to what others have to say. Be open to new and unconventional ideas and resist the urge to dismiss them too quickly.

Finally, use brainstorming to generate a wide range of potential solutions. This is the place where you can let your imagination run wild. At this stage, don’t worry about the feasibility or practicality of the solutions; instead, focus on generating as many ideas as possible. Write down everything that comes to mind, no matter how ridiculous or unusual it may appear. This can be done individually or in groups.

Once you’ve compiled a list of potential solutions, it’s time to assess them and select the best one. This is the next step in the problem-solving process, which we’ll go over in greater detail in the following section.

Step 3 – Evaluate Options and Choose the Best Solution

Once you’ve compiled a list of potential solutions, it’s time to assess them and select the best one. This is the third step in effective problem solving, and it entails weighing the advantages and disadvantages of each solution, considering their feasibility and practicability, and selecting the solution that is most likely to solve the problem effectively.

To begin, weigh the advantages and disadvantages of each solution. This will assist you in determining the potential outcomes of each solution and deciding which is the best option. For example, a quick and easy solution may not be the most effective in the long run, whereas a more complex and time-consuming solution may be more effective in solving the problem in the long run.

Consider each solution’s feasibility and practicability. Consider the following:

Can the solution be implemented within the available resources, time, and budget?
What are the possible barriers to implementing the solution?
Is the solution feasible in today’s political, economic, and social environment?

You’ll be able to tell which solutions are likely to succeed and which aren’t by assessing their feasibility and practicability.

Finally, choose the solution that is most likely to effectively solve the problem. This solution should be based on the criteria you’ve established, such as the advantages and disadvantages of each solution, their feasibility and practicability, and your overall goals.

It is critical to remember that there is no one-size-fits-all solution to problems. What is effective for one person or situation may not be effective for another. This is why it is critical to consider a wide range of solutions and evaluate each one based on its ability to effectively solve the problem.

Step 4 – Implement and Monitor the Solution

When you’ve decided on the best solution, it’s time to put it into action. The fourth and final step in effective problem solving is to put the solution into action, monitor its progress, and make any necessary adjustments.

To begin, implement the solution. This may entail delegating tasks, developing a strategy, and allocating resources. Ascertain that everyone involved understands their role and responsibilities in the solution’s implementation.

Next, keep an eye on the solution’s progress. This may entail scheduling regular check-ins, tracking metrics, and soliciting feedback from others. You will be able to identify any potential roadblocks and make any necessary adjustments in a timely manner if you monitor the progress of the solution.

Finally, make any necessary modifications to the solution. This could entail changing the solution, altering the plan of action, or delegating different tasks. Be willing to make changes if they will improve the solution or help it solve the problem more effectively.

It’s important to remember that problem solving is an iterative process, and there may be times when you need to start from scratch. This is especially true if the initial solution does not effectively solve the problem. In these situations, it’s critical to be adaptable and flexible and to keep trying new solutions until you find the one that works best.

To summarise, effective problem solving is a critical skill that can assist individuals and organisations in overcoming challenges and achieving their objectives. Effective problem solving consists of four key steps: defining the problem, generating potential solutions, evaluating alternatives and selecting the best solution, and implementing the solution.

You can increase your chances of success in problem solving by following these steps and considering factors such as the pros and cons of each solution, their feasibility and practicability, and making any necessary adjustments. Furthermore, keep in mind that problem solving is an iterative process, and there may be times when you need to go back to the beginning and restart. Maintain your adaptability and try new solutions until you find the one that works best for you.

Novick, L.R. and Bassok, M., 2005. Problem Solving . Cambridge University Press.

Daniel Croft

Daniel Croft is a seasoned continuous improvement manager with a Black Belt in Lean Six Sigma. With over 10 years of real-world application experience across diverse sectors, Daniel has a passion for optimizing processes and fostering a culture of efficiency. He's not just a practitioner but also an avid learner, constantly seeking to expand his knowledge. Outside of his professional life, Daniel has a keen Investing, statistics and knowledge-sharing, which led him to create the website learnleansigma.com, a platform dedicated to Lean Six Sigma and process improvement insights.

Free Lean Six Sigma Templates

Improve your Lean Six Sigma projects with our free templates. They're designed to make implementation and management easier, helping you achieve better results.

5S Floor Marking Best Practices

In lean manufacturing, the 5S System is a foundational tool, involving the steps: Sort, Set…

How to Measure the ROI of Continuous Improvement Initiatives

When it comes to business, knowing the value you’re getting for your money is crucial,…

8D Problem-Solving: Common Mistakes to Avoid

In today’s competitive business landscape, effective problem-solving is the cornerstone of organizational success. The 8D…

The Evolution of 8D Problem-Solving: From Basics to Excellence

In a world where efficiency and effectiveness are more than just buzzwords, the need for…

8D: Tools and Techniques

Are you grappling with recurring problems in your organization and searching for a structured way…

How to Select the Right Lean Six Sigma Projects: A Comprehensive Guide

Going on a Lean Six Sigma journey is an invigorating experience filled with opportunities for…

How it works

For Business

Join Mind Tools

Article • 7 min read

What Is Problem Solving?

By the Mind Tools Content Team

We all spend a lot of our time solving problems, both at work and in our personal lives.

Some problems are small, and we can quickly sort them out ourselves. But others are complex challenges that take collaboration, creativity, and a considerable amount of effort to solve.

At work, the types of problems we face depend largely on the organizations we're in and the jobs we do. A manager in a cleaning company, for example, might spend their day untangling staffing issues, resolving client complaints, and sorting out problems with equipment and supplies. An aircraft designer, on the other hand, might be grappling with a problem about aerodynamics, or trying to work out why a new safety feature isn't working. Meanwhile, a politician might be exploring solutions to racial injustice or climate change.

But whatever issues we face, there are some common ways to tackle them effectively. And we can all boost our confidence and ability to succeed by building a strong set of problem-solving skills.

Mind Tools offers a large collection of resources to help you do just that!

How Well Do You Solve Problems?

Start by taking an honest look at your existing skills. What's your current approach to solving problems, and how well is it working? Our quiz, How Good Is Your Problem Solving? lets you analyze your abilities, and signposts ways to address any areas of weakness.

Define Every Problem

The first step in solving a problem is understanding what that problem actually is. You need to be sure that you're dealing with the real problem – not its symptoms. For example, if performance in your department is substandard, you might think that the problem lies with the individuals submitting work. However, if you look a bit deeper, the real issue might be a general lack of training, or an unreasonable workload across the team.

Tools like 5 Whys , Appreciation and Root Cause Analysis get you asking the right questions, and help you to work through the layers of a problem to uncover what's really going on.

However, defining a problem doesn't mean deciding how to solve it straightaway. It's important to look at the issue from a variety of perspectives. If you commit yourself too early, you can end up with a short-sighted solution. The CATWOE checklist provides a powerful reminder to look at many elements that may contribute to the problem, keeping you open to a variety of possible solutions.

Understanding Complexity

As you define your problem, you'll often discover just how complicated it is. There are likely several interrelated issues involved. That's why it's important to have ways to visualize, simplify and make sense of this tangled mess!

Affinity Diagrams are great for organizing many different pieces of information into common themes, and for understanding the relationships between them.

Another popular tool is the Cause-and-Effect Diagram . To generate viable solutions, you need a solid understanding of what's causing the problem.

When your problem occurs within a business process, creating a Flow Chart , Swim Lane Diagram or a Systems Diagram will help you to see how various activities and inputs fit together. This may well highlight a missing element or bottleneck that's causing your problem.

Quite often, what seems to be a single problem turns out to be a whole series of problems. The Drill Down technique prompts you to split your problem into smaller, more manageable parts.

General Problem-Solving Tools

When you understand the problem in front of you, you’re ready to start solving it. With your definition to guide you, you can generate several possible solutions, choose the best one, then put it into action. That's the four-step approach at the heart of good problem solving.

There are various problem-solving styles to use. For example:

Constructive Controversy is a way of widening perspectives and energizing discussions.
Inductive Reasoning makes the most of people’s experiences and know-how, and can speed up solution finding.
Means-End Analysis can bring extra clarity to your thinking, and kick-start the process of implementing solutions.

Specific Problem-Solving Systems

Some particularly complicated or important problems call for a more comprehensive process. Again, Mind Tools has a range of approaches to try, including:

Simplex , which involves an eight-stage process: problem finding, fact finding, defining the problem, idea finding, selecting and evaluating, planning, selling the idea, and acting. These steps build upon the basic, four-step process described above, and they create a cycle of problem finding and solving that will continually improve your organization.
Appreciative Inquiry , which is a uniquely positive way of solving problems by examining what's working well in the areas surrounding them.
Soft Systems Methodology , which takes you through four stages to uncover more details about what's creating your problem, and then define actions that will improve the situation.

Further Problem-Solving Strategies

Good problem solving requires a number of other skills – all of which are covered by Mind Tools.

For example, we have a large section of resources to improve your Creativity , so that you come up with a range of possible solutions.

By strengthening your Decision Making , you'll be better at evaluating the options, selecting the best ones, then choosing how to implement them.

And our Project Management collection has valuable advice for strengthening the whole problem-solving process. The resources there will help you to make effective changes – and then keep them working long term.

Problems are an inescapable part of life, both in and out of work. So we can all benefit from having strong problem-solving skills.

It's important to understand your current approach to problem solving, and to know where and how to improve.

Define every problem you encounter – and understand its complexity, rather than trying to solve it too soon.

There's a range of general problem-solving approaches, helping you to generate possible answers, choose the best ones, and then implement your solution.

Some complicated or serious problems require more specific problem-solving systems, especially when they relate to business processes.

By boosting your creativity, decision-making and project-management skills, you’ll become even better at solving all the problems you face.

You've accessed 1 of your 2 free resources.

Get unlimited access

Discover more content

Infographic

Creative Problem Solving Infographic

Infographic Transcript

Creative Problem Solving

Finding Innovative Solutions to Challenges

Add comment

Comments (0)

Be the first to comment!

Try Mind Tools for FREE

Get unlimited access to all our career-boosting content and member benefits with our 7-day free trial.

Sign-up to our newsletter

Subscribing to the Mind Tools newsletter will keep you up-to-date with our latest updates and newest resources.

Subscribe now

Business Skills

Personal Development

Leadership and Management

Member Extras

Discover something new today

Onboarding with steps.

Helping New Employees to Thrive

NEW! Pain Points Podcast - Perfectionism

Why Am I Such a Perfectionist?

How Emotionally Intelligent Are You?

Boosting Your People Skills

Self-Assessment

What's Your Leadership Style?

Learn About the Strengths and Weaknesses of the Way You Like to Lead

Recommended for you

An overview of process design.

A Introduction to What Is Involved in Process Design and Some Fundamental Design Types

Business Operations and Process Management

Strategy Tools

Customer Service

Business Ethics and Values

Handling Information and Data

Project Management

Knowledge Management

Self-Development and Goal Setting

Time Management

Presentation Skills

Learning Skills

Career Skills

Communication Skills

Negotiation, Persuasion and Influence

Working With Others

Difficult Conversations

Creativity Tools

Self-Management

Work-Life Balance

Stress Management and Wellbeing

Coaching and Mentoring

Change Management

Team Management

Managing Conflict

Delegation and Empowerment

Performance Management

Leadership Skills

Developing Your Team

Talent Management

Problem Solving

Decision Making

Member Podcast

Join our FREE training and learn the 5 things you can do to become a top 1% facilitator

What is problem-solving and how to do it right steps, processes, exercises.

The better your problem-solving skills are, the better (and easier!) your life will be. Organized problem-solving is a killer career skill - learn all about it here.

Whether we’re trying to solve a technical problem at work, or trying to navigate around a roadblock that Google Maps doesn’t see – most people are problem-solving every single day .

But how effective are you at tackling the challenges in your life? Do you have a bullet-proof process you follow that ensures solid outcomes, or... Do you act on a whim of inspiration (or lack thereof) to resolve your pressing problems?

Here’s the thing: the better your problem-solving skills are - the better (and easier!) your life will be (both professionally and personally). Organized problem-solving is a killer career (and life!) skill, so if you want to learn how to do it in the most efficient way possible, you’ve come to the right place.

Read along to learn more about the steps, techniques and exercises of the problem-solving process.

1. Do you want a Career in UX?
Learn the Principles of UX Design
Master a UX Design Tool ‍

What is Problem-Solving?

We’re faced with the reality of having to solve problems every day, both in our private and professional lives. So why do we even need to learn about problem-solving? Aren’t we versed in it well enough already?

Well, what separates problem-solving from dealing with the usual day-to-day issues is that it’s a distinct process that allows you to go beyond the standard approaches to solving a problem and allows you to come up with more effective and efficient solutions. Or in other words, problem-solving allows you to knock out those problems with less effort.

Just like with any other skill, there’s an efficient way to solve problems, and a non-efficient one. While it might be tempting to go for the quickest fix for your challenge without giving it much thought, it will only end up costing you more time down the road. Quick fixes are rarely (if ever!) effective and end up being massive time wasters.

What separates problem-solving from dealing with the usual day-to-day issues is that it’s a distinct process that allows you to go beyond the standard approaches to solving a problem and allows you to come up with more effective and efficient solutions.

On the other hand, following a systemized clear process for problem-solving allows you to shortcut inefficiencies and time-wasters, turn your challenges into opportunities, and tackle problems of any scope without the usual stress and hassle.

What is the process that you need to follow, then? We’re glad you asked...

The Five Stages of Problem-Solving

So what’s the best way to move through the problem-solving process? There’s a 5-step process that you can follow that will allow you to solve your challenges more efficiently and effectively. In short, you need to move through these 5 steps:

Defining a problem
Ideating on a solution
Committing to a course of action
Implementing your solution
And finally – analyzing the results.

Let’s look at each of those stages in detail.

Step 1: Defining The Problem

The first step might sound obvious, but trust us, you don’t want to skip it! Clearly defining and framing your challenge will help you guide your efforts and make sure you’re focussing on the things that matter, instead of being distracted by a myriad of other options, problems and issues that come up.

For once, you have to make sure you’re trying to solve the root cause, and not trying to mend the symptoms of it. For instance, if you keep losing users during your app onboarding process, you might jump to the conclusion that you need to tweak the process itself: change the copy, the screens, or the sequence of steps.

But unless you have clear evidence that confirms your hypothesis, your challenge might have an entirely different root cause, e.g. in confusing marketing communication prior to the app download.

Clearly defining and framing your challenge will help you guide your efforts and make sure you’re focussing on the things that matter, all the while ensuring that you’re trying to solve the root cause, and not trying to mend the symptoms of it

That’s why it’s essential you take a close look at the entire problem, not just at a fraction of it.

There are several exercises that can help you get a broader, more holistic view of the problem, some of our all-time favorites include Expert Interviews, How Might We, or The Map. Check out the step-by-step instructions on how to run them (along with 5 more exercises for framing your challenge!) here.

When in doubt, map out your challenge, and always try to tackle the bottlenecks that are more upstream - it’s likely that solving them will solve a couple of other challenges down the flow.

You also have to be mindful of how you frame the challenge: resist the urge to include a pre-defined solution into your problem statement. Priming your solutions to a predestined outcome destroys the purpose of following a step-by-step process in the first place!

Steer clear of formulations like:

We need to change the onboarding process... or We need to improve ad copy to increase conversions.

Instead, opt for more neutral, problem-oriented statements that don’t include a solution suggestion in them:

The drop off rate during the onboarding process is too high or Our ad conversion rates are below the norm.

Pro tip: Reframing your challenge as a ‘How Might We’ statement is a great way to spark up new ideas, opening your problem to a broader set of solutions, and is just a great way to reframe your problem into a more positive statement (without implying the possible solution!)

For example, following the onboarding drop-off rate problem we mentioned earlier, instead of framing it as a problem, you could opt for:

How Might We decrease the drop-off rate during the onboarding process?

Find out more about the best exercises for problem framing here!

Now that you have a clear idea of what you’re trying to solve, it’s move on to the next phase of the problem-solving process.

Learn more about facilitation and workshopping in our FREE FACILITATION COMMUNITY

Step 2: ideating a solution.

Get ready to roll up your sleeves and challenge the status quo! This step of the problem-solving process is all about thinking outside of the box, challenging old assumptions, and thinking laterally.

This stage is the one that tends to cause the most overwhelm in teams because it requires just the right balance of creativity and critical thinking, which tends to cause a lot of friction.

Our best advice?

Let go of the pressure to produce a polished, thought-through solution at this stage. You can hash out the details at a later point. Our goal right now is to come up with a direction, a prototype if you may, of where we want to move towards.

Embrace the “quantity over quality” motto, and let your creative juices flow! Now, we’re not saying you should roll with sub-par ideas. But you shouldn’t get too fixated on feasibility and viability just yet .

Your main goal during this step is to spark ideas, kick off your thinking process in the right direction, venture out of the familiar territories and think outside the box.

For the ideation to be the most effective your team will have to feel safe to challenge the norm and wide-spread assumptions. So lay judgment by side, there is no space for “that’s the way it’s always been done” in this step.

For your ideation sessions to be as efficient as possible, we highly recommend to run them in a workshop setting: this helps reduce the usual drawbacks of open discussions in teams (i.e. groupthink & team politics!)

Our favorite exercises to run during this phase include Lightning Demos, Sketching, and variations of Brainstorming. We crafted an entire article on how to run and facilitate these exercises in a separate article, so check it out of you’re going to be running an ideation session anytime soon!

Step 3: Choosing the Best Strategy & Committing

It’s time to decide which of the ideas that you generated in the last step will be the one you’ll implement.

This step is arguably the hardest one to complete smoothly: groupthink, team politics, differences in opinions and communication styles all make it very hard to align a team on a common course of action.

If you want to avoid the usual pitfalls of team decision-making, we recommend you steer clear of open unstructured discussion. While it’s useful in some scenarios, it’s a poor choice for when you need to make a decision, because it tends to reward the loudest people in the room, rather than give way to the best ideas.

It’s crucial you not only commit to a course of action but get full buy-in from the team. If your team members don’t understand the reasons for a decision, or are not fully onboard, the implementation of your decision will be half-hearted, and that’s definitely not what you want!

To achieve that, opt for anonymized, multi-layered voting, and include guided exercises like Storyboarding to prioritize your ideas.

We’ve gathered the list of our top-rated decision-making exercises, along with step-by-step instructions on how to run them in this article!

As a bonus tip, we recommend you involve a facilitator throughout the entire process. They will help align the team, and guide them through prioritizing and de-prioritizing solutions, as well as defining the next steps.

Pro tip : If you’re not the ultimate decision maker on the issue you’re trying to solve, make sure they’re in the room when the call is being made! Having a Decider in the room ensures that the decisions you come to will actually get executed on after, instead of getting shut down by your superiors after.

Join our FREE community and connect with other Facilitators and Workshoppers

Step 4: implementing your solution.

Here’s a truth that might be hard to swallow: it doesn’t matter how innovative, creative, or original your idea is, if your execution is weak.

One of our favourite illustrations of how this works in practice comes from the book “ Anything you want ” by Derek Sivers. He reveals that ideas should be treated as multipliers of execution. What this means is that a mediocre, “so-so” idea could be worth millions if executed well, while a “brilliant” idea can completely flop with bad execution.

That’s why this step is crucial if you want to really master the problem-solving process.

What do we mean by execution? Everything that happens after the whiteboards are wiped clean and your team starts to action the outcomes of your sessions, be it prototyping, development, or promotion.

But don’t just take our word for it, look at the example of how execution affected Nintendo’s sales:

In the past few years, Nintendo has come up with 3 products: the Wii, the Wii U and the Switch. Check out their sales figures on the graph below - Wii is the clear-cut leader, followed by Switch, and finally Wii U lagging behind.

The Wii was unbelievably successful - it was a genuinely unique, “brilliant”-level idea and it had a “brilliant” execution (20x $10 million = $200 million). It is one of the fastest selling game consoles of all time and it completely took over the market.

