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Overview of the Problem-Solving Mental Process

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

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

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 they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

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You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

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

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10 Problem-solving strategies to turn challenges on their head

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What is an example of problem-solving?

What are the 5 steps to problem-solving, 10 effective problem-solving strategies, what skills do efficient problem solvers have, how to improve your problem-solving skills.

Problems come in all shapes and sizes — from workplace conflict to budget cuts.

Creative problem-solving is one of the most in-demand skills in all roles and industries. It can boost an organization’s human capital and give it a competitive edge. 

Problem-solving strategies are ways of approaching problems that can help you look beyond the obvious answers and find the best solution to your problem . 

Let’s take a look at a five-step problem-solving process and how to combine it with proven problem-solving strategies. This will give you the tools and skills to solve even your most complex problems.

Good problem-solving is an essential part of the decision-making process . To see what a problem-solving process might look like in real life, let’s take a common problem for SaaS brands — decreasing customer churn rates.

To solve this problem, the company must first identify it. In this case, the problem is that the churn rate is too high. 

Next, they need to identify the root causes of the problem. This could be anything from their customer service experience to their email marketing campaigns. If there are several problems, they will need a separate problem-solving process for each one. 

Let’s say the problem is with email marketing — they’re not nurturing existing customers. Now that they’ve identified the problem, they can start using problem-solving strategies to look for solutions. 

This might look like coming up with special offers, discounts, or bonuses for existing customers. They need to find ways to remind them to use their products and services while providing added value. This will encourage customers to keep paying their monthly subscriptions.

They might also want to add incentives, such as access to a premium service at no extra cost after 12 months of membership. They could publish blog posts that help their customers solve common problems and share them as an email newsletter.

The company should set targets and a time frame in which to achieve them. This will allow leaders to measure progress and identify which actions yield the best results.

Perhaps you’ve got a problem you need to tackle. Or maybe you want to be prepared the next time one arises. Either way, it’s a good idea to get familiar with the five steps of problem-solving. 

Use this step-by-step problem-solving method with the strategies in the following section to find possible solutions to your problem.

1. Identify the problem

The first step is to know which problem you need to solve. Then, you need to find the root cause of the problem. 

The best course of action is to gather as much data as possible, speak to the people involved, and separate facts from opinions. 

Once this is done, formulate a statement that describes the problem. Use rational persuasion to make sure your team agrees .

2. Break the problem down 

Identifying the problem allows you to see which steps need to be taken to solve it. 

First, break the problem down into achievable blocks. Then, use strategic planning to set a time frame in which to solve the problem and establish a timeline for the completion of each stage.

3. Generate potential solutions

At this stage, the aim isn’t to evaluate possible solutions but to generate as many ideas as possible. 

Encourage your team to use creative thinking and be patient — the best solution may not be the first or most obvious one.

Use one or more of the different strategies in the following section to help come up with solutions — the more creative, the better.

4. Evaluate the possible solutions

Once you’ve generated potential solutions, narrow them down to a shortlist. Then, evaluate the options on your shortlist. 

There are usually many factors to consider. So when evaluating a solution, ask yourself the following questions:

• Will my team be on board with the proposition?
• Does the solution align with organizational goals ?
• Is the solution likely to achieve the desired outcomes?
• Is the solution realistic and possible with current resources and constraints?
• Will the solution solve the problem without causing additional unintended problems?

5. Implement and monitor the solutions

Once you’ve identified your solution and got buy-in from your team, it’s time to implement it. 

But the work doesn’t stop there. You need to monitor your solution to see whether it actually solves your problem. 

Request regular feedback from the team members involved and have a monitoring and evaluation plan in place to measure progress.

If the solution doesn’t achieve your desired results, start this step-by-step process again.

There are many different ways to approach problem-solving. Each is suitable for different types of problems. 

The most appropriate problem-solving techniques will depend on your specific problem. You may need to experiment with several strategies before you find a workable solution.

Here are 10 effective problem-solving strategies for you to try:

• Use a solution that worked before
• Brainstorming
• Work backward
• Use the Kipling method
• Draw the problem
• Use trial and error
• Sleep on it
• Get advice from your peers
• Use the Pareto principle
• Add successful solutions to your toolkit

Let’s break each of these down.

1. Use a solution that worked before

It might seem obvious, but if you’ve faced similar problems in the past, look back to what worked then. See if any of the solutions could apply to your current situation and, if so, replicate them.