The next product was called Wii U and it was a “great” concept but the execution was absolutely terrible. So even though this product was very interesting and innovative, the end result was 15x $1,000 = $15,000.

Finally, Nintendo took the Wii U concept and tried it again with the Switch. The idea was “so so” as it was already done before, but the execution was “brilliant”. So, 5x $10 million = $50 million! Much better.

Excellent execution is more important than a good idea.

Bottom line?

The same idea can either make no dent in the market and damage your share price OR become a market hit and increase your share price dramatically. The only difference between the two scenarios – execution.

So shift your focus from coming up with crazy, innovative, outlandish ideas that will disrupt the market, and concentrate on really nailing down your execution instead.

This is likely the least “workshoppy” step out of the entire problem-solving process because it requires less alignment and decision-making and more..well.. Execution!

But hey, we wouldn’t be called “Workshopper” if we didn't offer you at least one way to optimize and workshopify (yup, we’re making it a thing) your execution process.

Cue in….prototyping.

We’re huge fans of prototyping all big solutions (and testing them!) The main reason?

This saves us time AND money! Prototyping and testing your solutions (especially if they’re time and investment-demanding) is a great way to make sure you’re creating something that is actually needed.

The key with prototyping the right way is to keep it simple. Don’t invest too much time, or resources into it. The goal is to gather data for your future decisions, not to create a near-to-perfect mockup of your solution.

There are LOADS of prototyping forms and techniques, and if you’d like to learn more on the subject you should definitely check out our extensive prototyping guide.

Step 5: Analyzing the Results

You’re nearly done, woo! Now that you have defined the right problem to tackle, brainstormed the solutions, aligned your team on the course of action, and put your plan into action it’s time to take stock of your efforts.

Seek feedback from all involved parties, analyze the data you’ve gathered, look at the bottom line of your efforts, and take a hard look at your problem: did it get solved? And even more than that, did the process feel smoother, easier, and more efficient than it normally is?

Running a retrospective is a great way to highlight things that went well and that you should keep for your next round of problem.solving, as well as pinpoint inefficiencies that you can eliminate.

‍ But which kind of retrospective should you run? There are loads of options, and it’s easy to feel overwhelmed by them all, so we gathered our favorite retrospective variations in this article.

And there you have it, you just completed the cycle of problem-solving. We highly recommend you follow through with all the steps, without leaving any out. They all complement and build on each other, and it’s the combination of all 5 of them that makes the process effective.

Now that you have the problem solving process down, you might be wondering…

Do I need any special skills in order to be able to move through that process?

And the answer is… sort of! More in this in the next section.

Problem-Solving Skills

While your skill set will need to adapt and change based on the challenges you’ll be working on, most efficient problem-solvers have a solid foundation of these key skills:

Active listening. While you might be the expert in the area of your challenge, there’s not a single person on Earth that knows it all! Being open to others’ perspectives and practicing active listening will come in very handy during step 1 of the process, as you’re trying to define the scope and the exact angle of the problem you’re working on.
Analytical approach. Your analytical skills will help you understand problems and effectively develop solutions. You will also need analytical skills during research to help distinguish between effective and ineffective solutions.
Communication. Is there a single area of expertise that DOESN’T require strong communication skills? We honestly don’t think so! Just like with any other life area, clear communication can make or break your problem-solving process. Being able to clearly communicate why you need to solve this challenge to your team, as well as align your team on the course of action are crucial for the success of the process.
Decision-making. Ultimately, you will need to make a decision about how to solve problems that arise. A process without outcomes–regardless of how well thought-out and elaborate–is useless! If you want your problem-solving huddles to be effective, you have to come to grips with prioritization techniques and decision-making frameworks.
Facilitation. Problem-solving revolves around being able to guide a group or a team to a common decision, and facilitation skills are essential in making that happen. Knowing how to facilitate will make it easy to keep the group focussed on the challenge, shortcut circular discussions, and make sure you’re moving along to solving the problem instead of just treading waters with fruitless discussions.

Not checking every single skill of your list just yet? Not to worry, the next section will give you practical tools on how to level up and improve your problem-solving skills.

How to Improve Your Problem-Solving Skills

Just like with any other skill, problem-solving is not an innate talent that you either have or you don’t. There are concrete steps you can take to improve your skills.

Here are some things that will get you closer to mastering the problem-solving process:

Practice, Practice, Practice

Practice makes perfect, and problem-solving skills are no exception! Seek opportunities to utilize and develop these skills any time you can.

If you don’t know where or how to start just yet, here’s a suggestion that will get you up and running in no time: run a quick problem-solving session on a challenge that has been bothering your team for a while now.

It doesn’t need to be the big strategic decision or the issue defining the future of the company. Something easy and manageable (like optimizing office space or improving team communication) will do.

As you start feeling more comfortable with the problem-solving techniques, you can start tackling bigger challenges. Before you know it, you’ll master the art of creative problem-solving!

Use a tried and tested problem-solving workshop

Facilitation is one of the essential skills for problem-solving. But here’s the thing… Facilitation skills on their own won’t lead you to a solved challenge.

While being able to shortcut aimless discussions is a great skill, you have to make sure your problem-solving session has tangible outcomes. Using a tried and tested method, a workshop, is one of the easiest ways to do that.

Our best advice is to get started with a tried and tested problem-solving workshop like the Lightning Decision Jam . The LDJ has all the right ingredients for quick, effective problem solving that leads to tangible outcomes. Give it a go!

Learn from your peers

You may have colleagues who are skilled problem solvers. Observing how those colleagues solve problems can help you improve your own skills.

If possible, ask one of your more experienced colleagues if you can observe their techniques. Ask them relevant questions and try to apply as many of the new found skills i your career as possible.

Learn & Practice the best problem-solving exercises

Having a toolbox of problem-solving exercises to pull from that can fit any type of challenge will make you a more versatile problem-solver and will make solving challenges that much easier for you!

Once you get used to the groove of learning how to combine them into effective sessions or workshops, there’ll be no stopping you. What are some of the most effective problem-solving exercises? Glad you asked! We’ve gathered our favorite ones here, check it out!

And there you have it, you’re now fully equipped for running creative problem-sessions with confidence and ease! Whichever method or exercise you choose, remember to keep track of your wins, and learn as much as you can from your losses!

Anastasia Ushakova

Brand Strategist, Digital Marketer, and a Workshopper.

When Do You Need a Facilitator?

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse varius enim in eros elementum tristique. Duis cursus.

The Ultimate Facilitation Glossary: 50 Facilitation Terms You Should Know (From A-Z)

How To Improve Team Collaboration

Bipolar Disorder
Therapy Center
When To See a Therapist
Types of Therapy
Best Online Therapy
Best Couples Therapy
Best Family Therapy
Managing Stress
Sleep and Dreaming
Understanding Emotions
Self-Improvement
Healthy Relationships
Student Resources
Personality Types
Guided Meditations
Verywell Mind Insights
2023 Verywell Mind 25
Mental Health in the Classroom
Editorial Process
Meet Our Review Board
Crisis Support

Problem-Solving Strategies and Obstacles

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Sean is a fact-checker and researcher with experience in sociology, field research, and data analytics.

JGI / Jamie Grill / Getty Images

Application
Improvement

From deciding what to eat for dinner to considering whether it's the right time to buy a house, problem-solving is a large part of our daily lives. Learn some of the problem-solving strategies that exist and how to use them in real life, along with ways to overcome obstacles that are making it harder to resolve the issues you face.

What Is Problem-Solving?

In cognitive psychology , the term 'problem-solving' refers to the mental process that people go through to discover, analyze, and solve problems.

A problem exists when there is a goal that we want to achieve but the process by which we will achieve it is not obvious to us. Put another way, there is something that we want to occur in our life, yet we are not immediately certain how to make it happen.

Maybe you want a better relationship with your spouse or another family member but you're not sure how to improve it. Or you want to start a business but are unsure what steps to take. Problem-solving helps you figure out how to achieve these desires.

The problem-solving process involves:

Discovery of the problem
Deciding to tackle the issue
Seeking to understand the problem more fully
Researching available options or solutions
Taking action to resolve the issue

Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.

Problem-Solving Mental Processes

Several mental processes are at work during problem-solving. Among them are:

Perceptually recognizing the problem
Representing the problem in memory
Considering relevant information that applies to the problem
Identifying different aspects of the problem
Labeling and describing the problem

Problem-Solving Strategies

There are many ways to go about solving a problem. Some of these strategies might be used on their own, or you may decide to employ multiple approaches when working to figure out and fix a problem.

An algorithm is a step-by-step procedure that, by following certain "rules" produces a solution. Algorithms are commonly used in mathematics to solve division or multiplication problems. But they can be used in other fields as well.

In psychology, algorithms can be used to help identify individuals with a greater risk of mental health issues. For instance, research suggests that certain algorithms might help us recognize children with an elevated risk of suicide or self-harm.

One benefit of algorithms is that they guarantee an accurate answer. However, they aren't always the best approach to problem-solving, in part because detecting patterns can be incredibly time-consuming.

There are also concerns when machine learning is involved—also known as artificial intelligence (AI)—such as whether they can accurately predict human behaviors.

Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.

If you find yourself sitting in a traffic jam, for example, you may quickly consider other routes, taking one to get moving once again. When shopping for a new car, you might think back to a prior experience when negotiating got you a lower price, then employ the same tactics.

While heuristics may be helpful when facing smaller issues, major decisions shouldn't necessarily be made using a shortcut approach. Heuristics also don't guarantee an effective solution, such as when trying to drive around a traffic jam only to find yourself on an equally crowded route.

Trial and Error

A trial-and-error approach to problem-solving involves trying a number of potential solutions to a particular issue, then ruling out those that do not work. If you're not sure whether to buy a shirt in blue or green, for instance, you may try on each before deciding which one to purchase.

This can be a good strategy to use if you have a limited number of solutions available. But if there are many different choices available, narrowing down the possible options using another problem-solving technique can be helpful before attempting trial and error.

In some cases, the solution to a problem can appear as a sudden insight. You are facing an issue in a relationship or your career when, out of nowhere, the solution appears in your mind and you know exactly what to do.

Insight can occur when the problem in front of you is similar to an issue that you've dealt with in the past. Although, you may not recognize what is occurring since the underlying mental processes that lead to insight often happen outside of conscious awareness .

Research indicates that insight is most likely to occur during times when you are alone—such as when going on a walk by yourself, when you're in the shower, or when lying in bed after waking up.

How to Apply Problem-Solving Strategies in Real Life

If you're facing a problem, you can implement one or more of these strategies to find a potential solution. Here's how to use them in real life:

Create a flow chart . If you have time, you can take advantage of the algorithm approach to problem-solving by sitting down and making a flow chart of each potential solution, its consequences, and what happens next.
Recall your past experiences . When a problem needs to be solved fairly quickly, heuristics may be a better approach. Think back to when you faced a similar issue, then use your knowledge and experience to choose the best option possible.
Start trying potential solutions . If your options are limited, start trying them one by one to see which solution is best for achieving your desired goal. If a particular solution doesn't work, move on to the next.
Take some time alone . Since insight is often achieved when you're alone, carve out time to be by yourself for a while. The answer to your problem may come to you, seemingly out of the blue, if you spend some time away from others.

Obstacles to Problem-Solving

Problem-solving is not a flawless process as there are a number of obstacles that can interfere with our ability to solve a problem quickly and efficiently. These obstacles include:

Assumptions: When dealing with a problem, people can make assumptions about the constraints and obstacles that prevent certain solutions. Thus, they may not even try some potential options.
Functional fixedness : This term refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
Irrelevant or misleading information: When trying to solve a problem, it's important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. The more complex the problem, the easier it is to focus on misleading or irrelevant information.
Mental set: A mental set is a tendency to only use solutions that have worked in the past rather than looking for alternative ideas. A mental set can work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.

How to Improve Your Problem-Solving Skills

In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:

Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.

You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.

Sarathy V. Real world problem-solving . Front Hum Neurosci . 2018;12:261. doi:10.3389/fnhum.2018.00261

Dunbar K. Problem solving . A Companion to Cognitive Science . 2017. doi:10.1002/9781405164535.ch20

Stewart SL, Celebre A, Hirdes JP, Poss JW. Risk of suicide and self-harm in kids: The development of an algorithm to identify high-risk individuals within the children's mental health system . Child Psychiat Human Develop . 2020;51:913-924. doi:10.1007/s10578-020-00968-9

Rosenbusch H, Soldner F, Evans AM, Zeelenberg M. Supervised machine learning methods in psychology: A practical introduction with annotated R code . Soc Personal Psychol Compass . 2021;15(2):e12579. doi:10.1111/spc3.12579

Mishra S. Decision-making under risk: Integrating perspectives from biology, economics, and psychology . Personal Soc Psychol Rev . 2014;18(3):280-307. doi:10.1177/1088868314530517

Csikszentmihalyi M, Sawyer K. Creative insight: The social dimension of a solitary moment . In: The Systems Model of Creativity . 2015:73-98. doi:10.1007/978-94-017-9085-7_7

Chrysikou EG, Motyka K, Nigro C, Yang SI, Thompson-Schill SL. Functional fixedness in creative thinking tasks depends on stimulus modality . Psychol Aesthet Creat Arts . 2016;10(4):425‐435. doi:10.1037/aca0000050

Huang F, Tang S, Hu Z. Unconditional perseveration of the short-term mental set in chunk decomposition . Front Psychol . 2018;9:2568. doi:10.3389/fpsyg.2018.02568

National Alliance on Mental Illness. Warning signs and symptoms .

Mayer RE. Thinking, problem solving, cognition, 2nd ed .

Schooler JW, Ohlsson S, Brooks K. Thoughts beyond words: When language overshadows insight. J Experiment Psychol: General . 1993;122:166-183. doi:10.1037/0096-3445.2.166

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

INTERPERSONAL SKILLS
Problem Solving and Decision Making

Identifying and Structuring Problems

Search SkillsYouNeed:

Interpersonal Skills:

A - Z List of Interpersonal Skills
Interpersonal Skills Self-Assessment
Communication Skills
Emotional Intelligence
Conflict Resolution and Mediation Skills
Customer Service Skills
Team-Working, Groups and Meetings
Decision-Making and Problem-Solving
Effective Decision Making
Decision-Making Framework
Introduction to Problem Solving
Investigating Ideas and Solutions
Implementing a Solution and Feedback
Creative Problem-Solving
Social Problem-Solving
Negotiation and Persuasion Skills
Personal and Romantic Relationship Skills

Subscribe to our FREE newsletter and start improving your life in just 5 minutes a day.

You'll get our 5 free 'One Minute Life Skills' and our weekly newsletter.

We'll never share your email address and you can unsubscribe at any time.

This page continues from Problem Solving an Introduction that introduces problem solving as a concept and outlines the stages used to successfully solve problems.

This page covers the first two stages in the problem solving process: Identifying the Problem and Structuring the Problem .

Stage One: Identifying the Problem

Before being able to confront a problem its existence needs to be identified. This might seem an obvious statement but, quite often, problems will have an impact for some time before they are recognised or brought to the attention of someone who can do anything about them.

In many organisations it is possible to set up formal systems of communication so that problems are reported early on, but inevitably these systems do not always work. Once a problem has been identified, its exact nature needs to be determined: what are the goal and barrier components of the problem? Some of the main elements of the problem can be outlined, and a first attempt at defining the problem should be made. This definition should be clear enough for you to be able to easily explain the nature of the problem to others.

Looking at the problem in terms of goals and barriers can offer an effective way of defining many problems and splitting bigger problems into more manageable sub-problems.

Sometimes it will become apparent that what seems to be a single problem, is more accurately a series of sub-problems. For example, in the problem:

“I have been offered a job that I want, but I don't have the transport to get there and I don't have enough money to buy a car.”

“ I want to take a job ” (main problem)

“ But I don't have transport to get there ” (sub-problem 1)

“ And I don't have enough money to buy a car ” (sub-problem 2)

Useful ways of describing more complex problems are shown in the section, ' Structuring the Problem' , below.

During this first stage of problem solving, it is important to get an initial working definition of the problem. Although it may need to be adapted at a later stage, a good working definition makes it possible to describe the problem to others who may become involved in the problem solving process. For example:

Stage Two: Structuring the Problem

The second stage of the problem solving process involves gaining a deeper understanding of the problem. Firstly, facts need to be checked.

The questions have to be asked, is the stated goal the real goal? Are the barriers actual barriers and what other barriers are there? In this example, the problem at first seems to be:

This is also a good opportunity to look at the relationships between the key elements of the problem . For example, in the 'Job-Transport-Money' problem, there are strong connections between all the elements.

By looking at all the relationships between the key elements, it appears that the problem is more about how to achieve any one of three things, i.e. job, transport or money, because solving one of these sub-problems will, in turn, solve the others.

This example shows how useful it is to have a representation of a problem.

Problems can be represented in the following ways:

Visually: using pictures, models or diagrams.
Verbally: describing the problem in words.

Visual and verbal representations include:

Chain diagrams
Flow charts
Tree diagrams

Chain Diagrams

Chain diagrams are powerful and simple ways of representing problems using a combination of diagrams and words. The elements of the problem are set out in words, usually placed in boxes, and positioned in different places on a sheet of paper, using lines to represent the relationship between them.

Chain Diagrams are the simplest type, where all the elements are presented in an ordered list, each element being connected only with the elements immediately before and after it. Chain diagrams usually represent a sequence of events needed for a solution. A simple example of a chain diagram illustrates the job-transport-money example as as follows:

Flow Charts

Flow charts allow for inclusion of branches, folds, loops, decision points and many other relationships between the elements. In practice, flow charts can be quite complicated and there are many conventions as to how they are drawn but, generally, simple diagrams are easier to understand and aid in 'seeing' the problem more readily.

Tree Diagrams

Tree diagrams and their close relative, the Decision Tree , are ways of representing situations where there are a number of choices or different possible events to be considered. These types of diagram are particularly useful for considering all the possible consequences of solutions.

Remember that the aim of a visualisation is to make the problem clearer. Over-complicated diagrams will just confuse and make the problem harder to understand.

Listing the elements of a problem can also help to represent priorities, order and sequences in the problem. Goals can be listed in order of importance and barriers in order of difficulty. Separate lists could be made of related goals or barriers. The barriers could be listed in the order in which they need to be solved, or elements of the problem classified in a number of different ways. There are many possibilities, but the aim is to provide a clearer picture of the problem.

A visual representation and a working definition together makes it far easier to describe a problem to others. Many problems will be far more complex than the example used here.

Continue to: Investigating Ideas and Possible Solutions

See also: Social Problem Solving Project Management Risk Management

University Human Resources

8-step problem solving process, organizational effectiveness.

121 University Services Building, Suite 50 Iowa City , IA 52242-1911 United States

Step 1: Define the Problem

What is the problem?
How did you discover the problem?
When did the problem start and how long has this problem been going on?
Is there enough data available to contain the problem and prevent it from getting passed to the next process step? If yes, contain the problem.

Step 2: Clarify the Problem

What data is available or needed to help clarify, or fully understand the problem?
Is it a top priority to resolve the problem at this point in time?
Are additional resources required to clarify the problem? If yes, elevate the problem to your leader to help locate the right resources and form a team.
Consider a Lean Event (Do-it, Burst, RPI, Project).
∙Ensure the problem is contained and does not get passed to the next process step.

Step 3: Define the Goals

What is your end goal or desired future state?
What will you accomplish if you fix this problem?
What is the desired timeline for solving this problem?

Step 4: Identify Root Cause of the Problem

Identify possible causes of the problem.
Prioritize possible root causes of the problem.
What information or data is there to validate the root cause?

Step 5: Develop Action Plan

Generate a list of actions required to address the root cause and prevent problem from getting to others.
Assign an owner and timeline to each action.
Status actions to ensure completion.

Step 6: Execute Action Plan

Implement action plan to address the root cause.
Verify actions are completed.

Step 7: Evaluate the Results

Monitor and Collect Data.
Did you meet your goals defined in step 3? If not, repeat the 8-Step Process.
Were there any unforeseen consequences?
If problem is resolved, remove activities that were added previously to contain the problem.

Step 8: Continuously Improve

Look for additional opportunities to implement solution.
Ensure problem will not come back and communicate lessons learned.
If needed, repeat the 8-Step Problem Solving Process to drive further improvements.

.css-s5s6ko{margin-right:42px;color:#F5F4F3;}@media (max-width: 1120px){.css-s5s6ko{margin-right:12px;}} AI that works. Coming June 5th, Asana redefines work management—again. .css-1ixh9fn{display:inline-block;}@media (max-width: 480px){.css-1ixh9fn{display:block;margin-top:12px;}} .css-1uaoevr-heading-6{font-size:14px;line-height:24px;font-weight:500;-webkit-text-decoration:underline;text-decoration:underline;color:#F5F4F3;}.css-1uaoevr-heading-6:hover{color:#F5F4F3;} .css-ora5nu-heading-6{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;-webkit-box-pack:start;-ms-flex-pack:start;-webkit-justify-content:flex-start;justify-content:flex-start;color:#0D0E10;-webkit-transition:all 0.3s;transition:all 0.3s;position:relative;font-size:16px;line-height:28px;padding:0;font-size:14px;line-height:24px;font-weight:500;-webkit-text-decoration:underline;text-decoration:underline;color:#F5F4F3;}.css-ora5nu-heading-6:hover{border-bottom:0;color:#CD4848;}.css-ora5nu-heading-6:hover path{fill:#CD4848;}.css-ora5nu-heading-6:hover div{border-color:#CD4848;}.css-ora5nu-heading-6:hover div:before{border-left-color:#CD4848;}.css-ora5nu-heading-6:active{border-bottom:0;background-color:#EBE8E8;color:#0D0E10;}.css-ora5nu-heading-6:active path{fill:#0D0E10;}.css-ora5nu-heading-6:active div{border-color:#0D0E10;}.css-ora5nu-heading-6:active div:before{border-left-color:#0D0E10;}.css-ora5nu-heading-6:hover{color:#F5F4F3;} Get early access .css-1k6cidy{width:11px;height:11px;margin-left:8px;}.css-1k6cidy path{fill:currentColor;}

Business strategy |
Problem management: 8 steps to better p ...

Problem management: 8 steps to better problem solving

Problem management is an 8 step framework most commonly used by IT teams. You can use problem management to solve for repeating major incidents. By organizing and structuring your problem solving, you can more effectively get to the root cause of high-impact problems—and devise a solution. Solving the root cause prevents recurrence and creates a repeatable solution to use on similar errors in the future.

In an IT department, errors and mishaps are part of the job. You can't always control these problems, but you can control how you respond to them with problem management. Problem management helps you solve larger problems and reduce the risk that they’ll happen again by identifying all connected problems, solving them, and planning for the future.

What is problem management?

Problem management is an 8 step framework most commonly used by IT teams. Your team can use problem management to solve for repeating major incidents. By organizing and structuring your problem solving, you can more effectively get to the root cause of high-impact problems—and devise a solution. Problem management is a process—used mostly by IT teams—to identify, react, and respond to issues. It’s not for every problem, but it’s a useful response when multiple major incidents occur that cause large work interruptions. Unlike problem solving, problem management goes beyond the initial incident to discover and dissect the root causes, preventing future incidents with permanent solutions.

The goals of problem management are to:

Prevent problems before they start.

Solve for repetitive errors.

Lessen each incident’s impact.

Problem management vs. incident management

Example: Someone leaves their unprotected laptop in a coffee shop, causing a security breach. The security team can use incident management to solve for this one, isolated event. In this case, the team could manually shut down the accounts connected to that laptop. If this continues to happen, IT would use problem management to solve the root of this issue—perhaps installing more security features on each company laptop so that if employees lose them, no one else can access the information.

Problem management vs. problem solving

While similar in name, problem management differs slightly from problem-solving. Problem management focuses on every aspect of the incident—identifying the root cause of the problem, solving it, and prevention. Problem solving is, as the name implies, focused solely on the solution step.

Example: You’re launching a new password management system when it crashes—again. You don’t know if anything leaked, but you know it could contain confidential information. Plus, it’s happened before. You start the problem management process to ensure it doesn’t happen again. In that process, you’ll use problem solving as a step to fix the issue. In this case, perhaps securing confidential information before you try to launch a new software.

Problem management vs. change management

Change management targets large transitions within your workplace, good and bad. These inevitable changes aren’t always negative, so you can’t always apply problem management as a solution. That’s where change management comes in—a framework that helps you adjust to any new scenario.

Example: Your company is transitioning to a new cloud platform. The transition happens incident-free—meaning you won’t need problem management—but you can ease the transition by implementing some change management best practices. Preparing and training team members in the new software is a good place to start.

Problem management vs. project management

Project management is the framework for larger collections of work. It’s the overarching method for how you work on any project, hit goals, and get results. You can use project management to help you with problem management, but they are not the same thing. Problem management and project management work together to solve issues as part of your problem management process.

Example: During problem management, you uncover a backend security issue that needs to be addressed—employees are using storage software with outdated security measures. To solve this, you create a project and outline the tasks from start to finish. In this case, you might need to alert senior executives, get approval to remove the software, and alert employees. You create a project schedule with a defined timeline and assign the tasks to relevant teams. In this process, you identified a desired outcome—remove the unsafe software—and solved it. That’s project management.

The 8 steps of problem management

It’s easy to get upset when problems occur. In fact, it’s totally normal. But an emotional response is not always the best response when faced with new incidents. Having a reliable system—such as problem management—removes the temptation to respond emotionally. Proactive project management gives your team a framework for problem solving. It’s an iterative process —the more you use it, the more likely you are to have fewer problems, faster response times, and better outputs.

1. Identify the problem

During problem identification, you’re looking at the present—what’s happening right now? Here, you’ll define what the incident is and its scale. Is this a small, quick-fix, or a full overhaul? Consider using problem framing to define, prioritize, and understand the obstacles involved with these more complex problems.

2. Diagnose the cause

Use problem analysis or root cause analysis to strategically look at the cause of a problem. Follow the trail of issues all the way back to its beginnings.

To diagnose the underlying cause, you’ll want to answer:

What factors or conditions led to the incident?

Do you see related incidents? Could those be coming from the same source?

Did someone miss a step? Are processes responsible for this problem?

3. Organize and prioritize

Now it’s time to build out your framework. Use an IT project plan to organize information in a space where everyone can make and see updates in real time. The easiest way to do this is with a project management tool where you can input ‌tasks, assign deadlines, and add dependencies to ensure nothing gets missed. To better organize your process, define:

What needs to be done?

Who’s responsible for each aspect? If no one is, can we assign someone?

When does each piece need to be completed?

What is the final number of incidents related to this problem?

Are any of these tasks dependent on another one? Do you need to set up dependencies ?

What are your highest priorities? How do they affect our larger business goals ?

How should you plan for this in the future?

4. Create a workaround

If the incident has stopped work or altered it, you might need to create a workaround. This is not always necessary, but temporary workarounds can keep work on track and avoid backlog while you go through the problem management steps. When these workarounds are especially effective, you can make them permanent processes.

5. Update your known error database

Every time an incident occurs, create a known error record and add it to your known error database (KEDB). Recording incidents helps you catch recurrences and logs the solution, so you know how to solve similar errors in the future.

[product ui] Incident log example (lists)

6. Pause for change management (if necessary)

Larger, high-impact problems might require change management. For example, if you realize the problem’s root cause is a lack of staff, you might dedicate team members to help. You can use change management to help them transition their responsibilities, see how these new roles fit in with the entire team, and determine how they will collaborate moving forward.

7. Solve the problem

This is the fun part—you get to resolve problems. At this stage, you should know exactly what you’re dealing with and the steps you need to take. But remember—with problem management, it’s not enough to solve the current problem. You’ll want to take any steps to prevent this from happening again in the future. That could mean hiring a new role to cover gaps in workflows , investing in new softwares and tools, or training staff on best practices to prevent these types of incidents.

Read: Turn your team into skilled problem solvers with these problem-solving strategies

8. Reflect on the process

The problem management process has the added benefit of recording the process in its entirety, so you can review it in the future. Once you’ve solved the problem, take the time to review each step and reflect on the lessons learned during this process. Make note of who was involved, what you needed, and any opportunities to improve your response to the next incident. After you go through the problem management process a few times and understand the basic steps, stakeholders, workload, and resources you need, create a template to make the kickoff process easier in the future.

5 benefits of problem management

Problem management helps you discover every piece of the problem—from the current scenario down to its root cause. Not only does this have an immediate positive impact on the current issue at hand, it also promotes collaboration and helps to build a better product overall.

Here are five other ways ‌problem management can benefit your team:

Avoids repeat incidents. When you manage the entire incident from start to finish, you will address the foundational problems that caused it. This leads to fewer repeat incidents.

Boosts cross-functional collaboration. Problem management is a collaborative process. One incident might require collaboration from IT, the security team, and legal. Depending on the level of the problem, it might trickle all the way back down to the product or service team, where core changes need to be made.

Creates a better user experience. It’s simple—the fewer incidents you have, the better your customer’s experience will be. Reducing incidents means fewer delays, downtime, and frustrations for your users, and a higher rate of customer satisfaction.

Improves response time. As you develop a flow and framework with a project management process, you’ll be better equipped to handle future incidents—even if they’re different scenarios.

Organizes problem solving. Problem management provides a structured, thoughtful approach to solving problems. This reduces impulsive responses and helps you keep a better problem record of incidents and solutions.

Problem management leads to better, faster solutions

IT teams will always have to deal with incidents, but they don’t have to be bogged down by them. That’s because problem management works. Whether you employ a full problem management team or choose to apply these practices to your current IT infrastructure, problem management—especially when combined with a project management tool—saves you time and effort down the road.

With IT project plans, we’ve made it easier than ever to track your problem management work in a shared tool. Try our free IT project template to see your work come together, effortlessly.

Related resources

How Asana uses work management to optimize resource planning

How Asana uses work management for organizational planning

Solve your tech overload with an intelligent transformation

9 steps to craft a successful go-to-market (GTM) strategy

The problem-solving process, how to solve problems: 5 steps, train to solve problems with lean today, what is problem solving steps, techniques, & best practices explained.

Problem solving is the art of identifying problems and implementing the best possible solutions. Revisiting your problem-solving skills may be the missing piece to leveraging the performance of your business, achieving Lean success, or unlocking your professional potential.

Ask any colleague if they’re an effective problem-solver and their likely answer will be, “Of course! I solve problems every day.”

Problem solving is part of most job descriptions, sure. But not everyone can do it consistently.

Problem solving is the process of defining a problem, identifying its root cause, prioritizing and selecting potential solutions, and implementing the chosen solution.

There’s no one-size-fits-all problem-solving process. Often, it’s a unique methodology that aligns your short- and long-term objectives with the resources at your disposal. Nonetheless, many paradigms center problem solving as a pathway for achieving one’s goals faster and smarter.

One example is the Six Sigma framework , which emphasizes eliminating errors and refining the customer experience, thereby improving business outcomes. Developed originally by Motorola, the Six Sigma process identifies problems from the perspective of customer satisfaction and improving product delivery.

Lean management, a similar method, is about streamlining company processes over time so they become “leaner” while producing better outcomes.

Trendy business management lingo aside, both of these frameworks teach us that investing in your problem solving process for personal and professional arenas will bring better productivity.

1. Precisely Identify Problems

As obvious as it seems, identifying the problem is the first step in the problem-solving process. Pinpointing a problem at the beginning of the process will guide your research, collaboration, and solutions in the right direction.

At this stage, your task is to identify the scope and substance of the problem. Ask yourself a series of questions:

What’s the problem?
How many subsets of issues are underneath this problem?
What subject areas, departments of work, or functions of business can best define this problem?

Although some problems are naturally large in scope, precision is key. Write out the problems as statements in planning sheets . Should information or feedback during a later step alter the scope of your problem, revise the statements.

Framing the problem at this stage will help you stay focused if distractions come up in later stages. Furthermore, how you frame a problem will aid your search for a solution. A strategy of building Lean success, for instance, will emphasize identifying and improving upon inefficient systems.

2. Collect Information and Plan

The second step is to collect information and plan the brainstorming process. This is another foundational step to road mapping your problem-solving process. Data, after all, is useful in identifying the scope and substance of your problems.

Collecting information on the exact details of the problem, however, is done to narrow the brainstorming portion to help you evaluate the outcomes later. Don’t overwhelm yourself with unnecessary information — use the problem statements that you identified in step one as a north star in your research process.

This stage should also include some planning. Ask yourself:

What parties will ultimately decide a solution?
Whose voices and ideas should be heard in the brainstorming process?
What resources are at your disposal for implementing a solution?

Establish a plan and timeline for steps 3-5.

3. Brainstorm Solutions

Brainstorming solutions is the bread and butter of the problem-solving process. At this stage, focus on generating creative ideas. As long as the solution directly addresses the problem statements and achieves your goals, don’t immediately rule it out.

Moreover, solutions are rarely a one-step answer and are more like a roadmap with a set of actions. As you brainstorm ideas, map out these solutions visually and include any relevant factors such as costs involved, action steps, and involved parties.

With Lean success in mind, stay focused on solutions that minimize waste and improve the flow of business ecosystems.

Become a Quality Management Professional

10% Growth In Jobs Of Quality Managers Profiles By 2025
11% Revenue Growth For Organisations Improving Quality

Certified Lean Six Sigma Green Belt

4 hands-on projects to perfect the skills learnt
4 simulation test papers for self-assessment

Lean Six Sigma Expert

IASSC® Lean Six Sigma Green Belt and Black Belt certification
13 Projects, 12 Simulation exams, 18 Case Studies & 114 PDUs

Here's what learners are saying regarding our programs:

Xueting Liu

Mechanical engineer student at sargents pty. ltd. ,.

A great training and proper exercise with step-by-step guide! I'll give a rating of 10 out of 10 for this training.

Abdus Salam

I have completed the Lean Six Sigma Expert Master’s Program from Simplilearn. And after the course, I could take up new projects and perform better. My average pay rate for a research position increased by 21%.

4. Decide and Implement

The most critical stage is selecting a solution. Easier said than done. Consider the criteria that has arisen in previous steps as you decide on a solution that meets your needs.

Once you select a course of action, implement it.

Practicing due diligence in earlier stages of the process will ensure that your chosen course of action has been evaluated from all angles. Often, efficient implementation requires us to act correctly and successfully the first time, rather than being hurried and sloppy. Further compilations will create more problems, bringing you back to step 1.

5. Evaluate

Exercise humility and evaluate your solution honestly. Did you achieve the results you hoped for? What would you do differently next time?

As some experts note, formulating feedback channels into your evaluation helps solidify future success. A framework like Lean success, for example, will use certain key performance indicators (KPIs) like quality, delivery success, reducing errors, and more. Establish metrics aligned with company goals to assess your solutions.

Master skills like measurement system analysis, lean principles, hypothesis testing, process analysis and DFSS tools with our Lean Six Sigma Green Belt Training Course . Sign-up today!

Become a quality expert with Simplilearn’s Lean Six Sigma Green Belt . This Lean Six Sigma certification program will help you gain key skills to excel in digital transformation projects while improving quality and ultimate business results.

In this course, you will learn about two critical operations management methodologies – Lean practices and Six Sigma to accelerate business improvement.

Our Quality Management Courses Duration And Fees

Explore our top Quality Management Courses and take the first step towards career success

Get Free Certifications with free video courses

Quality Management

Lean Management

Project Management

Learn from industry experts with free masterclasses, digital marketing.

The Top 10 AI Tools You Need to Master Marketing in 2024

Unlock Digital Marketing Career Success Secrets for 2024 with Purdue University

Your Gateway to Game-changing Digital Marketing Careers in 2024 with Purdue University

Get Affiliated Certifications with Live Class programs

PMP, PMI, PMBOK, CAPM, PgMP, PfMP, ACP, PBA, RMP, SP, and OPM3 are registered marks of the Project Management Institute, Inc.

SUGGESTED TOPICS
The Magazine
Newsletters
Managing Yourself
Managing Teams
Work-life Balance
The Big Idea
Data & Visuals
Reading Lists
Case Selections
HBR Learning
Topic Feeds
Account Settings
Email Preferences

How to Solve Problems

Laura Amico

To bring the best ideas forward, teams must build psychological safety.

Teams today aren’t just asked to execute tasks: They’re called upon to solve problems. You’d think that many brains working together would mean better solutions, but the reality is that too often problem-solving teams fall victim to inefficiency, conflict, and cautious conclusions. The two charts below will help your team think about how to collaborate better and come up with the best solutions for the thorniest challenges.

Laura Amico is a former senior editor at Harvard Business Review.

Partner Center

Business Essentials
Leadership & Management
Credential of Leadership, Impact, and Management in Business (CLIMB)
Entrepreneurship & Innovation
Digital Transformation
Finance & Accounting
Business in Society
For Organizations
Support Portal
Media Coverage
Founding Donors
Leadership Team

Harvard Business School →
HBS Online →
Business Insights →

Business Insights

Harvard Business School Online's Business Insights Blog provides the career insights you need to achieve your goals and gain confidence in your business skills.

Career Development
Communication
Decision-Making
Earning Your MBA
Negotiation
News & Events
Productivity
Staff Spotlight
Student Profiles
Work-Life Balance
AI Essentials for Business
Alternative Investments
Business Analytics
Business Strategy
Business and Climate Change
Design Thinking and Innovation
Digital Marketing Strategy
Disruptive Strategy
Economics for Managers
Entrepreneurship Essentials
Financial Accounting
Global Business
Launching Tech Ventures
Leadership Principles
Leadership, Ethics, and Corporate Accountability
Leading with Finance
Management Essentials
Negotiation Mastery
Organizational Leadership
Power and Influence for Positive Impact
Strategy Execution
Sustainable Business Strategy
Sustainable Investing
Winning with Digital Platforms

What Is Creative Problem-Solving & Why Is It Important?

Business team using creative problem-solving

01 Feb 2022

One of the biggest hindrances to innovation is complacency—it can be more comfortable to do what you know than venture into the unknown. Business leaders can overcome this barrier by mobilizing creative team members and providing space to innovate.

There are several tools you can use to encourage creativity in the workplace. Creative problem-solving is one of them, which facilitates the development of innovative solutions to difficult problems.

Here’s an overview of creative problem-solving and why it’s important in business.

Access your free e-book today.

What Is Creative Problem-Solving?

Research is necessary when solving a problem. But there are situations where a problem’s specific cause is difficult to pinpoint. This can occur when there’s not enough time to narrow down the problem’s source or there are differing opinions about its root cause.

In such cases, you can use creative problem-solving , which allows you to explore potential solutions regardless of whether a problem has been defined.

Creative problem-solving is less structured than other innovation processes and encourages exploring open-ended solutions. It also focuses on developing new perspectives and fostering creativity in the workplace . Its benefits include:

Finding creative solutions to complex problems : User research can insufficiently illustrate a situation’s complexity. While other innovation processes rely on this information, creative problem-solving can yield solutions without it.
Adapting to change : Business is constantly changing, and business leaders need to adapt. Creative problem-solving helps overcome unforeseen challenges and find solutions to unconventional problems.
Fueling innovation and growth : In addition to solutions, creative problem-solving can spark innovative ideas that drive company growth. These ideas can lead to new product lines, services, or a modified operations structure that improves efficiency.

Design Thinking and Innovation | Uncover creative solutions to your business problems | Learn More

Creative problem-solving is traditionally based on the following key principles :

1. Balance Divergent and Convergent Thinking

Creative problem-solving uses two primary tools to find solutions: divergence and convergence. Divergence generates ideas in response to a problem, while convergence narrows them down to a shortlist. It balances these two practices and turns ideas into concrete solutions.