2. Brainstorming

The more people you enlist to help solve the problem, the more potential solutions you can come up with.

Use different brainstorming techniques to workshop potential solutions with your team. They’ll likely bring something you haven’t thought of to the table.

3. Work backward

Working backward is a way to reverse engineer your problem. Imagine your problem has been solved, and make that the starting point.

Then, retrace your steps back to where you are now. This can help you see which course of action may be most effective.

4. Use the Kipling method

This is a method that poses six questions based on Rudyard Kipling’s poem, “ I Keep Six Honest Serving Men .” 

• What is the problem?
• Why is the problem important?
• When did the problem arise, and when does it need to be solved?
• How did the problem happen?
• Where is the problem occurring?
• Who does the problem affect?

Answering these questions can help you identify possible solutions.

5. Draw the problem

Sometimes it can be difficult to visualize all the components and moving parts of a problem and its solution. Drawing a diagram can help.

This technique is particularly helpful for solving process-related problems. For example, a product development team might want to decrease the time they take to fix bugs and create new iterations. Drawing the processes involved can help you see where improvements can be made.

6. Use trial-and-error

A trial-and-error approach can be useful when you have several possible solutions and want to test them to see which one works best.

7. Sleep on it

Finding the best solution to a problem is a process. Remember to take breaks and get enough rest . Sometimes, a walk around the block can bring inspiration, but you should sleep on it if possible.

A good night’s sleep helps us find creative solutions to problems. This is because when you sleep, your brain sorts through the day’s events and stores them as memories. This enables you to process your ideas at a subconscious level. 

If possible, give yourself a few days to develop and analyze possible solutions. You may find you have greater clarity after sleeping on it. Your mind will also be fresh, so you’ll be able to make better decisions.

8. Get advice from your peers

Getting input from a group of people can help you find solutions you may not have thought of on your own. 

For solo entrepreneurs or freelancers, this might look like hiring a coach or mentor or joining a mastermind group. 

For leaders , it might be consulting other members of the leadership team or working with a business coach .

It’s important to recognize you might not have all the skills, experience, or knowledge necessary to find a solution alone. 

9. Use the Pareto principle

The Pareto principle — also known as the 80/20 rule — can help you identify possible root causes and potential solutions for your problems.

Although it’s not a mathematical law, it’s a principle found throughout many aspects of business and life. For example, 20% of the sales reps in a company might close 80% of the sales. 

You may be able to narrow down the causes of your problem by applying the Pareto principle. This can also help you identify the most appropriate solutions.

10. Add successful solutions to your toolkit

Every situation is different, and the same solutions might not always work. But by keeping a record of successful problem-solving strategies, you can build up a solutions toolkit. 

These solutions may be applicable to future problems. Even if not, they may save you some of the time and work needed to come up with a new solution.

Improving problem-solving skills is essential for professional development — both yours and your team’s. Here are some of the key skills of effective problem solvers:

• Critical thinking and analytical skills
• Communication skills , including active listening
• Decision-making
• Planning and prioritization
• Emotional intelligence , including empathy and emotional regulation
• Time management
• Data analysis
• Research skills
• Project management

And they see problems as opportunities. Everyone is born with problem-solving skills. But accessing these abilities depends on how we view problems. Effective problem-solvers see problems as opportunities to learn and improve.

Ready to work on your problem-solving abilities? Get started with these seven tips.

1. Build your problem-solving skills

One of the best ways to improve your problem-solving skills is to learn from experts. Consider enrolling in organizational training , shadowing a mentor , or working with a coach .

2. Practice

Practice using your new problem-solving skills by applying them to smaller problems you might encounter in your daily life. 

Alternatively, imagine problematic scenarios that might arise at work and use problem-solving strategies to find hypothetical solutions.

3. Don’t try to find a solution right away

Often, the first solution you think of to solve a problem isn’t the most appropriate or effective.

Instead of thinking on the spot, give yourself time and use one or more of the problem-solving strategies above to activate your creative thinking. 

4. Ask for feedback

Receiving feedback is always important for learning and growth. Your perception of your problem-solving skills may be different from that of your colleagues. They can provide insights that help you improve. 

5. Learn new approaches and methodologies

There are entire books written about problem-solving methodologies if you want to take a deep dive into the subject. 

We recommend starting with “ Fixed — How to Perfect the Fine Art of Problem Solving ” by Amy E. Herman. 