2. Reframe Problems as Questions

By framing problems as questions, you shift from focusing on obstacles to solutions. This provides the freedom to brainstorm potential ideas.

3. Defer Judgment of Ideas

When brainstorming, it can be natural to reject or accept ideas right away. Yet, immediate judgments interfere with the idea generation process. Even ideas that seem implausible can turn into outstanding innovations upon further exploration and development.

4. Focus on "Yes, And" Instead of "No, But"

Using negative words like "no" discourages creative thinking. Instead, use positive language to build and maintain an environment that fosters the development of creative and innovative ideas.

Creative Problem-Solving and Design Thinking

Whereas creative problem-solving facilitates developing innovative ideas through a less structured workflow, design thinking takes a far more organized approach.

Design thinking is a human-centered, solutions-based process that fosters the ideation and development of solutions. In the online course Design Thinking and Innovation , Harvard Business School Dean Srikant Datar leverages a four-phase framework to explain design thinking.

The four stages are:

The four stages of design thinking: clarify, ideate, develop, and implement

Clarify: The clarification stage allows you to empathize with the user and identify problems. Observations and insights are informed by thorough research. Findings are then reframed as problem statements or questions.
Ideate: Ideation is the process of coming up with innovative ideas. The divergence of ideas involved with creative problem-solving is a major focus.
Develop: In the development stage, ideas evolve into experiments and tests. Ideas converge and are explored through prototyping and open critique.
Implement: Implementation involves continuing to test and experiment to refine the solution and encourage its adoption.

Creative problem-solving primarily operates in the ideate phase of design thinking but can be applied to others. This is because design thinking is an iterative process that moves between the stages as ideas are generated and pursued. This is normal and encouraged, as innovation requires exploring multiple ideas.

Creative Problem-Solving Tools

While there are many useful tools in the creative problem-solving process, here are three you should know:

Creating a Problem Story

One way to innovate is by creating a story about a problem to understand how it affects users and what solutions best fit their needs. Here are the steps you need to take to use this tool properly.

1. Identify a UDP

Create a problem story to identify the undesired phenomena (UDP). For example, consider a company that produces printers that overheat. In this case, the UDP is "our printers overheat."

2. Move Forward in Time

To move forward in time, ask: “Why is this a problem?” For example, minor damage could be one result of the machines overheating. In more extreme cases, printers may catch fire. Don't be afraid to create multiple problem stories if you think of more than one UDP.

3. Move Backward in Time

To move backward in time, ask: “What caused this UDP?” If you can't identify the root problem, think about what typically causes the UDP to occur. For the overheating printers, overuse could be a cause.

Following the three-step framework above helps illustrate a clear problem story:

The printer is overused.
The printer overheats.
The printer breaks down.

You can extend the problem story in either direction if you think of additional cause-and-effect relationships.

4. Break the Chains

By this point, you’ll have multiple UDP storylines. Take two that are similar and focus on breaking the chains connecting them. This can be accomplished through inversion or neutralization.

Inversion: Inversion changes the relationship between two UDPs so the cause is the same but the effect is the opposite. For example, if the UDP is "the more X happens, the more likely Y is to happen," inversion changes the equation to "the more X happens, the less likely Y is to happen." Using the printer example, inversion would consider: "What if the more a printer is used, the less likely it’s going to overheat?" Innovation requires an open mind. Just because a solution initially seems unlikely doesn't mean it can't be pursued further or spark additional ideas.
Neutralization: Neutralization completely eliminates the cause-and-effect relationship between X and Y. This changes the above equation to "the more or less X happens has no effect on Y." In the case of the printers, neutralization would rephrase the relationship to "the more or less a printer is used has no effect on whether it overheats."

Even if creating a problem story doesn't provide a solution, it can offer useful context to users’ problems and additional ideas to be explored. Given that divergence is one of the fundamental practices of creative problem-solving, it’s a good idea to incorporate it into each tool you use.

Brainstorming

Brainstorming is a tool that can be highly effective when guided by the iterative qualities of the design thinking process. It involves openly discussing and debating ideas and topics in a group setting. This facilitates idea generation and exploration as different team members consider the same concept from multiple perspectives.

Hosting brainstorming sessions can result in problems, such as groupthink or social loafing. To combat this, leverage a three-step brainstorming method involving divergence and convergence :

Have each group member come up with as many ideas as possible and write them down to ensure the brainstorming session is productive.
Continue the divergence of ideas by collectively sharing and exploring each idea as a group. The goal is to create a setting where new ideas are inspired by open discussion.
Begin the convergence of ideas by narrowing them down to a few explorable options. There’s no "right number of ideas." Don't be afraid to consider exploring all of them, as long as you have the resources to do so.

Alternate Worlds

The alternate worlds tool is an empathetic approach to creative problem-solving. It encourages you to consider how someone in another world would approach your situation.

For example, if you’re concerned that the printers you produce overheat and catch fire, consider how a different industry would approach the problem. How would an automotive expert solve it? How would a firefighter?

Be creative as you consider and research alternate worlds. The purpose is not to nail down a solution right away but to continue the ideation process through diverging and exploring ideas.

Which HBS Online Entrepreneurship and Innovation Course is Right for You? | Download Your Free Flowchart

Continue Developing Your Skills

Whether you’re an entrepreneur, marketer, or business leader, learning the ropes of design thinking can be an effective way to build your skills and foster creativity and innovation in any setting.

If you're ready to develop your design thinking and creative problem-solving skills, explore Design Thinking and Innovation , one of our online entrepreneurship and innovation courses. If you aren't sure which course is the right fit, download our free course flowchart to determine which best aligns with your goals.

About the Author

Modified crayfish optimization algorithm for solving multiple engineering application problems

Open access
Published: 24 April 2024
Volume 57 , article number 127 , ( 2024 )

Cite this article

You have full access to this open access article

Heming Jia 1 ,
Xuelian Zhou 1 ,
Jinrui Zhang 1 ,
Laith Abualigah 2 , 3 ,
Ali Riza Yildiz 4 &
Abdelazim G. Hussien 5

Explore all metrics

Crayfish Optimization Algorithm (COA) is innovative and easy to implement, but the crayfish search efficiency decreases in the later stage of the algorithm, and the algorithm is easy to fall into local optimum. To solve these problems, this paper proposes an modified crayfish optimization algorithm (MCOA). Based on the survival habits of crayfish, MCOA proposes an environmental renewal mechanism that uses water quality factors to guide crayfish to seek a better environment. In addition, integrating a learning strategy based on ghost antagonism into MCOA enhances its ability to evade local optimality. To evaluate the performance of MCOA, tests were performed using the IEEE CEC2020 benchmark function and experiments were conducted using four constraint engineering problems and feature selection problems. For constrained engineering problems, MCOA is improved by 11.16%, 1.46%, 0.08% and 0.24%, respectively, compared with COA. For feature selection problems, the average fitness value and accuracy are improved by 55.23% and 10.85%, respectively. MCOA shows better optimization performance in solving complex spatial and practical application problems. The combination of the environment updating mechanism and the learning strategy based on ghost antagonism significantly improves the performance of MCOA. This discovery has important implications for the development of the field of optimization.

Graphical Abstract

Crayfish optimization algorithm

Enhanced Tunicate Swarm Algorithm for Solving Large-Scale Nonlinear Optimization Problems

Hybrid beluga whale optimization algorithm with multi-strategy for functions and engineering optimization problems

Avoid common mistakes on your manuscript.

1 Introduction

For a considerable period, engineering application problems have been widely discussed by people. At present, improving the modern scientific level of engineering construction has become the goal of human continuous struggle, including constrained engineering design problems (Zhang et al. 2022a ; Mortazavi 2019 ) affected by a series of external factors and feature selection problems (Kira and Rendell 1992 ), and so on. Constrained engineering design problems refers to the problem of achieving optimization objectives and reducing calculation costs under many external constraints, which is widely used in mechanical engineering (Abualigah et al. 2022 ), electrical engineering (Razmjooy et al. 2021 ), civil engineering (Kaveh 2017 ), chemical engineering (Talatahari et al. 2021 ) and other engineering fields, such as workshop scheduling (Meloni et al. 2004 ), wind power generation (Lu et al. 2021 ), and UAV path planning (Belge et al. 2022 ), parameter extraction of photovoltaic models(Zhang et al. 2022b ; Zhao et al. 2022 ), Optimization of seismic foundation isolation system (Kandemir and Mortazavi 2022 ), optimal design of RC support foundation system of industrial buildings (Kamal et al. 2023 ), synchronous optimization of fuel type and external wall insulation performance of intelligent residential buildings (Moloodpoor and Mortazavi 2022 ), economic optimization of double-tube heaters (Moloodpoor et al. 2021 ).

Feature selection is the process of choosing specific subsets of features from a larger set based on defined criteria. In this approach, each original feature within the subset is individually evaluated using an assessment function. The aim is to select pertinent features that carry distinctive characteristics. This selection process reduces the dimensionality of the feature space, enhancing the model's generalization ability and accuracy. The ultimate goal is to create the best possible combination of features for the model. By employing feature selection, the influence of irrelevant factors is minimized. This reduction in irrelevant features not only streamlines the computational complexity but also reduces the time costs associated with processing the data. Through this method, redundant and irrelevant features are systematically removed from the model. This refinement improves the model’s accuracy and results in a higher degree of fit, ensuring that the model aligns more closely with the underlying data patterns.

In practical applications of feature selections, models are primarily refined using two main methods: the filter (Cherrington et al. 2019 ) and wrapper (Jović et al. 2015 ) techniques. The filter method employs a scoring mechanism to assess and rank the model's features. It selects the subset of features with the highest scores, considering it as the optimal feature combination. On the other hand, the wrapper method integrates the selection process directly into the learning algorithm. It embeds the feature subset evaluation within the learning process, assessing the correlation between the chosen features and the model. In recent years, applications inspired by heuristic algorithms can be seen everywhere in our lives and are closely related to the rapid development of today's society. These algorithms play an indispensable role in solving a myriad of complex engineering problems and feature selection challenges. They have proven particularly effective in addressing spatial, dynamic, and random problems, showcasing significant practical impact and tangible outcomes.

With the rapid development of society and science and technology, through continuous exploitation and exploration in the field of science, more and more complex and difficult to describe multi-dimensional engineering problems also appear in our research process. Navigating these complexities demands profound contemplation and exploration. While traditional heuristic algorithms have proven effective in simpler, foundational problems, they fall short when addressing the novel and intricate multi-dimensional challenges posed by our current scientific landscape and societal needs. Thus, researchers have embarked on a journey of continuous contemplation and experimentation. By cross-combining and validating existing heuristic algorithms, they have ingeniously devised a groundbreaking solution: Metaheuristic Algorithms (MAs) (Yang 2011 ). This innovative approach aims to tackle the complexities of our evolving problems, ensuring alignment with the rapid pace of social and technological development. MAs is a heuristic function based algorithm. It works by evaluating the current state of the problem and possible solutions to guide the algorithm in making choices in the search space. MAs improves the efficiency and accuracy of the problem solving process by combining multiple heuristic functions and updating the search direction at each step based on their weights. The diversity of MAs makes it a universal problem solver, adapting to the unique challenges presented by different problem domains. Essentially represents a powerful paradigm shift in computational problem solving, providing a powerful approach to address the complexity of modern engineering and scientific challenges. Compared with traditional algorithms, MAs has made great progress in finding optimal solutions, jumping out of local optima, and overcoming convergence difficulties in the later stage of solution through the synergy of different algorithms. These enhancements mark a significant progress, which not only demonstrates the adaptability of the scientific method, but also emphasizes the importance of continuous research and cooperation. It also has the potential to radically solve problems in domains of complex engineering challenges, enabling researchers to navigate complex problem landscapes with greater accuracy and efficiency.

Research shows that MAs are broadly classified into four different research directions: swarm-based, natural evolution-based, human-based, and physics-based. These categories include a wide range of innovative problem-solving approaches, each drawing inspiration from a different aspect of nature, human behavior, or physical principles. Researchers exploration these different pathways to solve complex challenges and optimize the solutions efficiently. First of all, the swarm-based optimization algorithm is the optimization algorithm that uses the wisdom of population survival to solve the problem. For example, Particle Swarm Optimization Algorithm (PSO) (Wang et al. 2018a ) is an optimization algorithm based on the group behavior of birds. PSO has a fast search speed and is only used for real-valued processing. However, it is not good at handling discrete optimization problems and has fallen into local optimization. Artificial Bee Colony Optimization Algorithm (ABC) (Jacob and Darney 2021 ) realizes the sharing and communication of information among individuals when bees collect honey according to their respective division of labor. In the Salp Swarm Algorithm (SSA) (Mirjalili et al. 2017 ), individual sea squirts are connected end to end and move and prey in a chain, and follow the leader with followers according to a strict “hierarchical” system. Ant Colony Optimization Algorithm (ACO) (Dorigo et al. 2006 ), ant foraging relies on the accumulation of pheromone on the path, and spontaneously finds the optimal path in an organized manner.

Secondly, a natural evolutionary algorithm inspired by the law of group survival of the fittest, an optimization algorithm that finds the best solution by preserving the characteristics of easy survival and strong individuals, such as: Genetic Programming Algorithm (GP) (Espejo et al. 2009 ), because biological survival and reproduction have certain natural laws, according to the structure of the tree to deduce certain laws of biological genetic and evolutionary process. Evolutionary Strategy Algorithm (ES) (Beyer and Schwefel 2002 ), the ability of a species to evolve itself to adapt to the environment, and produce similar but different offspring after mutation and recombination from the parent. Differential Evolution (DE) (Storn and Price 1997 ) eliminates the poor individuals and retains the good ones in the process of evolution, so that the good ones are constantly approaching the optimal solution. It has a strong global search ability in the initial iteration, but when there are fewer individuals in the population, individuals are difficult to update, and it is easy to fall into the local optimal. The Biogeography-based Optimization Algorithm (BBO) (Simon 2008 ), influenced by biogeography, filters out the global optimal value through the iteration of the migration and mutation of species information.

Then, Human-based optimization algorithms are optimization algorithms that take advantage of the diverse and complex human social relationships and activities in a specific environment to solve problems, such as: The teaching–learning-based Optimization (TLBO) (Rao and Rao 2016 ) obtained the optimal solution by simulating the Teaching relationship between students and teachers. It simplifies the information sharing mechanism within each round, and all evolved individuals can converge to the global optimal solution faster, but the algorithm often loses its advantage when solving some optimization problems far from the origin. Coronavirus Mask Protection Algorithm (CMPA) (Yuan et al. 2023 ), which is mainly inspired by the self-protection process of human against coronavirus, establishes a mathematical model of self-protection behavior and solves the optimization problem. Cultural Evolution Algorithm (CEA) (Kuo and Lin 2013 ), using the cultural model of system thinking framework for exploitation to achieve the purpose of cultural transformation, get the optimal solution. Volleyball Premier League Algorithm (VPL) (Moghdani and Salimifard 2018 ) simulates the process of training, competition and interaction of each team in the volleyball game to solve the global optimization problem.

Finally, Physics-based optimization algorithm is an optimization algorithm that uses the basic principles of physics to simulate the physical characteristics of particles in space to solve problems. For example, Snow Ablation Algorithm (SAO) (Deng and Liu 2023 ), inspired by the physical reaction of snow in nature, realizes the transformation among snow, water and steam by simulating the sublation and ablation of snow. RIME Algorithm (RIME) (Su et al. 2023 ) is a exploration and exploitation of mathematical model balance algorithm based on the growth process of soft rime and hard rime in nature. Central Force Optimization Algorithm (CFO) (Formato 2007 ), aiming at the problem of complex calculation of the initial detector, a mathematical model of uniform design is proposed to reduce the calculation time. Sine and cosine algorithm (SCA) (Mirjalili 2016 ) establishes mathematical models and seeks optimal solutions based on the volatility and periodicity characteristics of sine and cosine functions. Compared with the candidate solution set of a certain scale, the algorithm has a strong search ability and the ability to jump out of the local optimal, but the results of some test functions fluctuate around the optimal solution, and there is a certain precocious situation, and the convergence needs to be improved.

While the original algorithm is proposed, many improved MAs algorithms are also proposed to further improve the optimization performance of the algorithm in practical application problems, such as: Yujun-Zhang et al. combined the arithmetic optimization algorithm (AOA) with the Aquila Optimizer(AO) algorithm to propose a new meta-heuristic algorithm (AOAAO) (Zhang et al. 2022c ). CSCAHHO algorithm (Zhang et al. 2022d ) is a new algorithm obtained by chaotic mixing of sine and cosine algorithm (SCA) and Harris Hqwk optimization algorithm (HHO). Based on LMRAOA algorithm proposed to solve numerical and engineering problems (Zhang et al. 2022e ). Yunpeng Ma et al. proposed an improved teaching-based optimization algorithm to artificially reduce NOx emission concentration in circulating fluidized bed boilers (Ma et al. 2021 ). The improved algorithm SOS(MSOS) (Kumar et al. 2019 ), based on the natural Symbiotic search (SOS) algorithm, improves the search efficiency of the algorithm by introducing adaptive return factors and modified parasitic vectors. Modified beluga whale optimization with multi-strategies for solving engineering problems (MBWO) (Jia et al. 2023a ) by gathering Beluga populations for feeding and finding new habitats during long-distance migration. Betul Sultan Yh-ld-z et al. proposed a novel hybrid optimizer named AO-NM, which aims to optimize engineering design and manufacturing problems (Yıldız et al. 2023 ).

The Crayfish Optimization Algorithm (COA) (Jia et al. 2023b ) is a novel metaheuristic algorithm rooted in the concept of population survival wisdom, introduced by Heming Jia et al. in 2023. Drawing inspiration from crayfish behavior, including heat avoidance, competition for caves, and foraging, COA employs a dual-stage strategy. During the exploration stage, it replicates crayfish searching for caves in space for shelter, while the exploitation stage mimics their competition for caves and search for food. Crayfish, naturally averse to dry heat, thrive in freshwater habitats. To simulate their behavior and address challenges related to high temperatures and food scarcity, COA incorporates temperature variations into its simulation. By replicating crayfish habits, the algorithm dynamically adapts to environmental factors, ensuring robust problem-solving capabilities. Based on temperature fluctuations, crayfish autonomously select activities such as seeking shelter, competing for caves, and foraging. When the temperature exceeds 30°C, crayfish instinctively seek refuge in cool, damp caves to escape the heat. If another crayfish is already present in the cave, a competition ensues for occupancy. Conversely, when the temperature drops below 30°C, crayfish enter the foraging stage. During this phase, they make decisions about food consumption based on the size of the available food items. COA achieves algorithmic transformation between exploration and exploitation stages by leveraging temperature variations, aiming to balance the exploration and exploitation capabilities of the algorithm. However, COA solely emulates the impact of temperature on crayfish behavior, overlooking other significant crayfish habits, leading to inherent limitations. In the latter stages of global search, crayfish might cluster around local optimum positions, restricting movement. This hampers the crayfish's search behavior, slowing down convergence speed, and increasing the risk of falling into local optima, thereby making it challenging to find the optimal solution.

In response to the aforementioned challenges, this paper proposes a Modified Crayfish Optimization Algorithm (MCOA). MCOA introduces an environmental update mechanism inspired by crayfish's preference for living in fresh flowing water. MCOA incorporates crayfish's innate perception abilities to assess the quality of the surrounding aquatic environment, determining whether the current habitat is suitable for survival. The simulation of crayfish crawling upstream to find a more suitable aquatic environment is achieved by utilizing adaptive flow factors and leveraging the crayfish's second, third foot perceptions to determine the direction of water flow.This method partially replicates the survival and reproduction behavior of crayfish, ensuring the continual movement of the population. It heightens the randomness within the group, widens the search scope for crayfish, enhances the algorithm's exploration efficiency, and effectively strengthens the algorithm’s global optimization capabilities. Additionally, the ghost opposition-based learning strategy (Jia et al. 2023c ) is implemented to introduce random population initialization when the algorithm becomes trapped in local optima. This enhancement significantly improves the algorithm's capability to escape local optima, promoting better exploration of the solution space. After the careful integration of the aforementioned two strategies, the search efficiency and predation speed of the crayfish algorithm experience a substantial improvement. Moreover, the algorithm's convergence rate and global optimization ability are significantly enhanced, leading to more effective and efficient problem-solving capabilities.