6. Experiment

Tried-and-tested problem-solving techniques can be useful. However, they don’t teach you how to innovate and develop your own problem-solving approaches. 

Sometimes, an unconventional approach can lead to the development of a brilliant new idea or strategy. So don’t be afraid to suggest your most “out there” ideas.

7. Analyze the success of your competitors

Do you have competitors who have already solved the problem you’re facing? Look at what they did, and work backward to solve your own problem. 

For example, Netflix started in the 1990s as a DVD mail-rental company. Its main competitor at the time was Blockbuster. 

But when streaming became the norm in the early 2000s, both companies faced a crisis. Netflix innovated, unveiling its streaming service in 2007. 

If Blockbuster had followed Netflix’s example, it might have survived. Instead, it declared bankruptcy in 2010.

Use problem-solving strategies to uplevel your business

When facing a problem, it’s worth taking the time to find the right solution. 

Otherwise, we risk either running away from our problems or headlong into solutions. When we do this, we might miss out on other, better options.

Use the problem-solving strategies outlined above to find innovative solutions to your business’ most perplexing problems.

If you’re ready to take problem-solving to the next level, request a demo with BetterUp . Our expert coaches specialize in helping teams develop and implement strategies that work.

Elizabeth Perry

Content Marketing Manager, ACC

8 creative solutions to your most challenging problems

What are metacognitive skills examples in everyday life, 5 problem-solving questions to prepare you for your next interview, what is lateral thinking 7 techniques to encourage creative ideas, 31 examples of problem solving performance review phrases, learn what process mapping is and how to create one (+ examples), leadership activities that encourage employee engagement, can dreams help you solve problems 6 ways to try, how much do distractions cost 8 effects of lack of focus, similar articles, the pareto principle: how the 80/20 rule can help you do more with less, thinking outside the box: 8 ways to become a creative problem solver, experimentation brings innovation: create an experimental workplace, effective problem statements have these 5 components, contingency planning: 4 steps to prepare for the unexpected, stay connected with betterup, get our newsletter, event invites, plus product insights and research..

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35 problem-solving techniques and methods for solving complex problems

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All teams and organizations encounter challenges as they grow. There are problems that might occur for teams when it comes to miscommunication or resolving business-critical issues . You may face challenges around growth , design , user engagement, and even team culture and happiness. In short, problem-solving techniques should be part of every team’s skillset.

Problem-solving methods are primarily designed to help a group or team through a process of first identifying problems and challenges , ideating possible solutions , and then evaluating the most suitable .

Finding effective solutions to complex problems isn’t easy, but by using the right process and techniques, you can help your team be more efficient in the process.

So how do you develop strategies that are engaging, and empower your team to solve problems effectively?

In this blog post, we share a series of problem-solving tools you can use in your next workshop or team meeting. You’ll also find some tips for facilitating the process and how to enable others to solve complex problems.

Let’s get started! 

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!

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10 Best Problem-Solving Therapy Worksheets & Activities

Cognitive science tells us that we regularly face not only well-defined problems but, importantly, many that are ill defined (Eysenck & Keane, 2015).

Sometimes, we find ourselves unable to overcome our daily problems or the inevitable (though hopefully infrequent) life traumas we face.

Problem-Solving Therapy aims to reduce the incidence and impact of mental health disorders and improve wellbeing by helping clients face life’s difficulties (Dobson, 2011).

This article introduces Problem-Solving Therapy and offers techniques, activities, and worksheets that mental health professionals can use with clients.

Before you continue, we thought you might like to download our three Positive Psychology Exercises for free . These science-based exercises explore fundamental aspects of positive psychology, including strengths, values, and self-compassion, and will give you the tools to enhance the wellbeing of your clients, students, or employees.

This Article Contains:

What is problem-solving therapy, 14 steps for problem-solving therapy, 3 best interventions and techniques, 7 activities and worksheets for your session, fascinating books on the topic, resources from positivepsychology.com, a take-home message.

Problem-Solving Therapy assumes that mental disorders arise in response to ineffective or maladaptive coping. By adopting a more realistic and optimistic view of coping, individuals can understand the role of emotions and develop actions to reduce distress and maintain mental wellbeing (Nezu & Nezu, 2009).

“Problem-solving therapy (PST) is a psychosocial intervention, generally considered to be under a cognitive-behavioral umbrella” (Nezu, Nezu, & D’Zurilla, 2013, p. ix). It aims to encourage the client to cope better with day-to-day problems and traumatic events and reduce their impact on mental and physical wellbeing.

Clinical research, counseling, and health psychology have shown PST to be highly effective in clients of all ages, ranging from children to the elderly, across multiple clinical settings, including schizophrenia, stress, and anxiety disorders (Dobson, 2011).

Can it help with depression?

PST appears particularly helpful in treating clients with depression. A recent analysis of 30 studies found that PST was an effective treatment with a similar degree of success as other successful therapies targeting depression (Cuijpers, Wit, Kleiboer, Karyotaki, & Ebert, 2020).

Other studies confirm the value of PST and its effectiveness at treating depression in multiple age groups and its capacity to combine with other therapies, including drug treatments (Dobson, 2011).

The major concepts

Effective coping varies depending on the situation, and treatment typically focuses on improving the environment and reducing emotional distress (Dobson, 2011).

PST is based on two overlapping models:

Social problem-solving model

This model focuses on solving the problem “as it occurs in the natural social environment,” combined with a general coping strategy and a method of self-control (Dobson, 2011, p. 198).

The model includes three central concepts:

• Social problem-solving
• The problem
• The solution

The model is a “self-directed cognitive-behavioral process by which an individual, couple, or group attempts to identify or discover effective solutions for specific problems encountered in everyday living” (Dobson, 2011, p. 199).

Relational problem-solving model

The theory of PST is underpinned by a relational problem-solving model, whereby stress is viewed in terms of the relationships between three factors:

• Stressful life events
• Emotional distress and wellbeing
• Problem-solving coping

Therefore, when a significant adverse life event occurs, it may require “sweeping readjustments in a person’s life” (Dobson, 2011, p. 202).

• Enhance positive problem orientation
• Decrease negative orientation
• Foster ability to apply rational problem-solving skills
• Reduce the tendency to avoid problem-solving
• Minimize the tendency to be careless and impulsive

D’Zurilla’s and Nezu’s model includes (modified from Dobson, 2011):

• Initial structuring Establish a positive therapeutic relationship that encourages optimism and explains the PST approach.
• Assessment Formally and informally assess areas of stress in the client’s life and their problem-solving strengths and weaknesses.
• Obstacles to effective problem-solving Explore typically human challenges to problem-solving, such as multitasking and the negative impact of stress. Introduce tools that can help, such as making lists, visualization, and breaking complex problems down.
• Problem orientation – fostering self-efficacy Introduce the importance of a positive problem orientation, adopting tools, such as visualization, to promote self-efficacy.
• Problem orientation – recognizing problems Help clients recognize issues as they occur and use problem checklists to ‘normalize’ the experience.
• Problem orientation – seeing problems as challenges Encourage clients to break free of harmful and restricted ways of thinking while learning how to argue from another point of view.
• Problem orientation – use and control emotions Help clients understand the role of emotions in problem-solving, including using feelings to inform the process and managing disruptive emotions (such as cognitive reframing and relaxation exercises).
• Problem orientation – stop and think Teach clients how to reduce impulsive and avoidance tendencies (visualizing a stop sign or traffic light).
• Problem definition and formulation Encourage an understanding of the nature of problems and set realistic goals and objectives.
• Generation of alternatives Work with clients to help them recognize the wide range of potential solutions to each problem (for example, brainstorming).
• Decision-making Encourage better decision-making through an improved understanding of the consequences of decisions and the value and likelihood of different outcomes.
• Solution implementation and verification Foster the client’s ability to carry out a solution plan, monitor its outcome, evaluate its effectiveness, and use self-reinforcement to increase the chance of success.
• Guided practice Encourage the application of problem-solving skills across multiple domains and future stressful problems.
• Rapid problem-solving Teach clients how to apply problem-solving questions and guidelines quickly in any given situation.

Success in PST depends on the effectiveness of its implementation; using the right approach is crucial (Dobson, 2011).

Problem-solving therapy – Baycrest

The following interventions and techniques are helpful when implementing more effective problem-solving approaches in client’s lives.

First, it is essential to consider if PST is the best approach for the client, based on the problems they present.

Is PPT appropriate?

It is vital to consider whether PST is appropriate for the client’s situation. Therapists new to the approach may require additional guidance (Nezu et al., 2013).