In the experimental section, we conducted a comprehensive comparison between MCOA and nine other metaheuristic algorithms. We utilized the IEEE CEC2020 benchmark function to evaluate the performance of the algorithm. The evaluation involved statistical methods such as the Wilcoxon rank sum test and Friedman test to rank the averages, validating the efficiency of the MCOA algorithm and the effectiveness of the proposed improvements. Furthermore, MCOA was applied to address four constrained engineering design problems as well as the high-dimensional feature selection problem using the wrapper method. These practical applications demonstrated the practicality and effectiveness of MCOA in solving real-world engineering problems.

The main contributions of this paper are as follows:

In the environmental renewal mechanism, the water quality factor and roulette wheel selection method are introduced to simulate the process of crayfish searching for a more suitable water environment for survival.

The introduction of the ghost opposition-based learning strategy enhances the randomness of crayfish update locations, effectively preventing the algorithm from getting trapped in local optima, and improving the overall global optimization performance of the algorithm.

The fixed value of food intake is adaptively adjusted based on the number of evaluations, enhancing the algorithm's capacity to escape local optima. This adaptive change ensures a more dynamic exploration of the solution space, improving the algorithm's overall optimization effectiveness.

The MCOA’s performance is compared with nine metaheuristics, including COA, using the IEEE CEC2020 benchmark function. The comparison employs the Wilcoxon rank sum test and Friedman test to rank the averages, providing evidence for the efficiency of MCOA and the effectiveness of the proposed improvements.

The application of MCOA to address four constrained engineering design problems and the high-dimensional feature selection problem using the wrapper method demonstrates the practicality and effectiveness of MCOA in real-world applications.

The main structure of this paper is as follows, the first part of the paper serves as a brief introduction to the entire document, providing an overview of the topics and themes that will be covered. In the second part, the paper provides a comprehensive summary of the Crayfish Optimization Algorithm (COA). In the third part, a modified crawfish optimization algorithm (MCOA) is proposed. By adding environment updating mechanism and ghost opposition-based learning strategy, MCOA can enhance the global search ability and convergence speed to some extent. Section four shows the experimental results and analysis of MCOA in IEEE CEC2020 benchmark functions. The fifth part applies MCOA to four kinds of constrained engineering design problems. In Section six, MCOA is applied to the high-dimensional feature selection problem of wrapper methods to demonstrate the effectiveness of MCOA in practical application problems. Finally, Section seven concludes the paper.

2 Crayfish optimization algorithm (COA)

Crayfish is a kind of crustaceans living in fresh water, its scientific name is crayfish, also called red crayfish or freshwater crayfish, because of its food, fast growth rate, rapid migration, strong adaptability and the formation of absolute advantages in the ecological environment. Changes in temperature often cause changes in crayfish behavior. When the temperature is too high, crayfish choose to enter the cave to avoid the damage of high temperature, and when the temperature is suitable, they will choose to climb out of the cave to forage. According to the living habits of crayfish, it is proposed that the three stages of summer, competition for caves and going out to forage correspond to the three living habits of crayfish, respectively.

Crayfish belong to ectotherms and are affected by temperature to produce behavioral differences, which range from 20 °C to 35 °C. The temperature is calculated as follows:

where temp represents the temperature of the crayfish's environment.

2.1 Initializing the population

In the d -dimensional optimization problem of COA, each crayfish is a 1 × d matrix representing the solution of the problem. In a set of variables ( X 1 , X 2 , X 3 …… X d ), the position ( X ) of each crayfish is between the upper boundary ( ub ) and lower boundary ( lb ) of the search space. In each evaluation of the algorithm, an optimal solution is calculated, and the solutions calculated in each evaluation are compared, and the optimal solution is found and stored as the optimal solution of the whole problem. The position to initialize the crayfish population is calculated using the following formula.

where X i,j denotes the position of the i-th crayfish in the j-th dimension, ub j denotes the upper bound of the j-th dimension, lb j denotes the lower bound of the j-th dimension, and rand is a random number from 0 to 1.

2.2 Summer escape stage (exploration stage)

In this paper, the temperature of 30 °C is assumed to be the dividing line to judge whether the current living environment is in a high temperature environment. When the temperature is greater than 30 ℃ and it is in the summer, in order to avoid the harm caused by the high temperature environment, crayfish will look for a cool and moist cave and enter the summer to avoid the influence of high temperature. The caverns are calculated as follows.

where X G represents the optimal position obtained so far for this evaluation number, and X L represents the optimal position of the current population.

The behavior of crayfish competing for the cave is a random event. To simulate the random event of crayfish competing for the cave, a random number rand is defined, when rand < 0.5 means that there are no other crayfish currently competing for the cave, and the crayfish will go straight into the cave for the summer. At this point, the crayfish position update calculation formula is as follows.

Here, X new is the next generation position after location update, and C 2 is a decreasing curve. C 2 is calculated as follows.

Here, FEs represents the number of evaluations and MaxFEs represents the maximum number of evaluations.

2.3 Competition stage (exploitation stage)

When the temperature is greater than 30 °C and rand ≥ 0.5, it indicates that the crayfish have other crayfish competing with them for the cave when they search for the cave for summer. At this point, the two crayfish will struggle against the cave, and crayfish X i adjusts its position according to the position of the other crayfish X z . The adjustment position is calculated as follows.

Here, z represents the random individual of the crayfish, and the random individual calculation formula is as follows.

where, N is the population size.

2.4 Foraging stage (exploitation stage)

The foraging behavior of crayfish is affected by temperature, and temperature less than or equal to 30 ℃ is an important condition for crayfish to climb out of the cave to find food. When the temperature is less than or equal to 30 °C, the crayfish will drill out of the cave and judge the location of the food according to the optimal location obtained in this evaluation, so as to find the food to complete the foraging. The position of the food is calculated as follows.

The amount of food crayfish eat depends on the temperature. When the temperature is between 20 °C and 30°C, crayfish have strong foraging behavior, and the most food is found and the maximum food intake is also obtained at 25 °C. Thus, the food intake pattern of crayfish resembles a normal distribution. Food intake was calculated as follows.

Here, µ is the most suitable temperature for crayfish feeding, and σ and C 1 are the parameters used to control the variation of crayfish intake at different temperatures.

The food crayfish get depends not only on the amount of food they eat, but also on the size of the food. If the food is too large, the crayfish can't eat the food directly. They need to tear it up with their claws before eating the food. The size of the food is calculated as follows.

Here, C 3 is the food factor, which represents the largest food, and its value is 3, fitness i represents the fitness value of the i-th crayfish, and fitness food represents the fitness value of the location of the food.

Crayfish use the value of the maximum food Q to judge the size of the food obtained and thus decide the feeding method. When Q > ( C 3 + 1)/2, it means that the food is too large for the crayfish to eat directly, and it needs to tear the food with its claws and eat alternately with the second and third legs. The formula for shredding food is as follows.

After the food is shredded into a size that is easy to eat, the second and third claws are used to pick up the food and put it into the mouth alternately. In order to simulate the process of bipedal eating, the mathematical models of sine function and cosine function are used to simulate the crayfish eating alternately. The formula for crayfish alternating feeding is as follows.

When Q ≤ ( C 3 + 1)/2, it indicates that the food size is suitable for the crayfish to eat directly at this time, and the crayfish will directly move towards the food location and eat directly. The formula for direct crayfish feeding is as follows.

2.5 Pseudo-code for COA

Crayfish optimization algorithm pseudo-code

3 Modified crayfish optimization algorithm (MCOA)

Based on crayfish optimization algorithm, we propose a high-dimensional feature selection problem solving algorithm (MCOA) based on improved crayfish optimization algorithm. In MCOA, we know that the quality of the aquatic environment has a great impact on the survival of crayfish, according to the living habits of crayfish, which mostly feed on plants and like fresh water. Oxygen is an indispensable energy for all plants and animals to maintain life, the higher the content of dissolved oxygen in the water body, the more vigorous the feeding of crayfish, the faster the growth, the less disease, and the faster the water flow in the place of better oxygen permeability, more aquatic plants, suitable for survival, so crayfish has a strong hydrotaxis. When crayfish perceive that the current environment is too dry and hot or lack of food, they crawl backward according to their second, third and foot perception (r) to judge the direction of water flow, and find an aquatic environment with sufficient oxygen and food to sustain life. Good aquatic environment has sufficient oxygen and abundant aquatic plants, to a certain extent, to ensure the survival and reproduction of crayfish.

In addition, we introduce ghost opposition-based learning to help MCOA escape the local optimal trap. The ghost opposition-based learning strategy combines the candidate individual, the current individual and the optimal individual to randomly generate a new candidate position to replace the previous poor candidate position, and then takes the best point or the candidate solution as the central point, and then carries out more specific and extensive exploration of other positions. Traditional opposition-based learning (Mahdavi et al. 2018 ) is based on the central point and carries out opposition-based learning in a fixed format. Most of the points gather near the central point and their positions will not exceed the distance between the current point and the central point, and most solutions will be close to the optimal individual. However, if the optimal individual is not near the current exploration point, the algorithm will fall into local optimal and it is difficult to find the optimal solution. Compared with traditional opposition-based learning, ghost opposition-based learning is a opposition-based learning solution that can be dynamically changed by adjusting the size of parameter k, thereby expanding the algorithm's exploration range of space, effectively solving the problem that the optimal solution is not within the search range based on the center point, and making the algorithm easy to jump out of the local optimal.

According to the life habits of crayfish, this paper proposes a Modified Crayfish Optimization Algorithm (MCOA), which uses environment update mechanism and ghost opposition-based learning strategy to improve COA, and shows the implementation steps, pseudo-code and flow chart of MCOA algorithm as follows.

3.1 Environment update mechanism

In the environmental renewal mechanism, a water quality factor V is introduced to represent the quality of the aquatic environment at the current location. In order to simplify the design and computational complexity of the system, the water quality factor V of the MCOA is represented by a hierarchical discretization, and its value range is set to 0 to 5. Crayfish perceive the quality of the current aquatic environment through the perception ( r ) of the second and third legs, judge whether the current living environment can continue to survive through the perception, and independently choose whether to update the current location. The location update is calculated as follows.

Among them, each crayfish has a certain difference in its own perception of water environment r , X 2 is a random position between the candidate optimal position and the current position, which is calculated by Eq. ( 15 ), X 1 is a random position in the population, and B is an adaptive water flow factor, which is calculated by Eq. ( 16 ).

Among them, the sensing force r of the crayfish’s second and third legs is a random number [0,1]. c is a constant that represents the water flow velocity factor with a value of 2. When V ≤ 3, it indicates that the crayfish perceives the quality of the current living environment to be good and is suitable for continued survival. When V > 3, it indicates that the crayfish perceives that the current living environment quality is poor, and it needs to crawl in the opposite direction according to the direction of water flow that crayfish perceives, so as to find an aquatic environment with sufficient oxygen and abundant food Fig. 1 .

Classification of MAs

In the environmental updating mechanism, in order to describe the behavior of crayfish upstream in more detail, the perception area of crayfish itself is abstractly defined as a circle in MCOA, and crayfish is in the center of the circle. In each evaluation calculation, a random Angle θ is first calculated by the roulette wheel selection algorithm to determine the moving direction of the crayfish in the circular area, and then the moving path of the crayfish is determined according to the current moving direction. In the whole circle, random angles can be chosen from 0 to 360 degrees, from which the value of θ can be determined to be of magnitude [− 1,1]. The difference of random Angle indicates that each crayfish moves its position in a random direction, which broadens the search range of crayfish, enhances the randomness of position and the ability to escape from local optimum, and avoids local convergence Fig. 2 .

Schematic diagram of the environment update mechanism

3.2 Ghost opposition-based learning strategy

The ghost opposition-based learning strategy takes a two-dimensional space as an example. It is assumed that there is a two-dimensional space, as shown in Fig. 3 . On the X-axis, [ ub , lb ] represents the search range of the solution, and the ghost generation method is shown in Fig. 3 . Assuming that the position of a new candidate solution is Xnew and the height of the solution is h1 i , the position of the best solution on the X-axis is the projected position of the candidate solution, and the position and height are XG , h2 i , respectively. In addition, on the X-axis there is a projection position X i of the candidate solution with a height of h3 i. Thus, the position of the ghost is obtained. The projection position of the ghost on the X-axis is x i by vector calculation, and its height is h i . The ghost position is calculated using the following formula.

Schematic diagram of ghost opposition-based learning strategy

In Fig. 3 , the Y-axis represents the convex lens. Suppose there is a ghost position P i , where x i is its projection on the X-axis and h i is its height. P* i is the real image obtained by convex lens imaging. P* i is projected on the X-axis as x* i and has height h* i . Therefore, the opposite individual x* i of individual x i can be obtained. x* i is the corresponding point corresponding to the ghost individual x i obtained from O as the base point. According to the lens imaging principle, we can obtain Eq. ( 18 ), and the calculation formula is as follows.

The strategy formula of ghost opposition-based learning is evolved from Eq. ( 18 ). The strategy formula of ghost opposition-based learning is calculated as follows.

3.3 Implementation of MCOA algorithm

3.3.1 initialization phase.

Initialize the population size N , the population dimension d , and the number of evaluations FEs . The initialized population is shown in Eq. ( 2 ).

3.3.2 Environment update mechanism

Crayfish judge the quality of the current aquatic environment according to the water quality factor V , and speculate whether the current aquatic environment can continue to survive. When V > 3 indicates that the crawfish perceives the quality of the current aquatic environment as poor and is not suitable for survival. According to the sensory information of the second and third legs and the adaptive flow factor, the crawfish judges the direction of the current flow, and then moves upstream to find a better aquatic environment to update the current position. The position update formula is shown in Eq. ( 14 ). When V < 3, it means that the crayfish has a good perception of the current living environment and is suitable for survival, and does not need to update its position.

3.3.3 Exploration phase

When the temperature is greater than 30 ℃ and V > 3, it indicates that crayfish perceive the current aquatic environment quality is poor, and the cave is dry and without moisture, which cannot achieve the effect of summer vacation. It is necessary to first update the position by crawling in the reverse direction according to the flow direction, and find a cool and moist cave in a better quality aquatic environment for summer.

3.3.4 Exploitation stage

When the temperature is less than 30 ℃ and V > 3, it indicates that crayfish perceive the current aquatic environment is poor, and there is not enough food to maintain the survival of crayfish. It is necessary to escape from the current food shortage living environment by crawling in the reverse direction according to the current direction, and find a better aquatic environment to maintain the survival and reproduction of crayfish.

3.3.5 Ghost opposition-based learning strategy

Through the combination of the candidate individual, the current individual and the optimal individual, a candidate solution is randomly generated and compared with the current solution, the better individual solution is retained, the opposite individual is obtained, and the location of the ghost is obtained. The combination of multiple positions effectively prevents the algorithm from falling into local optimum, and the specific implementation formula is shown in Eq. ( 19 ).

3.3.6 Update the location

The position of the update is determined by comparing the fitness values. If the fitness of the current individual update is better, the current individual replaces the original individual. If the fitness of the original individual is better, the original individual is retained to exist as the optimal solution.

The pseudocode for MCOA is as follows (Algorithm 2).

Modified Crayfish optimization algorithm pseudo-code

The flow chart of the MCOA algorithm is as follows.

3.4 Computational complexity analysis

The complexity analysis of algorithms is an essential step to evaluate the performance of algorithms. In the experiment of complexity analysis of the algorithm, we choose the IEEE CEC2020 Special Session and Competition as the complexity evaluation standard of the single objective optimization algorithm. The complexity of MCOA algorithm mainly depends on several important parameters, such as the population size ( N = 30), the number of dimensions of the problem ( d = 10), the maximum number of evaluations of the algorithm ( MaxFEs = 100,000) and the solution function ( C ). Firstly, the running time of the test program is calculated and the running time ( T 0 ) of the test program is recorded, and the test program is shown in Algorithm 3. Secondly, under the same dimension of calculating the running time of the test program, the 10 test functions in the IEEE CEC2020 function set were evaluated 100,000 times, and their running time ( T 1 ) was recorded. Finally, the running time of 100,000 evaluations of 10 test functions performed by MCOA for 5 times under the same dimension was recorded, and the average value was taken as the running time of the algorithm ( T 2 ). Therefore, the formula for calculating the time complexity of MCOA algorithm is given in Eq. ( 21 ).

IEEE CEC2020 complexity analysis test program

The experimental data table of algorithm complexity analysis is shown in Table 1 . In the complexity analysis of the algorithm, we use the method of comparing MCOA algorithm with other seven metaheuristic algorithms to illustrate the complexity of MCOA. In Table 1 , we can see that the complexity of MCOA is much lower than other comparison algorithms such as ROA, STOA, and AOA. However, compared with COA, the complexity of MCOA is slightly higher than that of COA because it takes a certain amount of time to update the location through the environment update mechanism and ghost opposition-based learning strategy. Although the improved strategy of MCOA increases the computation time to a certain extent, the optimization performance of MOCA has been significantly improved through a variety of experiments in section four of this paper, which proves the good effect of the improved strategy.

4 Experimental results and discussion

The experiments are carried out on a 2.50 GHz 11th Gen Intel(R) Core(TM) i7-11,700 CPU with 16 GB memory and 64-bit Windows11 operating system using Matlab R2021a. In order to verify the performance of MCOA algorithm, MCOA is compared with nine metaheuristic algorithms in this subsection. In the experiments, we used the IEEE CEC2020 test function to evaluate the optimization performance of the MCOA algorithm Fig. 4 .

Flow chart of the MCOA algorithm

4.1 Experiments with IEEE CEC2020 test functions

In this subsection, using the Crayfish Optimization Algorithm (COA), Remora Optimization Algorithm (ROA) (Jia et al. 2021 ), Sooty Tern Optimization Algorithm (STOA) (Dhiman and Kaur 2019 ), Arithmetic Optimization Algorithm (AOA) (Abualigah et al. 2021 ), Harris Hawk Optimization Algorithm (HHO) (Heidari et al. 2019 ), Prairie Dog Optimization Algorithm (PDO) (Ezugwu et al. 2022 ), Genetic Algorithm (GA) (Mirjalili and Mirjalili 2019 ),Modified Sand Cat Swarm Optimization Algorithm (MSCSO) (Wu et al. 2022 ) and a competition algorithm LSHADE (Piotrowski 2018 ) were compared to verify the optimization effect of MCOA. The parameter Settings of each algorithm are shown in Table 2 .

In order to test the performance of MCOA, this paper selects 10 benchmark test functions of IEEE CEC2020 for simulation experiments. Where F1 is a unimodal function, F2–F3 is a multimodal function, F4 is a non-peak function, F5–F7 is a hybrid function, and F8-F10 is a composite function. The parameters of this experiment are uniformly set as follows: the maximum number of evaluation MaxFEs is 100,000, the population size N is 30, and the dimension size d is 10. The MCOA algorithm and the other nine algorithms are run independently for 30 times, and the average fitness value, standard deviation of fitness value and Friedman ranking calculation of each algorithm are obtained. The specific function Settings of the IEEE CEC2020 benchmark functions are shown in Table 3 .

4.1.1 Results statistics and convergence curve analysis of IEEE CEC2020 benchmark functions

In order to more clearly and intuitively compare the ability of MCOA and various algorithms to find individual optimal solutions, the average fitness value, standard deviation of fitness value and Friedman ranking obtained by running MCOA and other comparison algorithms independently for 30 times are presented in the form of tables and images. The data and images are shown in Table 4 and Fig. 5 respectively.