Therapists should consider the following questions before beginning PST with a client (modified from Nezu et al., 2013):

• Has PST proven effective in the past for the problem? For example, research has shown success with depression, generalized anxiety, back pain, Alzheimer’s disease, cancer, and supporting caregivers (Nezu et al., 2013).
• Is PST acceptable to the client?
• Is the individual experiencing a significant mental or physical health problem?

All affirmative answers suggest that PST would be a helpful technique to apply in this instance.

Five problem-solving steps

The following five steps are valuable when working with clients to help them cope with and manage their environment (modified from Dobson, 2011).

Ask the client to consider the following points (forming the acronym ADAPT) when confronted by a problem:

• Attitude Aim to adopt a positive, optimistic attitude to the problem and problem-solving process.
• Define Obtain all required facts and details of potential obstacles to define the problem.
• Alternatives Identify various alternative solutions and actions to overcome the obstacle and achieve the problem-solving goal.
• Predict Predict each alternative’s positive and negative outcomes and choose the one most likely to achieve the goal and maximize the benefits.
• Try out Once selected, try out the solution and monitor its effectiveness while engaging in self-reinforcement.

If the client is not satisfied with their solution, they can return to step ‘A’ and find a more appropriate solution.

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Positive self-statements

When dealing with clients facing negative self-beliefs, it can be helpful for them to use positive self-statements.

Use the following (or add new) self-statements to replace harmful, negative thinking (modified from Dobson, 2011):

• I can solve this problem; I’ve tackled similar ones before.
• I can cope with this.
• I just need to take a breath and relax.
• Once I start, it will be easier.
• It’s okay to look out for myself.
• I can get help if needed.
• Other people feel the same way I do.
• I’ll take one piece of the problem at a time.
• I can keep my fears in check.
• I don’t need to please everyone.

5 Worksheets and workbooks

Problem-solving self-monitoring form.

Answering the questions in the Problem-Solving Self-Monitoring Form provides the therapist with necessary information regarding the client’s overall and specific problem-solving approaches and reactions (Dobson, 2011).

Ask the client to complete the following:

• Describe the problem you are facing.
• What is your goal?
• What have you tried so far to solve the problem?
• What was the outcome?

Reactions to Stress

It can be helpful for the client to recognize their own experiences of stress. Do they react angrily, withdraw, or give up (Dobson, 2011)?

The Reactions to Stress worksheet can be given to the client as homework to capture stressful events and their reactions. By recording how they felt, behaved, and thought, they can recognize repeating patterns.

What Are Your Unique Triggers?

Helping clients capture triggers for their stressful reactions can encourage emotional regulation.

When clients can identify triggers that may lead to a negative response, they can stop the experience or slow down their emotional reaction (Dobson, 2011).

The What Are Your Unique Triggers ? worksheet helps the client identify their triggers (e.g., conflict, relationships, physical environment, etc.).

Problem-Solving worksheet

Imagining an existing or potential problem and working through how to resolve it can be a powerful exercise for the client.

Use the Problem-Solving worksheet to state a problem and goal and consider the obstacles in the way. Then explore options for achieving the goal, along with their pros and cons, to assess the best action plan.

Getting the Facts

Clients can become better equipped to tackle problems and choose the right course of action by recognizing facts versus assumptions and gathering all the necessary information (Dobson, 2011).

Use the Getting the Facts worksheet to answer the following questions clearly and unambiguously:

• Who is involved?
• What did or did not happen, and how did it bother you?
• Where did it happen?
• When did it happen?
• Why did it happen?
• How did you respond?

2 Helpful Group Activities

While therapists can use the worksheets above in group situations, the following two interventions work particularly well with more than one person.

Generating Alternative Solutions and Better Decision-Making

A group setting can provide an ideal opportunity to share a problem and identify potential solutions arising from multiple perspectives.

Use the Generating Alternative Solutions and Better Decision-Making worksheet and ask the client to explain the situation or problem to the group and the obstacles in the way.

Once the approaches are captured and reviewed, the individual can share their decision-making process with the group if they want further feedback.

Visualization

Visualization can be performed with individuals or in a group setting to help clients solve problems in multiple ways, including (Dobson, 2011):

• Clarifying the problem by looking at it from multiple perspectives
• Rehearsing a solution in the mind to improve and get more practice
• Visualizing a ‘safe place’ for relaxation, slowing down, and stress management

Guided imagery is particularly valuable for encouraging the group to take a ‘mental vacation’ and let go of stress.