Convergence curve of MCOA algorithm in IEEE CEC2020

In Table 4 , mean represents the average fitness value, std represents the standard deviation of fitness value, rank represents the Friedman ranking, Friedman average rank represents the average ranking of the algorithm among all functions, and Friedman rank represents the final ranking of this algorithm. Compared with other algorithms, MCOA achieved the best results in average fitness value, standard deviation of fitness value and Friedman ranking. In unimodal function F1, although MCOA algorithm is slightly worse than LSHADE algorithm, MCOA is superior to other algorithms in mean fitness value, standard deviation of fitness value, Friedman ranking and other aspects. In the multimodal functions F2 and F3, although the average fitness value of MCOA is slightly worse, it also achieves a good result of ranking second. The standard deviation of fitness value in F3 is better than other comparison algorithms in terms of stability. In the peakless function F4, except GA and LSHADE algorithm, other algorithms can find the optimal individual solution stably. In the mixed functions F5, F6, and F7, although the mean fitness value of LSHADE is better than that of MCOA, the standard deviation of the fitness value of MCOA is better than that of the other algorithms compared. Among the composite functions of F8, F9 and F10, the standard deviation of MCOA's fitness value at F8 is slightly worse than that of LSHADE, but the average fitness value and standard deviation of fitness value are the best in other composite functions, and it has achieved the first place in all composite functions. Finally, from the perspective of Friedman average rank, MCOA has a strong comprehensive performance and still ranks first. Through the analysis of the data in Table 4 , it can be seen that MCOA ranks first overall and has good optimization effect, and its optimization performance is better than other 9 comparison algorithms.

Figure 5 shows that in the IEEE CEC2020 benchmark functions, for the unimodal function F1, although LSHADE algorithm has a better optimization effect, compared with similar meta-heuristic algorithms, MCOA has a slower convergence rate in the early stage, but can be separated from local optimal and converge quickly in the middle stage. In the multimodal functions F2 and F3, similar to F1, MCOA converges faster in the middle and late stages, effectively exiting the local optimal. Although the convergence speed is slower than that of LSHADE, the optimal value can still be found. In the peak-free function F4, the optimal value can be found faster by all algorithms except LSHADE, STOA and PDO because the function is easy to implement. In the mixed functions F5, F6 and F7, although the convergence rate of MCOA is slightly slower than that of COA algorithm in the early stage, it can still find better values than the other eight algorithms except LSHADE in the later stage. For the composite functions F8, F9 and F10, MCOA can find the optimal value faster than the other nine algorithms.

Based on the above, although LSHADE has a stronger ability to find the optimal value in a small number of functions, MCOA can still find the optimal value in most functions in the later stage, and compared with the other eight pair algorithms of the same type, MCOA has more obvious enhancement in optimization ability and avoidance of local optimization, and has better application effect.

4.1.2 Analysis of Wilcoxon rank sum test results

In the comparison experiment, the different effects of multiple algorithms solving the same problem are used to judge whether each algorithm has high efficiency and more obvious influence on solving the current problem, such as the convergence speed of the convergence curve, the fitness value of the optimal solution, the ability to jump out of the local optimum, etc. At present, only the average fitness value, the standard deviation of fitness value and the convergence curve can not be used as the basis for judging whether the performance of the algorithm is efficient. Therefore, the data and images presented by each algorithm in solving the current problem are comprehensively analyzed, and the Wilcoxon rank sum test is used to further verify the difference between MCOA and the other nine comparison algorithms. In this experiment, the significance level is defined as 5%. If its calculated value is less than 5%, it proves that there is a significant difference between the two algorithms, and if it is greater than 5%, it proves that there is no significant difference between the two algorithms. Table 5 shows the Wilcoxon rank-sum test results of the MCOA algorithm and the other nine comparison algorithms. Where the symbols “ + ”, “−” and “ = ” table the performance of MCOA better, worse and equal to the comparison algorithms, respectively.

In the calculation of the function F4 without peak, the value of 1 appears in the comparison of various algorithms such as MCOA, COA, ROA, STOA and other algorithms, indicating that in this function, a variety of algorithms have found the optimal value, there is no obvious difference, which can be ignored. However, in most of the remaining functions, the significance level of MCOA compared with the other nine algorithms is less than 5%, which is a significant difference.

From the overall table, the MCOA algorithm also achieves good results in the Wilcoxon rank-sum test of the IEEE CEC2020 benchmark function, and the contrast ratio with other algorithms is less than 5%, which proves that the MCOA algorithm has a significant difference from the other nine algorithms, and MCOA has better optimization performance. According to the comparison results with the original algorithm, it is proved that MCOA algorithm has a good improvement effect.

4.2 Comparison experiment of single strategy

MCOA adopts two strategies, environment update mechanism and ghost opposition-based learning strategy, to improve COA. In order to prove the effectiveness of these two strategies for algorithm performance optimization, a single strategy comparison experiment is added in this section. In the experiment in this section, EUCOA algorithm which only adds environment update mechanism and GOBLCOA algorithm which only adds ghost opposition-based learning strategy are compared with the basic COA algorithm. The experiments are independently run 30 times in IEEE CEC2020 benchmark test function, and the statistical data obtained are shown in Table 6 . In order to make the table easy to view the statistical results, the poor data in the table will be bolded to make the statistical results more clear and intuitive. It can be seen from the table that among the best fitness values, average fitness values and standard deviation of fitness values of the 10 test functions, GOBLCOA and EUCOA account for less bolded data, while most data of the original algorithm COA are bolded in the table, which effectively proves that both the environment update mechanism and the ghost opposition-based learning strategy play a certain role in COA. The comprehensive performance of COA has been significantly improved.

4.3 Parameter sensitivity analysis of water flow velocity factor c

In order to better prove the influence of flow velocity coefficient on MCOA, we choose different flow velocity coefficient c values for comparison experiments. Table 7 shows the statistical results of 30 independent runs of different water flow velocity coefficients in CEC2020. The bold sections represent the best results. As can be seen from the table, the result obtained by c = 2 is significantly better than the other values. Only in individual test functions are the results slightly worse. In the F1 function, c = 5 has the best std. In the F5 function, std is best at c = 6. Among F10 functions, c = 5 has the best std. Among the other test functions, both the mean fitness value and std at water flow velocity factor c = 2 are optimal. Through the above analysis, it is proved that the water flow velocity factor c = 2 has a good optimization effect.

4.4 Experimental summary

In this section, we first test MCOA's optimization performance on the IEEE CEC2020 benchmark function. The improved MCOA is compared with the original algorithm COA and six other meta-heuristic algorithms in the same environment and the experimental analysis is carried out. Secondly, the rank sum test is used to verify whether there are significant differences between MCOA and the other nine comparison algorithms. Finally, three algorithms, EUCOA with environment update mechanism, GOBLCOA with ghost opposition-based learning strategy, COA and MCOA, are tested to improve performance. These three experimental results show that MCOA has a good ability to find optimal solutions and get rid of local optimal solutions.

5 Constrained engineering design problems

With the new development of the era of big data, the solution process becomes complicated and the calculation results become accurate, and more and more people pay close attention to the dynamic development of the feasibility and practicality of the algorithm, so as to ensure that the algorithm has good practical performance on constrained engineering design problems. In order to verify the optimization effect of MCOA in practical applications, four constrained engineering design problems are selected for application testing of MCOA to evaluate the performance of MCOA in solving practical application problems. Every constrained engineering design problems has a minimization objective function (Papaioannou and Koulocheris 2018 ) that is used to calculate the fitness value for a given problem. In addition, each problem contains a varying number of constraints that are taken into account during the calculation of the objective function. If the constraints are not met, the penalty function (Yeniay 2005 ) is used to adjust the fitness value. However, the processing of constraints is not the focus of our research, our focus is on the optimization of parameters in a convex region composed of constraints (Liu and Lu 2014 ). In order to ensure the fairness of the experiment, the parameters of all experiments in this section are set as follows: the maximum evaluation time MaxFEs is 10,000 and the overall scale N is 30. In each experiment, all the algorithms were analyzed 500 times and the optimal results were obtained.

5.1 Multi-disc clutch braking problem

In the field of vehicle engineering, there is a common constrained engineering design problems multi-disc clutch braking problem, and the purpose of our algorithm is to minimize the mass of the multi-disc clutch by optimizing eight constraints and five variables, so as to improve the performance of the multi-disc clutch. Among them, the five variables are: inner diameter r i , outer diameter r o , brake disc thickness t , driving force F , and surface friction coefficient Z . The specific structure of the multi-disc clutch is shown in Fig. 6 .

Schematic diagram of the multi-disc clutch braking problem

The mathematical formulation of the multi-disc clutch braking problem is as follows.

Objective function:

Subject to:

Variable range:

Other parameters:

After calculation and experiments, the experimental results of the multi-disc clutch braking problem are made into a table as shown in Table 8 . In Table 8 , MCOA concluded that the inner diameter r i = 70, the outer diameter r 0 = 90, the thickness of the brake disc t = 1, the driving force F = 600, and the surface friction coefficient Z = 2. At this time, the minimum weight obtained is 0.2352424, it is 11.16% higher than the original algorithm. Compared with MCOA, the other five algorithms in the calculation of this problem show that the optimization effect is far lower than that of MCOA.

5.2 Design problem of welding beam

The welded beam design problem is very common in the field of structural engineering and is constrained not only by four decision variables (welding width h , connecting beam length l , beam height t , and connecting beam thickness b ) but also by seven other different conditions. Therefore, it is challenging to solve this problem. The purpose of the optimization algorithm is to achieve the best structural performance of the welded beam and reduce its weight by optimizing the small problems such as the shape, size and layout of the weld under many constraints. The specific structure of the welded beam is shown in Fig. 7 .

Schematic diagram of the welded beam design problem

The mathematical formulation of the welded beam design problem is as follows.

Boundaries:

The experimental results of the welding beam design problem are shown in Table 9 . In the table, the welding width obtained by the MCOA algorithm h = 0.203034,the length of the connecting beam is l = 3.310032, the height of the beam is t = 9.084002, and the thickness of the connecting beam is b = 0.20578751. At this time, the minimum weight is 1.707524, it is 1.46% higher than the original algorithm. In the welding beam design problem, the weight determines the application effect of the algorithm in the practical problem. The weight of MCOA algorithm is smaller than that of other algorithms. Therefore, the practical application effect of MCOA is much greater than that of other algorithms.

5.3 Design problem of reducer

A reducer is a mechanical device used to reduce the speed of rotation and increase the torque. Among them, gears and bearings are an indispensable part of the reducer design, which have a great impact on the transmission efficiency, running stability and service life of the reducer. The weight of the reducer also determines the use of the reducer. Therefore, we will adjust the number of teeth, shape, radius and other parameters of the gear in the reducer to maximize the role of the reducer, reduce the friction between the parts, and extend the service life of the reducer. In this problem, a total of seven variables are constrained, which are the gear width x 1 , the gear modulus x 2 , the gear teeth x 3 , the length of the first axis between bearings x 4 , the length of the second axis between bearings x 5 , the diameter of the first axis x 6 and the diameter of the second axis x 7 . The specific structure of the reducer is shown in Fig. 8 .

Schematic diagram of the reducer design problem

The mathematical model of the reducer design problem is as follows.

The experimental results of the reducer design problem are shown in Table 10 . From Table 10 , it is known that the gear width calculated by the MCOA algorithm is x 1 = 3.47635, the gear modulus x 2 = 0.7, the gear teeth x 3 = 17, the length of the first axis between the bearings x 4 = 7.3, the length of the second axis between the bearings × 5 = 7.8, and the length of the first axis between the bearings x 5 = 7.8. The diameter of the first axis is x 6 = 3.348620, the diameter of the second axis is x 7 = 5.2768, and the minimum weight is 2988.27135, it is 0.08% higher than the original algorithm. In this experiment, it can be concluded that MCOA has the smallest data among the minimum weights obtained by MCOA and other comparison algorithms in this problem, which proves that MCOA has the best optimization effect in solving such problems.

5.4 Design problem of three-bar truss

Three-bar truss structure is widely used in bridge, building, and mechanical equipment and other fields. However, the size, shape and connection mode of the rod need to be further explored by human beings. Therefore, A 1 = x 1 and A 2 = x 2 determined by the pairwise property of the system need to be considered in solving this problem. In addition to this, there will be constraints on the total support load, material cost, and other conditions such as cross-sectional area. The structural diagram of the three-bar truss is shown in Fig. 9 .

Schematic diagram of the three-bar truss design problem

The mathematical formulation of the three-bar truss design problem is as follows.

The experimental results of the three-bar truss design problem are shown in Table 11 , from which it can be concluded that x 1 = 0.7887564and x 2 = 0.4079948of the MCOA algorithm on the three-bar truss design problem. At this time, the minimum weight value is 263.85438633, it is 0.24% higher than the original algorithm. Compared with the minimum weight value of other algorithms, the value of MCOA is the smallest. It is concluded that the MCOA algorithm has a good optimization effect on the three-bar truss design problem.

The experimental results of four constrained engineering design problems show that MCOA has good optimization performance in dealing with problems similar to constrained engineering design problems. In addition, we will also introduce the high-dimensional feature selection problem of the wrapper method, and further judge whether MCOA has good optimization performance and the ability to deal with diversified problems through the classification and processing effect of data.

6 High-dimensional feature selection problem

The objective of feature selection is to eliminate redundant and irrelevant features, thereby obtaining a more accurate model. However, in high-dimensional feature spaces, feature selection encounters challenges such as high computational costs and susceptibility to over-fitting. To tackle these issues, this paper propose novel high-dimensional feature selection methods based on metaheuristic algorithms. These methods aim to enhance the efficiency and effectiveness of feature selection in complex, high-dimensional datasets.

High-dimensional feature selection, as discussed in reference (Ghaemi and Feizi-Derakhshi 2016 ), focuses on processing high-dimensional data to extract relevant features while eliminating redundant and irrelevant ones. This process enhances the model's generalization ability and reduces computational costs. The problem of high-dimensional feature selection is often referred to as sparse modeling, encompassing two primary methods: filter and wrapper. Filter methods, also called classifier-independent methods, can be categorized into univariate and multivariate methods. Univariate methods consider individual features independently, leveraging the correlation and dependence within the data to quickly screen and identify the optimal feature subset. On the other hand, multivariate methods assess relationships between multiple features simultaneously, aiming to comprehensively select the most informative feature combinations. Wrapper methods offer more diverse solutions. This approach treats feature selection as an optimization problem, utilizing specific performance measures of classifiers and objective functions. Wrapper methods continuously explore and evaluate various feature combinations to find the best set of features that maximizes the model’s performance. Unlike filter methods, wrapper methods provide a more customized and problem-specific approach to feature selection.

Filter methods, being relatively single and one-sided, approach the problem of feature selection in a straightforward manner by considering individual features and their relationships within the dataset. However, they might lack the flexibility needed for complex and specific problem scenarios. However, wrapper methods offer tailored and problem-specific solutions. They exhibit strong adaptability, wide applicability, and high relevance to the specific problem at hand. Wrapper methods can be seamlessly integrated into any learning algorithm, allowing for a more customized and targeted approach to feature selection. By treating feature selection as an optimization problem and continuously evaluating different feature combinations, wrapper methods can maximize the effectiveness of the algorithm and optimize its performance to a greater extent compared to filter methods. In summary, wrapper methods provide a more sophisticated and problem-specific approach to feature selection, enabling the algorithm to achieve its maximum potential by selecting the most relevant and informative features for the given task.

6.1 Fitness function

In this subsection, the wrapper method in high-dimensional feature selection is elucidated, employing the classification error rate (CEE) (Wang et al. 2005 ) as an illustrative example. CEE is utilized as the fitness function or objective function to assess the optimization effectiveness of the feature selection algorithm for the problem at hand. Specifically, CEE quantifies the classification error rate when employing the k-nearest-neighbors (KNN) algorithm (Datasets | Feature Selection @ ASU. 2019 ), with the Euclidean distance (ED) (The UCI Machine Learning Repository xxxx) serving as the metric for measuring the distance between the current model being tested and its neighboring models. By using CEE as the fitness function, the wrapper method evaluates different feature subsets based on their performance in the context of the KNN algorithm. This approach enables the algorithm to identify the most relevant features that lead to the lowest classification error rate, thereby optimizing the model's performance. By focusing on the accuracy of classification in a specific algorithmic context, the wrapper method ensures that the selected features are highly tailored to the problem and the chosen learning algorithm. This targeted feature selection process enhances the overall performance and effectiveness of the algorithm in handling high-dimensional data.

where X denotes feat, Y denotes label, both X and Y are specific features in the given data model, and D is the total number of features recorded.

In the experimental setup, each dataset is partitioned into a training set and a test set, with an 80% and 20% ratio. The training set is initially utilized to select the most characteristic features and fine-tune the parameters of the KNN model. Subsequently, the test set is employed to evaluate and calculate the data model and algorithm performance. To address concerns related to fitting ability and overfitting, hierarchical cross-validation with K = 10 was employed in this experiment. In hierarchical cross-validation, the training portion is divided into ten equal-sized subsets. The KNN classifier is trained using 9 out of the 10 folds (K-1 folds) to identify the optimal KNN classifier, while the remaining fold is used for validation purposes. This process is repeated 10 times, ensuring that each subset serves both as a validation set and as part of the training data. This iterative approach is a crucial component of our evaluation methodology, providing a robust assessment of the algorithm's performance. By repeatedly employing replacement validation and folding training, we enhance the reliability and accuracy of our evaluation, enabling a comprehensive analysis of the algorithm's effectiveness across various datasets.

6.2 High-dimensional datasets

In this subsection, the optimization performance of MCOA is assessed using 12 high-dimensional datasets sourced from the Arizona State University (Too et al. 2021 ) and University of California Irvine (UCI) Machine Learning databases (Chandrashekar and Sahin 2014 ). By conducting experiments on these high-dimensional datasets, the results obtained are not only convincing but also pose significant challenges. These datasets authentically capture the intricacies of real-life spatial problems, making the experiments more meaningful and applicable to complex and varied spatial scenarios. For a detailed overview of the 12 high-dimensional datasets, please refer to Table 12 .

6.3 Experimental results and analysis

In order to assess the effectiveness and efficiency of MCOA in feature selection, we conducted comparative tests using MCOA as well as several other algorithms including COA, SSA, PSO, ABC, WSA (Baykasoğlu et al. 2020 ), FPA (Yang 2012 ), and ABO (Qi et al. 2017 ) on 12 datasets. In this section of the experiment, the fitness value of each algorithm was calculated, and the convergence curve, feature selection accuracy (FS Accuracy), and selected feature size for each algorithm were analyzed. Figures 10 , 11 and 12 display the feature selection (FS) convergence curve, FS Accuracy, and selected feature size for the eight algorithms across the 12 datasets. From these figures, it is evident that the optimization ability and prediction accuracy of the MCOA algorithm surpass those of the other seven comparison algorithms. Taking the dataset CLL-SUB-111 as an example in Figs. 11 and 12 , MCOA selected 20 features, while the other seven algorithms selected more than 2000 features. Moreover, the prediction accuracy achieved by MCOA was higher than that of the other seven algorithms. Across all 12 datasets, the comparison figures indicate that the MCOA algorithm consistently outperforms the others. Specifically, the MCOA algorithm tends to select smaller feature subsets, leading to higher prediction accuracy and stronger optimization capabilities. This pattern highlights the superior performance of MCOA in feature selection, demonstrating its effectiveness in optimizing feature subsets for improved prediction accuracy.