Ask the group to begin with slow, deep breathing that fills the entire diaphragm. Then ask them to visualize a favorite scene (real or imagined) that makes them feel relaxed, perhaps beside a gently flowing river, a summer meadow, or at the beach.

The more the senses are engaged, the more real the experience. Ask the group to think about what they can hear, see, touch, smell, and even taste.

Encourage them to experience the situation as fully as possible, immersing themselves and enjoying their place of safety.

Such feelings of relaxation may be able to help clients fall asleep, relieve stress, and become more ready to solve problems.

We have included three of our favorite books on the subject of Problem-Solving Therapy below.

1. Problem-Solving Therapy: A Treatment Manual – Arthur Nezu, Christine Maguth Nezu, and Thomas D’Zurilla

This is an incredibly valuable book for anyone wishing to understand the principles and practice behind PST.

Written by the co-developers of PST, the manual provides powerful toolkits to overcome cognitive overload, emotional dysregulation, and the barriers to practical problem-solving.

Find the book on Amazon .

2. Emotion-Centered Problem-Solving Therapy: Treatment Guidelines – Arthur Nezu and Christine Maguth Nezu

Another, more recent, book from the creators of PST, this text includes important advances in neuroscience underpinning the role of emotion in behavioral treatment.

Along with clinical examples, the book also includes crucial toolkits that form part of a stepped model for the application of PST.

3. Handbook of Cognitive-Behavioral Therapies – Keith Dobson and David Dozois

This is the fourth edition of a hugely popular guide to Cognitive-Behavioral Therapies and includes a valuable and insightful section on Problem-Solving Therapy.

This is an important book for students and more experienced therapists wishing to form a high-level and in-depth understanding of the tools and techniques available to Cognitive-Behavioral Therapists.

For even more tools to help strengthen your clients’ problem-solving skills, check out the following free worksheets from our blog.

• Case Formulation Worksheet This worksheet presents a four-step framework to help therapists and their clients come to a shared understanding of the client’s presenting problem.
• Understanding Your Default Problem-Solving Approach This worksheet poses a series of questions helping clients reflect on their typical cognitive, emotional, and behavioral responses to problems.
• Social Problem Solving: Step by Step This worksheet presents a streamlined template to help clients define a problem, generate possible courses of action, and evaluate the effectiveness of an implemented solution.

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While we are born problem-solvers, facing an incredibly diverse set of challenges daily, we sometimes need support.

Problem-Solving Therapy aims to reduce stress and associated mental health disorders and improve wellbeing by improving our ability to cope. PST is valuable in diverse clinical settings, ranging from depression to schizophrenia, with research suggesting it as a highly effective treatment for teaching coping strategies and reducing emotional distress.

Many PST techniques are available to help improve clients’ positive outlook on obstacles while reducing avoidance of problem situations and the tendency to be careless and impulsive.

The PST model typically assesses the client’s strengths, weaknesses, and coping strategies when facing problems before encouraging a healthy experience of and relationship with problem-solving.

Why not use this article to explore the theory behind PST and try out some of our powerful tools and interventions with your clients to help them with their decision-making, coping, and problem-solving?

We hope you enjoyed reading this article. Don’t forget to download our three Positive Psychology Exercises for free .

• Cuijpers, P., Wit, L., Kleiboer, A., Karyotaki, E., & Ebert, D. (2020). Problem-solving therapy for adult depression: An updated meta-analysis. European P sychiatry ,  48 (1), 27–37.
• Dobson, K. S. (2011). Handbook of cognitive-behavioral therapies (3rd ed.). Guilford Press.
• Dobson, K. S., & Dozois, D. J. A. (2021). Handbook of cognitive-behavioral therapies  (4th ed.). Guilford Press.
• Eysenck, M. W., & Keane, M. T. (2015). Cognitive psychology: A student’s handbook . Psychology Press.
• Nezu, A. M., & Nezu, C. M. (2009). Problem-solving therapy DVD . Retrieved September 13, 2021, from https://www.apa.org/pubs/videos/4310852
• Nezu, A. M., & Nezu, C. M. (2018). Emotion-centered problem-solving therapy: Treatment guidelines. Springer.
• Nezu, A. M., Nezu, C. M., & D’Zurilla, T. J. (2013). Problem-solving therapy: A treatment manual . Springer.