Convergence curve of FS

Comparison plot of verification accuracy of eight algorithms

Comparison plots of feature sizes of the eight algorithms

To address the randomness and instability inherent in experiments, a single experiment may not fully demonstrate the effectiveness of algorithm performance. Therefore, we conducted 30 independent experiments using 12 datasets and 8 algorithms. For each algorithm and dataset combination, we calculated the average fitness value, standard deviation of the fitness value, and Friedman rank. Subsequently, the Wilcoxon rank sum test was employed to determine significant differences between the performance of different algorithms across various datasets. Throughout the experiment, a fixed population size of 10 and a maximum of 100 iterations were used. The 12 datasets were utilized to evaluate the 8 algorithms 300 times (tenfold cross-validation × 30 runs). It is essential to note that all algorithms were assessed using the same fitness function derived from the dataset, ensuring a consistent evaluation criterion across the experiments. By conducting multiple independent experiments and statistical analyses, the study aimed to provide a comprehensive and robust assessment of algorithm performance. This approach helps in drawing reliable conclusions regarding the comparative effectiveness of the algorithms under consideration across different datasets, accounting for the inherent variability and randomness in the experimental process.

Table 13 presents the average fitness calculation results from 30 independent experiments for the eight algorithms, it is 55.23% higher than the original algorithm. According to the table, in the Ionosphere dataset, MCOA exhibits the best average fitness, albeit with slightly lower stability compared to ABC. Similarly, in the WarpAR10P dataset, MCOA achieves the best average fitness, with stability slightly lower than COA. After conducting Friedman ranking on the fitness calculation results of the 30 independent experiments, it is concluded that although MCOA shows slightly lower stability in some datasets, it ranks first overall. Among the other seven algorithms, PSO ranks second, ABO ranks third, COA ranks fourth, and ABC, SSA, FPA, and WSA rank fifth to ninth, respectively. These results demonstrate that MCOA exhibits robust optimization performance and high stability in solving high-dimensional feature selection problems. Moreover, MCOA outperforms COA, showcasing its superior improvement in solving these complex problems.

Table 14 presents the accuracy calculation results of the eight algorithms for 30 independent experiments, it is 10.85% higher than the original algorithm. According to the table, the average accuracy of MCOA is the highest across all datasets. Notably, in the Colon dataset, MCOA performs exceptionally well with a perfect average accuracy of 100%. However, in the Ionosphere dataset, MCOA exhibits slightly lower stability compared to ABC, and in the WarpAR10P dataset, it is slightly less stable than COA. Upon conducting Friedman ranking on the average accuracy calculation results of 30 independent experiments, it is evident that MCOA ranks first overall. Among the other seven algorithms, PSO ranks second, ABC ranks third, COA ranks fourth, and ABO, FPA, SSA, and WSA rank fifth to ninth, respectively. These results highlight that MCOA consistently achieves high accuracy and stability in solving high-dimensional feature selection problems. Its superior performance across various datasets underscores its effectiveness and reliability in real-world applications.

Table 15 demonstrates that the MCOA algorithm has shown significant results in the Wilcoxon rank sum test for high-dimensional feature selection fitness. The comparison values with other algorithms are less than 5%, indicating that the MCOA algorithm exhibits significant differences compared to the other seven algorithms. This result serves as evidence that MCOA outperforms the other algorithms, showcasing its superior optimization performance. Additionally, when comparing the results with the original algorithm, it becomes evident that the MCOA algorithm has a substantial and positive impact, demonstrating its effectiveness and improvement over existing methods. These findings underscore the algorithm's potential and its ability to provide substantial enhancements in the field of high-dimensional feature selection.

7 Conclusions and future work

The Crayfish Optimization Algorithm (COA) is grounded in swarm intelligence, drawing inspiration from crayfish behavior to find optimal solutions within a specific range. However, COA’s limitations stem from neglecting crucial survival traits of crayfish, such as crawling against water to discover better aquatic environments. This oversight weakens COA’s search ability, making it susceptible to local optima and hindering its capacity to find optimal solutions. To address these issues, this paper introduces a Modified Crayfish Optimization Algorithm (MCOA). MCOA incorporates an environmental updating mechanism, enabling crayfish to randomly select directions toward better aquatic environments for location updates, enhancing search ability. The addition of the ghost opposition-based learning strategy expands MCOA’s search range and promotes escape from local optima. Experimental validations using IEEE CEC2020 benchmark functions confirm MCOA’s outstanding optimization performance.

Moreover, MCOA’s practical applicability is demonstrated through applications to four constrained engineering problems and high-dimensional feature selection challenges. These experiments underscore MCOA’s efficacy in real-world scenarios, but MCOA can only solve the optimization problem of a single goal. In future studies, efforts will be made to further optimize MCOA and enhance its function. We will exploitation multi-objective version of the algorithm to increase the search ability and convergence of the algorithm through non-dominated sorting, multi-objective selection, crossover and mutation, etc., to solve more complex practical problems. It is extended to wireless sensor network coverage, machine learning, image segmentation and other practical applications.

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Abualigah L, Diabat A, Mirjalili S, Abd Elaziz M, Gandomi AH (2021) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609. https://doi.org/10.1016/j.cma.2020.113609

Article MathSciNet Google Scholar

Abualigah L, Elaziz MA, Khasawneh AM, Alshinwan M, Ibrahim RA, Al-Qaness MA, Gandomi AH (2022) Meta-heuristic optimization algorithms for solving real-world mechanical engineering design problems: a comprehensive survey, applications, comparative analysis, and results. Neural Comput Appl. https://doi.org/10.1007/s00521-021-06747-4

Article Google Scholar

Ahmed AM, Rashid TA, Saeed SAM (2020) Cat swarm optimization algorithm: a survey and performance evaluation. Comput Intell Neurosci. https://doi.org/10.1155/2020/4854895

Baykasoğlu A, Ozsoydan FB, Senol ME (2020) Weighted superposition attraction algorithm for binary optimization problems. Oper Res Int Journal 20:2555–2581. https://doi.org/10.1007/s12351-018-0427-9

Baykasoglu A, Ozsoydan FB (2015) Adaptive firefly algorithm with chaos for mechanical design optimization problems. Appl Soft Comput 36:152–164. https://doi.org/10.1016/j.asoc.2015.06.056

Belge E, Altan A, Hacıoğlu R (2022) Metaheuristic optimization-based path planning and tracking of quadcopter for payload hold-release mission. Electronics 11(8):1208. https://doi.org/10.3390/electronics11081208

Beyer HG, Schwefel HP (2002) Evolution strategies–a comprehensive introduction. Nat Comput 1:3–52. https://doi.org/10.1023/A:1015059928466

Chandrashekar G, Sahin F (2014) A survey on feature selection methods. Comput Electr Eng 40(1):16–28. https://doi.org/10.1016/j.compeleceng.2013.11.024

Cherrington, M., Thabtah, F., Lu, J., & Xu, Q. (2019, April). Feature selection: filter methods performance challenges. In 2019 International Conference on Computer and Information Sciences (ICCIS) (pp. 1–4). IEEE. https://doi.org/10.1109/ICCISci.2019.8716478

Datasets | Feature Selection @ ASU. Accessed from 3 Oct 2019 https://jundongl.github.io/scikit-feature/OLD/home_old.html .

Deng L, Liu S (2023) Snow ablation optimizer: a novel metaheuristic technique for numerical optimization and engineering design. Expert Syst Appl 225:120069. https://doi.org/10.1016/j.eswa.2023.120069

Dhiman G, Kaur A (2019) STOA: a bio-inspired based optimization algorithm for industrial engineering problems. Eng Appl Artif Intell 82:148–174. https://doi.org/10.1016/j.engappai.2019.03.021

Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39. https://doi.org/10.1109/MCI.2006.329691

Eskandar H, Sadollah A, Bahreininejad A, Hamdi M (2012) Water cycle algorithm–a novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput Struct 110:151–166. https://doi.org/10.1016/j.compstruc.2012.07.010

Espejo, P. G., Ventura, S., & Herrera, F. (2009) A survey on the application of genetic programming to classification. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews). 40(2): 121–144. https://doi.org/10.1109/TSMCC.2009.2033566

Ezugwu AE, Agushaka JO, Abualigah L, Mirjalili S, Gandomi AH (2022) Prairie dog optimization algorithm. Neural Comput Appl 34(22):20017–20065. https://doi.org/10.1007/s00521-022-07530-9

Faramarzi A, Heidarinejad M, Mirjalili S, Gandomi AH (2020) Marine predators algorithm: a nature-inspired metaheuristic. Expert Syst Appl 152:113377. https://doi.org/10.1016/j.eswa.2020.113377

Formato RA (2007) Central force optimization. Prog Electromagn Res 77(1):425–491. https://doi.org/10.2528/PIER07082403

Ghaemi M, Feizi-Derakhshi MR (2016) Feature selection using forest optimization algorithm. Pattern Recogn 60:121–129. https://doi.org/10.1016/j.patcog.2016.05.012

Guedria NB (2016) Improved accelerated PSO algorithm for mechanical engineering optimization problems. Appl Soft Comput 40:455–467. https://doi.org/10.1016/j.asoc.2015.10.048

He Q, Wang L (2007) An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng Appl Artif Intel 20:89–99. https://doi.org/10.1016/j.engappai.2006.03.003

Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: algorithm and applications. Futur Gener Comput Syst 97:849–872. https://doi.org/10.1016/j.future.2019.02.028

Jacob DIJ, Darney DPE (2021) Artificial bee colony optimization algorithm for enhancing routing in wireless networks. J Artif Intell Capsule Networks 3(1):62–71. https://doi.org/10.36548/jaicn.2021.1.006

Jia H, Peng X, Lang C (2021) Remora optimization algorithm. Expert Syst Appl 185:115665. https://doi.org/10.1016/j.eswa.2021.115665

Jia H, Wen Q, Wu D, Wang Z, Wang Y, Wen C, Abualigah L (2023a) Modified beluga whale optimization with multi-strategies for solving engineering problems. J Comput Design Eng 10(6):2065–2093. https://doi.org/10.1093/jcde/qwad089

Jia H, Rao H, Wen C, Mirjalili S (2023b) Crayfish optimization algorithm. Artif Intell Rev. https://doi.org/10.1007/s10462-023-10567-4

Jia H, Lu C, Wu D, Wen C, Rao H, Abualigah L (2023c) An improved reptile search algorithm with ghost opposition-based learning for global optimization problems. J Comput Design Eng. https://doi.org/10.1093/jcde/qwad048

Jović, A., Brkić, K., & Bogunović, N. (2015). A review of feature selection methods with applications. In 2015 38th international convention on information and communication technology, electronics and microelectronics (MIPRO) (pp. 1200–1205). IEEE. https://doi.org/10.1109/MIPRO.2015.7160458

Kamal M, Mortazavi A, Cakici Z (2023) Optimal design of RC bracket and footing systems of precast industrial buildings using fuzzy differential evolution incorporated virtual mutant. Arabian J Sci Eng. https://doi.org/10.3934/mbe.2022263

Kandemir EC, Mortazavi A (2022) Optimization of seismic base isolation system using a fuzzy reinforced swarm intelligence. Adv Eng Softw 174:103323. https://doi.org/10.1016/j.advengsoft.2022.103323

Kaveh A (2017) Applications of metaheuristic optimization algorithms in civil engineering. Springer International Publishing, Basel, Switzerland. https://doi.org/10.1007/978-3-319-48012-1

Book Google Scholar

Kaveh A, Khayatazad M (2012) A new meta-heuristic method: ray optimization. Comput Struct 112:283–294. https://doi.org/10.1016/j.compstruc.2012.09.003

Kaveh A, Mahdavi V (2014) Colliding bodies optimization: a novel meta-heuristic method. Comput Struct 139:18–27. https://doi.org/10.1016/j.compstruc.2014.04.005

Kira, K., & Rendell, L. A. (1992). The feature selection problem: Traditional methods and a new algorithm. In Proceedings of the tenth national conference on Artificial intelligence (pp. 129–134). https://doi.org/10.5555/1867135.1867155

Kiran MS (2015) TSA: tree-seed algorithm for continuous optimization. Expert Syst Appl 42(19):6686–6698. https://doi.org/10.1016/j.eswa.2015.04.055

Kumar S, Tejani GG, Mirjalili S (2019) Modified symbiotic organisms search for structural optimization. Eng with Comput 35(4):1269–1296. https://doi.org/10.1007/s00366-018-0662-y

Kuo HC, Lin CH (2013) Cultural evolution algorithm for global optimizations and its applications. J Appl Res Technol 11(4):510–522

Liu X, Lu P (2014) Solving nonconvex optimal control problems by convex optimization. J Guid Control Dyn 37(3):750–765. https://doi.org/10.2514/1.62110

Lu P, Ye L, Zhao Y, Dai B, Pei M, Tang Y (2021) Review of meta-heuristic algorithms for wind power prediction: methodologies, applications and challenges. Appl Energy 301:117446. https://doi.org/10.1016/j.apenergy.2021.117446

Ma Y, Zhang X, Song J, Chen L (2021) A modified teaching–learning-based optimization algorithm for solving optimization problem. Knowl-Based Syst 212:106599. https://doi.org/10.1016/j.knosys.2023.110554

Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579. https://doi.org/10.1016/j.amc.2006.11.033

Mahdavi S, Rahnamayan S, Deb K (2018) Opposition based learning: a literature review. Swarm Evol Comput 39:1–23. https://doi.org/10.1016/j.swevo.2017.09.010

Meloni C, Pacciarelli D, Pranzo M (2004) A rollout metaheuristic for job shop scheduling problems. Ann Oper Res 131:215–235. https://doi.org/10.1023/B:ANOR.0000039520.24932.4b

Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249. https://doi.org/10.1016/j.knosys.2015.07.006

Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133. https://doi.org/10.1016/j.knosys.2015.12.022

Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27:495–513. https://doi.org/10.1007/s00521-015-1870-7

Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191. https://doi.org/10.1016/j.advengsoft.2017.07.002

Mirjalili, S., & Mirjalili, S. (2019). Genetic algorithm. Evolutionary Algorithms and Neural Networks: Theory and Applications, 43–55. https://doi.org/10.1007/978-3-319-93025-1_4

Moghdani R, Salimifard K (2018) Volleyball premier league algorithm. Appl Soft Comput 64:161–185. https://doi.org/10.1016/j.asoc.2017.11.043

Moloodpoor M, Mortazavi A (2022) Simultaneous optimization of fuel type and exterior walls insulation attributes for residential buildings using a swarm intelligence. Int J Environ Sci Technol 19(4):2809–2822. https://doi.org/10.1007/s13762-021-03323-0

Moloodpoor M, Mortazavi A, Özbalta N (2021) Thermo-economic optimization of double-pipe heat exchanger using a compound swarm intelligence. Heat Transfer Res. https://doi.org/10.1615/HeatTransRes.2021037293

Mortazavi A (2019) Comparative assessment of five metaheuristic methods on distinct problems. Dicle Üniversitesi Mühendislik Fakültesi Mühendislik Dergisi 10(3):879–898. https://doi.org/10.24012/dumf.585790

Papaioannou G, Koulocheris D (2018) An approach for minimizing the number of objective functions in the optimization of vehicle suspension systems. J Sound Vib 435:149–169. https://doi.org/10.1016/j.jsv.2018.08.009

Piotrowski AP (2018) L-SHADE optimization algorithms with population-wide inertia. Inf Sci 468:117–141. https://doi.org/10.1016/j.ins.2018.08.030

Qi X, Zhu Y, Zhang H (2017) A new meta-heuristic butterfly-inspired algorithm. Journal of Computational Science 23:226–239. https://doi.org/10.1016/j.jocs.2017.06.003

Rao H, Jia H, Wu D, Wen C, Li S, Liu Q, Abualigah L (2022) A modified group teaching optimization algorithm for solving constrained engineering optimization problems. Mathematics 10(20):3765. https://doi.org/10.3390/math10203765

Rao, R. V., & Rao, R. V. (2016). Teaching-learning-based optimization algorithm (pp. 9–39). Springer International Publishing. https://doi.org/10.1016/j.cad.2010.12.015

Rashedi E, Nezamabadi-Pour HS (2009) GSA: a gravitational search algorithm. Inform Sci 179:2232–2248. https://doi.org/10.1016/j.ins.2009.03.004

Razmjooy, N., Ashourian, M., & Foroozandeh, Z. (Eds). (2021). Metaheuristics and optimization in computer and electrical engineering. https://doi.org/10.1007/978-3-030-56689-0

Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2013) Mine blast algorithm: a new population based algorithm for solving constrained engineering optimization problems. Appl Soft Comput 13:2592–2612. https://doi.org/10.1016/j.asoc.2012.11.026

Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47. https://doi.org/10.1016/j.advengsoft.2017.01.004

Sayed GI, Darwish A, Hassanien AE (2018) A new chaotic multi-verse optimization algorithm for solving engineering optimization problems. J Exp Theor Artif Intell 30(2):293–317. https://doi.org/10.1080/0952813X.2018.1430858

Shadravan S, Naji HR, Bardsiri VK (2019) The sailfish optimizer: a novel nature-inspired metaheuristic algorithm for solving constrained engineering optimization problems. Eng Appl Artif Intell 80:20–34. https://doi.org/10.1016/j.engappai.2019.01.001

Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713. https://doi.org/10.1109/TEVC.2008.919004

Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359. https://doi.org/10.1023/A:1008202821328

Su H, Zhao D, Heidari AA, Liu L, Zhang X, Mafarja M, Chen H (2023) RIME: a physics-based optimization. Neurocomputing 532:183–214. https://doi.org/10.1016/j.neucom.2023.02.010

Talatahari S, Azizi M, Gandomi AH (2021) Material generation algorithm: a novel metaheuristic algorithm for optimization of engineering problems. Processes 9(5):859. https://doi.org/10.3390/pr9050859

Markelle Kelly, Rachel Longjohn, Kolby Nottingham, The UCI Machine Learning Repository, https://archive.ics.uci.edu

Too J, Mafarja M, Mirjalili S (2021) Spatial bound whale optimization algorithm: an efficient high-dimensional feature selection approach. Neural Comput Appl 33:16229–16250. https://doi.org/10.1007/s00521-021-06224-y

Wang L, Zhang Y, Feng J (2005) On the Euclidean distance of images. IEEE Trans Pattern Anal Mach Intell 27(8):1334–1339. https://doi.org/10.1109/TPAMI.2005.165

Wang D, Tan D, Liu L (2018a) Particle swarm optimization algorithm: an overview. Soft Comput 22:387–408. https://doi.org/10.1007/s00500-016-2474-6

Wang H, Hu Z, Sun Y, Su Q, Xia X (2018b) Modified backtracking search optimization algorithm inspired by simulated annealing for constrained engineering optimization problems. Comput Intell Neurosci. https://doi.org/10.1155/2018/9167414

Wang S, Hussien AG, Jia H, Abualigah L, Zheng R (2022) Enhanced remora optimization algorithm for solving constrained engineering optimization problems. Mathematics 10(10):1696. https://doi.org/10.3390/math10101696

Wu D, Rao H, Wen C, Jia H, Liu Q, Abualigah L (2022) Modified sand cat swarm optimization algorithm for solving constrained engineering optimization problems. Mathematics 10(22):4350. https://doi.org/10.3390/math10224350

Yang, X. S. (2011). Metaheuristic optimization: algorithm analysis and open problems. In International symposium on experimental algorithms (pp. 21–32). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-20662-7_2

Yang, X. S. (2012, September). Flower pollination algorithm for global optimization. In International conference on unconventional computing and natural computation (pp. 240–249). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-32894-7_27

Yang XS, Deb S (2014) Cuckoo search: recent advances and applications. Neural Comput Appl 24:169–174. https://doi.org/10.1007/s00521-013-1367-1

Yeniay Ö (2005) Penalty function methods for constrained optimization with genetic algorithms. Math Comput Appl 10(1):45–56. https://doi.org/10.3390/mca10010045

Yıldız BS, Kumar S, Panagant N, Mehta P, Sait SM, Yildiz AR, Mirjalili S (2023) A novel hybrid arithmetic optimization algorithm for solving constrained optimization problems. Knowledge-Based Syst 271:110554. https://doi.org/10.1016/j.knosys.2023.110554