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Problem Solving Games, Activities & Exercises for Adults

Here is our list of the best problem solving games, activities and exercises for adults.

Problem solving games are activities that require players to use critical thinking skills to solve puzzles. Example activities include escape rooms, Sudoku, and murder mysteries. The purpose of these exercises is to sharpen reasoning and decision-making skills in group settings and to do team building with employees.

These activities are a subset of remote team games , found in problem solving books , and are similar to team puzzles , team building brain teasers and team riddles .

This article contains:

• team building problem solving activities for employees
• free problem solving games for adults
• virtual problem solving activities for students
• group problem solving activities
• problem solving team builders

Here we go!

List of problem solving games & activities

From word and number puzzles to role-playing games, here is a list of inexpensive and free problem solving team builders that help groups practice the art of critical thinking and compromise.

1. Espionage! (Team Favorite)

For an exciting game of social deduction, check out Espionage! This thrilling experience will put your team’s wits and instincts to the test.

Espionage! offers the following:

• a 90-minute session led by an experienced host
• undercover teams of agents and spies
• challenging puzzles, tasks, and maneuvers
• team conversations to help uncover secret identities

The best part is we will bring all the necessary game materials to your preferred location. If you are interested in boosting communication and critical-thinking skills within your team, then consider Espionage!

Learn more about Espionage!

2. Art Heist: The Vanishing of Van Gogh (Hosted)

You can turn your team into skilled detectives with Art Heist: The Vanishing of Van Gogh! In this captivating mystery, participants will locate the stolen artwork, The Bedroom .

Key features of this experience include:

• a 90-minute adventure led by a world-class host
• detailed puzzles, clues, and mysteries to unravel
• trails of evidence and hidden secrets
• group discussions to find the art

Additionally, you can include a cocktail kit to spice up your event. Through Art Heist, you will enhance your team’s ingenuity and problem-solving skills!

Learn more about Art Heist: The Vanishing of Van Gogh .

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• icebreaker games
• bingo cards

3. War of the Wizards (Popular)

With War of the Wizards, teams roleplay as minions of powerful wizards to vanquish forces of evil. Participants will play thrilling games and go on a quest to restore harmony to the realm!

War of the Wizards offers the following:

• a 90-minute journey guided by a distinguished host
• immersive storytelling that transports players into a magical realm
• engaging activities like world-building, role-playing games, and storytelling
• opportunities for forming alliances, facing challenges, and going on quests

Through the power of imagination and teamwork, your team can overcome tasks and participate in an epic fantasy battle. To improve communication and bonds, include War of the Wizards in your agenda!

Learn more about War of the Wizards .

Sudoku is one of the most popular free problem solving games for adults. The objective of this game is to fill each box of a 9×9 grid so that every row, column, and letter contains each number from one to nine. The puzzle makes a great team challenge. To play Sudoku on Zoom, screen share the game board. Then, turn on the annotation features. Using the add text functions, participants can fill in the numbers on the grid.

We made a starter puzzle you can use in your next meeting or virtual team bonding session:

Here are more online Sudoku puzzles .

5. Crossword puzzles

Crossword puzzles are word games that ask players to fill in words based on clues. Words interconnect, and players must think critically about the surrounding words to select the right phrase for the space.

You can use an online crossword puzzle maker to create a custom puzzle. Here are a few themes you may want to consider:

• teammates’ tastes and interests
• company knowledge and history
• industry terms and trends

Or, create a miscellaneous puzzle just for fun.

We made a sample puzzle you can use for your game:

To complete puzzles during online meetings, you can use the share screen function and add text through annotations.

Or, subscribers can play the New York Times’ daily crossword puzzle virtually . Dictionary.com also offers a free daily online crossword puzzle .

Check out more vocabulary games .

6. Online Escape Rooms

Escape rooms are timed games that get groups working together to solve puzzles. Traditionally, players enter a locked room and must complete all puzzles in an hour or two to unlock the door. However, groups can also play escape rooms online.

Digital escape rooms typically come in one of two forms: in a Zoom room and led by a host, or in a choose-your-own adventure format via Google Forms or websites. To play escape rooms virtually, enter a video meeting and follow the prompts, or screen share the Google Form and work out the puzzles together.

Check out our full list of online escape rooms .

7. Murder Mysteries

Murder Mysteries are story-based games that ask players to take on the roles of suspects or detectives while trying to identify a killer. These games often involve reading lines from a script, searching for clues, and occasionally solving puzzles to get hints.