Yuan Y, Shen Q, Wang S, Ren J, Yang D, Yang Q, Mu X (2023) Coronavirus mask protection algorithm: a new bio-inspired optimization algorithm and its applications. J Bionic Eng. https://doi.org/10.1007/s42235-023-00359-5

Zhang Y, Jin Z (2020) Group teaching optimization algorithm: a novel metaheuristic method for solving global optimization problems. Expert Syst Appl 148:113246. https://doi.org/10.1016/j.eswa.2020.113246

Zhang YJ, Wang YF, Tao LW, Yan YX, Zhao J, Gao ZM (2022a) Self-adaptive classification learning hybrid JAYA and Rao-1 algorithm for large-scale numerical and engineering problems. Eng Appl Artif Intell 114:105069. https://doi.org/10.1016/j.engappai.2022.105069

Zhang Y, Wang Y, Li S, Yao F, Tao L, Yan Y, Gao Z (2022b) An enhanced adaptive comprehensive learning hybrid algorithm of Rao-1 and JAYA algorithm for parameter extraction of photovoltaic models. Math Biosci Eng 19(6):5610–5637. https://doi.org/10.3934/mbe.2022263

Zhang YJ, Yan YX, Zhao J, Gao ZM (2022c) AOAAO: The hybrid algorithm of arithmetic optimization algorithm with aquila optimizer. IEEE Access 10:10907–10933. https://doi.org/10.1109/ACCESS.2022.3144431

Zhang YJ, Yan YX, Zhao J, Gao ZM (2022d) CSCAHHO: chaotic hybridization algorithm of the Sine Cosine with Harris Hawk optimization algorithms for solving global optimization problems. PLoS ONE 17(5):e0263387. https://doi.org/10.1371/journal.pone.0263387

Zhang YJ, Wang YF, Yan YX, Zhao J, Gao ZM (2022e) LMRAOA: An improved arithmetic optimization algorithm with multi-leader and high-speed jum** based on opposition-based learning solving engineering and numerical problems. Alex Eng J 61(12):12367–12403. https://doi.org/10.1016/j.aej.2022.06.017

Zhao J, Zhang Y, Li S, Wang Y, Yan Y, Gao Z (2022) A chaotic self-adaptive JAYA algorithm for parameter extraction of photovoltaic models. Math Biosci Eng 19:5638–5670. https://doi.org/10.3934/mbe.2022264

Zhao S, Zhang T, Ma S, Wang M (2023) Sea-horse optimizer: a novel nature-inspired meta-heuristic for global optimization problems. Appl Intell 53(10):11833–11860. https://doi.org/10.1007/s10489-022-03994-3

Download references

Acknowledgements

The authors would like to thank the support of Fujian Key Lab of Agriculture IOT Application, IOT Application Engineering Research Center of Fujian Province Colleges and Universities, Guiding Science and Technology Projects in Sanming City (2023-G-5), Industry-University Cooperation Project of Fujian Province (2021H6039), Fujian Province Industrial Guidance (Key) Project (2022H0053), Sanming Major Science and Technology Project of Industry-University-Research Collaborative Innovation (2022-G-4), and also the anonymous reviewers and the editor for their careful reviews and constructive suggestions to help us improve the quality of this paper.

Author information

Authors and affiliations.

School of Information Engineering, Sanming University, Sanming, 365004, China

Heming Jia, Xuelian Zhou & Jinrui Zhang

Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman, 19328, Jordan

Laith Abualigah

MEU Research Unit, Middle East University, Amman, 11831, Jordan

Department of Mechanical Engineering, Bursa Uludağ University, 16059, Görükle, Bursa, Turkey

Ali Riza Yildiz

Department of Computer and Information Science, Linköping University, 58183, Linköping, Sweden

Abdelazim G. Hussien

You can also search for this author in PubMed Google Scholar

Contributions

Heming Jia: Methodology, Formal analysis, Investigation, Resources, Funding acquisition, Project administration; Xuelian Zhou: Investigation, Conceptualization, Software, Data Curation, Writing—Original Draft; Jinrui Zhang: Validation, Conceptualization; Laith Abualigah: Supervision, Writing—Review & Editing; Ali Riza Yildiz: Visualization, Writing—Review & Editing; Abdelazim G. Hussien: Writing—Review & Editing.

Corresponding author

Correspondence to Heming Jia .

Ethics declarations

Competing interest.

We declare that we have no conflict of interest.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and permissions

About this article

Jia, H., Zhou, X., Zhang, J. et al. Modified crayfish optimization algorithm for solving multiple engineering application problems. Artif Intell Rev 57 , 127 (2024). https://doi.org/10.1007/s10462-024-10738-x

Download citation

Accepted : 24 February 2024

Published : 24 April 2024

DOI : https://doi.org/10.1007/s10462-024-10738-x

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Crayfish Optimization Algorithm
Environmental updating mechanism
Ghost opposition-based learning strategy
Global optimization problem
Constrained engineering design problems
High dimensional feature selection
Find a journal
Publish with us
Track your research

Social science takes the stage in a live storytelling event at the Cantor Arts Center

Stanford researchers shared stories of psychotic breaks, economic disparities, and criminal justice reform at an event Tuesday hosted by Stanford Impact Labs in collaboration with The Story Collider.

Dr. Rania Awaad retells the event that encouraged her to pursue a career in psychiatry. (Image credit: Christine Baker)

Late one night years ago, Rania Awaad and her husband were at home when they heard a loud and sudden knock at their front door. When they opened it, Awaad saw a young woman she’d met before at their local Muslim community center.

“Before I could say anything, she runs right past me into the apartment,” Awaad, now a clinical professor of psychiatry and behavioral sciences at Stanford’s School of Medicine, recalled on Tuesday evening at a show titled Testing Ground Live! Social Science on Stage , held at the Cantor Arts Center.

Awaad shared how she and her husband found the woman ducked behind their couch, her eyes wide and terrified. “I need to speak to the imam, my religious leader!” the woman said. Awaad told her that the imam was not in their apartment.

Moments later the woman ran out of the apartment to the community center across the street, still searching for the imam. After deliberating on how to help the woman, some members at the center began to pray for her. Meanwhile, Awaad’s husband contacted a community elder.

“This is a psychotic episode,” the elder said. “She needs to go to the emergency room.”

The woman eventually got the help she needed, but the event left a lasting impact on Awaad, who was struck that no one at the center recognized the woman’s psychiatric emergency and her need for medical attention.

It made Awaad, who was a fourth-year medical student studying to become an obstetrician, realize the importance of mental health, and led her to switch her studies to psychiatry.

Tuesday’s event was hosted by Stanford Impact Labs (SIL) in collaboration with The Story Collider . It featured Stanford researchers like Awaad, a former SIL design fellow , sharing stories of pivotal moments in their lives that changed how they approached their work in mental health, digital literacy, and criminal justice reform, among other societal issues.

SIL is a cross-university initiative that launched in the 2019-20 academic year as part of the university’s Long-range Vision to train and support researchers to serve the public good by using data-driven, social science research to develop actionable ways to address pernicious and pervasive social problems.

Hannah Melville-Rea, a PhD student from Australia, shares what she’s learned about America’s home insurance system and the impact it has on various communities. (Image credit: Christine Baker)

Wild wild west

Another presenter was Hannah Melville-Rea, a PhD student from Australia. At Stanford, she’s studying environment and resources at the Stanford Doerr School of Sustainability, is a Knight-Hennessy Scholar, and was a 2023 SIL Summer PhD Fellow . Taking the stage, she shared that to better understand America’s home insurance system and how (or whether) it serves communities impacted by significant flood risk, she attended two local events. The first was a workshop in Menlo Park for residents to learn how to get the most out of their insurance. She recalled expensive cars parked outside the event. Inside were tables with Tiffany-blue tablecloths and appetizers.

“I look around the room at the other attendees. Everyone is white. Everyone is over the age of 65. I think everyone knows each other because they only asked me to introduce myself,” Melville-Rea recalled.

“I realize this [event] is only applicable if you’re a homeowner with insurance,” she said.

A couple of weeks later, Melville-Rea attended a crowded community meeting in East Palo Alto where residents shared their frustration with flooding and a lack of support from FEMA, the Federal Emergency Management Agency, tasked with responding to natural disasters.

“I cannot get over how different these two community meetings were [and] only three miles apart,” she said. “Up the hill, a bunch of homeowners with good insurance, who honestly, probably could weather a storm without it. Down the road, a bunch of renters who we now know had no insurance, who are really at the frontlines of these climate impacts, and now they’re being ghosted by FEMA.”

She said that as an Australian, she assumed the government would always step in to provide quality security for residents, regardless of their economic status. But she was surprised to learn the opposite was true in the United States.

“We live in the wild west. It is up to the individual. Everyone needs their own safety net,” she said. “And we urgently need to get everyone insurance.”

Alex Chohlas-Wood speaks at Testing Ground Live! Social Science on Stage at the Cantor Arts Center. (Image credit: Christine Baker)

High stakes decisions

Alex Chohlas-Wood is the executive director of the Computational Policy Lab (CPL), which has twice been funded by SIL and where he uses technology and data science to support criminal justice reform. He spoke about a pilot project he worked on for the San Francisco District Attorney’s office focused on “race-blind charging.” The idea, he explained, was to develop an artificial intelligence tool that could automatically redact race-related information from police reports that prosecutors review when deciding whether to charge or dismiss a crime.

His team got to work developing an algorithm for redacting potential indicators of race in police reports, including names and addresses. By the summer of 2019, they had a reliable system, but the project was cut short due to the COVID-19 pandemic. Officials in Yolo County, California expressed interest in the system, so Chohlas-Wood’s team developed one for their district attorney.

“He was so excited about this idea, that he got his own legislator to write a bill mandating that all prosecutors across the state of California use race blind charging by the beginning of 2025,” Chohlas-Wood said.

In 2022, the bill passed unanimously in both state houses and Governor Newsom signed it into law. Chohlas-Wood said he was excited to see his work lead to such meaningful policy changes.

“At the same time, I felt a real sense of responsibility to make sure this thing was done right, and to make sure that we could actually evaluate its impacts and charging decisions – really high stakes decisions – that prosecutors make, that can have profound impacts on people’s lives,” he said.

The next steps CPL is taking to evaluate and scale race-blind charging across California have been funded by a Stanford Impact Labs Stage 2 investment .

In total, six storytellers shared five stories on stage at Tuesday’s event. Recordings of each will soon be available on SIL’s website .

IMAGES

5 step problem solving method
three stages of problem solving according to traditional models
What Is Problem-Solving? Steps, Processes, Exercises to do it Right
Problem Solving Cycle
PPT
Stages of problem solving technique activity.

VIDEO

Problem Solving IQ Pedestal
MarbleRun Can you cross the Rattling rail bridge? Block castle mystery solving stage ASMR #stisfying
Solving Stage 5 in Dodoco Bomb-tastic Adventure
Team Energy Boost
Lean Coach: Problem Solving Coaching / Avoiding Jumping to Solutions
Born for Greatness: 5 Signs of Future Success!

COMMENTS

What is Problem Solving? Steps, Process & Techniques
Brainstorming and team problem-solving techniques are both useful tools in this stage of problem solving. Many alternative solutions to the problem should be generated before final evaluation. A common mistake in problem solving is that alternatives are evaluated as they are proposed, so the first acceptable solution is chosen, even if it's ...
The Problem-Solving Process
The main stages of problem-solving are outlined below, though not all are required for every problem that needs to be solved. 1. Define the Problem. Clarify the problem before trying to solve it. A common mistake with problem-solving is to react to what the problem appears to be, rather than what it actually is.
The Problem-Solving Process
Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue. The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything ...
What is Problem Solving? (Steps, Techniques, Examples)
The problem-solving process typically includes the following steps: Identify the issue: Recognize the problem that needs to be solved. Analyze the situation: Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present. Generate potential solutions: Brainstorm a list of possible ...
The 5 phases of problem solving
Many times that means stopping looking outside for the culprits and searching within, wondering why a situation is particularly bothering or hindering us. 2. Understand the problem. Many times the problem brings with it the seed of the solution. So one of the steps in solving a problem is making sure we understand it.
35 problem-solving techniques and methods for solving complex problems
Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward. Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.
How to master the seven-step problem-solving process
In this episode of the McKinsey Podcast, Simon London speaks with Charles Conn, CEO of venture-capital firm Oxford Sciences Innovation, and McKinsey senior partner Hugo Sarrazin about the complexities of different problem-solving strategies.. Podcast transcript. Simon London: Hello, and welcome to this episode of the McKinsey Podcast, with me, Simon London.
The Art of Effective Problem Solving: A Step-by-Step Guide
Step 1 - Define the Problem. The definition of the problem is the first step in effective problem solving. This may appear to be a simple task, but it is actually quite difficult. This is because problems are frequently complex and multi-layered, making it easy to confuse symptoms with the underlying cause.
The 5 Stages of Problem-Solving
From Why Groups Struggle to Solve Problems Together , Nov 07, 2019. Find new ideas and classic advice on strategy, innovation and leadership, for global leaders from the world's best business and ...
What Is Problem Solving?
Simplex, which involves an eight-stage process: problem finding, fact finding, defining the problem, idea finding, selecting and evaluating, planning, selling the idea, and acting. These steps build upon the basic, four-step process described above, and they create a cycle of problem finding and solving that will continually improve your ...
What Is Problem-Solving? Steps, Processes, Exercises to do it Right
This step of the problem-solving process is all about thinking outside of the box, challenging old assumptions, and thinking laterally. This stage is the one that tends to cause the most overwhelm in teams because it requires just the right balance of creativity and critical thinking, which tends to cause a lot of friction.
Problem-Solving Strategies and Obstacles
Problem-solving is a vital skill for coping with various challenges in life. This webpage explains the different strategies and obstacles that can affect how you solve problems, and offers tips on how to improve your problem-solving skills. Learn how to identify, analyze, and overcome problems with Verywell Mind.
Problem Solving
This page continues from Problem Solving an Introduction that introduces problem solving as a concept and outlines the stages used to successfully solve problems.. This page covers the first two stages in the problem solving process: Identifying the Problem and Structuring the Problem. Stage One: Identifying the Problem. Before being able to confront a problem its existence needs to be identified.
The McKinsey guide to problem solving
May 14, 2023 - Leaders today are confronted with more problems, of greater magnitude, than ever before. In these volatile times, it's natural to react based on what's worked best in the past. But when you're solving the toughest business challenges on an ongoing basis, it's crucial to start from a place of awareness.
8-Step Problem Solving Process
Step 8: Continuously Improve. Look for additional opportunities to implement solution. Ensure problem will not come back and communicate lessons learned. If needed, repeat the 8-Step Problem Solving Process to drive further improvements. 8-Step Problem Solving Process.
Mastering Problem-Solving: Unveiling the 5 Essential Stages ...
Explore the 5 critical stages of problem-solving in our comprehensive guide. Learn to identify, analyze, brainstorm, evaluate, and implement solutions effectively for personal and professional growth.
5 Steps (And 4 Techniques) for Effective Problem Solving
4. Implement the Solution. At this stage of problem solving, be prepared for feedback, and plan for this. When you roll out the solution, request feedback on the success of the change made. 5. Review, Iterate, and Improve. Making a change shouldn't be a one time action.
Problem management: 8 steps to better problem solving
Summary. Problem management is an 8 step framework most commonly used by IT teams. You can use problem management to solve for repeating major incidents. By organizing and structuring your problem solving, you can more effectively get to the root cause of high-impact problems—and devise a solution. Solving the root cause prevents recurrence ...
How To Put Problem-Solving Skills To Work in 6 Steps
Here are the basic steps involved in problem-solving: 1. Define the problem. The first step is to analyze the situation carefully to learn more about the problem. A single situation may solve multiple problems. Identify each problem and determine its cause. Try to anticipate the behavior and response of those affected by the problem.
What Is Problem Solving? Steps, Techniques, and Best ...
How to Solve Problems: 5 Steps. 1. Precisely Identify Problems. As obvious as it seems, identifying the problem is the first step in the problem-solving process. Pinpointing a problem at the beginning of the process will guide your research, collaboration, and solutions in the right direction. At this stage, your task is to identify the scope ...
Problem-Solving Strategies: Definition and 5 Techniques to Try
In insight problem-solving, the cognitive processes that help you solve a problem happen outside your conscious awareness. 4. Working backward. Working backward is a problem-solving approach often ...
How to Solve Problems
How to Solve Problems. To bring the best ideas forward, teams must build psychological safety. by. Laura Amico. October 29, 2021. HBR Staff/EschCollection/Getty Images. Teams today aren't just ...
What Is Creative Problem-Solving & Why Is It Important?
Creative problem-solving primarily operates in the ideate phase of design thinking but can be applied to others. This is because design thinking is an iterative process that moves between the stages as ideas are generated and pursued. This is normal and encouraged, as innovation requires exploring multiple ideas.
Modified crayfish optimization algorithm for solving multiple
Crayfish Optimization Algorithm (COA) is innovative and easy to implement, but the crayfish search efficiency decreases in the later stage of the algorithm, and the algorithm is easy to fall into local optimum. To solve these problems, this paper proposes an modified crayfish optimization algorithm (MCOA). Based on the survival habits of crayfish, MCOA proposes an environmental renewal ...
Social science takes the stage in a live storytelling event at the
Social Science on Stage, held at the Cantor Arts Center. Awaad shared how she and her husband found the woman ducked behind their couch, her eyes wide and terrified. "I need to speak to the imam ...

What is Problem Solving? (Steps, Techniques, Examples)

What Is Problem Solving?

Problem-Solving Steps

Defining the Problem

Generating Solutions

Evaluating and Selecting Solutions

Implementing and Monitoring the Solution

Problem-Solving Techniques

Brainstorming

Root Cause Analysis

SWOT Analysis

Mind Mapping

Examples of Problem Solving in Various Contexts

The 5 phases of problem solving

To Solve a Problem, Experience Does not Always Work in Our Favor

The Stages of Problem Solving We Can All Apply

Jennifer Delgado

Marriage wears out women more than men, according to science

How anxiety medications work?

The biggest mistake we all make when trying to persuade others

35 problem-solving techniques and methods for solving complex problems

Design your next session with SessionLab

Recommended Articles

How do you identify problems?

Complete problem-solving methods

Problem-solving warm-up activities

Tips for more effective problem solving

Clearly define the problem

Don’t jump to conclusions

Try different approaches

Don’t take it personally

Get the right people in the room

Document everything

Bring a facilitator

Develop your problem-solving skills

Design a great agenda

1. Six Thinking Hats

2. Lightning Decision Jam

3. Problem Definition Process

4. The 5 Whys

5. World Cafe

6. Discovery & Action Dialogue (DAD)

7. Design Sprint 2.0

8. Open space technology

Techniques to identify and analyze problems

10. The Creativity Dice

11. Fishbone Analysis

12. Problem Tree

13. SWOT Analysis

14. Agreement-Certainty Matrix

16. Speed Boat

17. The Journalistic Six

18. LEGO Challenge

19. What, So What, Now What?

20. Journalists

Problem-solving techniques for developing solutions

21. Mindspin

22. Improved Solutions

23. Four Step Sketch

24. 15% Solutions

25. How-Now-Wow Matrix

26. Impact and Effort Matrix

27. Dotmocracy

28. Check-in / Check-out

29. Doodling Together

30. Show and Tell

31. Constellations

32. Draw a Tree

How do I conclude a problem-solving process?

33. One Breath Feedback

34. Who What When Matrix

35. Response cards

Save time and effort discovering the right solutions

Over to you

Leave a Comment Cancel reply

Design your next workshop with SessionLab

Table of Contents

A3 Problem Solving Method:

Step 1 – Define the Problem

Step 2 – Gather Information and Brainstorm Ideas