These games make participants pay attention to conversations, analyze other characters’ behavior, and search for hidden meaning in the script. Players must use their powers of observation and logic to unravel the mystery.

Check out our list of Zoom murder mystery games .

8. Treasure Hunts

Treasure hunts are scavenger hunts with intention. While virtual scavenger hunts often ask players to collect random items, treasure hunts require participants to locate clues that lead to other prompts and hints. The game typically ends with players finding a treasure or solving a mystery, sometimes both.

The treasure hunt can have a specific theme such as secret agent missions or a hunt for pirate treasure, or you can run a more general hunt. Teammates can either compete simultaneously via Zoom call, or can play the hunt on an app individually and compete to beat each other’s scores.

Check out our list of treasure hunt apps .

9. Poem or story challenge

Most team building problem solving activities for employees revolve around science, math, and logic. Poem/story challenges rely on writing skills and are sure to appeal to the language lovers on your team.

Each player receives a limited word bank to use to create a story or poem. Then, players have a few minutes to craft their pieces. Afterward, everyone reads out or screen shares their creations.

Here are a few word challenge activities you can do remotely:

• Found poems or stories : Participants make poems or stories out of words they find by visiting websites, searching emails, glancing out the window, or taking a walk or drive around the neighborhood.
• Random word generators : Teammates use a random word generator to populate a word bank, and must use each word in the poem or story.
• Poetry magnets : Group members make poems using poetry magnets. You can send poetry magnet sets to employees and assemble the verses on a cookie pan during a Zoom call. Or, teammates can play with poetry magnets online .
• Page poems: Participants receive one page of a book or magazine, and must make a poem or story by blocking out other words so only the chosen text remains visible. This activity is part storytelling, part art, since story crafters can illustrate the pages as part of the design.
• Ransom note stories or poems : Players cut out letters from magazines and must form new words to make poems and stories. Or, players can receive a mix of random letters, form words, and run the text through a ransom note generator .

These activities are suitable for teams and individual players.

10. Moral challenge

Some problems are ethical rather than factual. Moral judgment plays just as important a role in the decision-making process as technical prowess. Players can flex their moral problem-solving skills by tackling ethical dilemmas or social puzzles.

Here are some social problem solving games online:

• Moral machine
• Scruples – the game of moral dilemmas
• Morality play

To play these games, either download the apps, or pull up the website and then screen share the prompts. These games are best played when discussed as a group, because the more belief systems and opinions, the harder an issue is to resolve. These exercises provide practice for real-life conflict resolution.

You can find similar challenges on our list of online personality tests .

11. Frostbite

Frostbite is a group game that hones team leaders’ communication skills while sharpening teammates’ listening and cooperation skills. The premise behind the game is that a group of explorers gets caught in a snowstorm and must build a shelter. Frostbite has paralyzed the leaders’ hands and snow-blinded the rest of the team. The leader must give the team instructions to build a tent that can resist arctic winds.

To play Frostbite, each teammate wears a blindfold. Then, the leader gives directions. Once the structures are complete, players turn on a fan to test whether tents can withstand the wind.

Frostbite is usually an in-person game, however you can also play virtually. In the remote version of the game, teammates construct tents out of cards and tape, while the leader surveys the scene on screen.

This exercise demonstrates the challenges of leading remotely, as teams need to operate with minimal oversight or supervisor observation. Therefore, instructions need to be clear and direct to be effective.

Check out more team building games .

12. Virtual Hackathons

Hackathons are events where participants have a set amount of time to design and pitch a new product or solution. This type of event originated in the programming world and is often used to create new apps, however you can apply the game to any industry or school subject.

Virtual hackathons are online versions of the event. Teams enter the competition, then work with each other via virtual meeting software or remote work communication platforms to design the solution. At the end of the competition, teams pitch ideas to a panel of judges and a winner is decided.

To run a virtual hackathon, first announce the theme of the event and collect sign-ups. So that no teams work ahead, hint at the general idea of the issue, and only explain the precise problem when the event begins. Then, give teams anywhere from a few hours to a few days to complete the project.

Discover more virtual hackathon ideas .

13. Improv games

Improv games are excellent problem solving activities. These exercises force participants to think and respond quickly to keep scenes moving in a logical and entertaining way.

Here are some good problem solving improv games:

Banned words : Performers cannot say certain words. Scene partners will conceive of situations that encourage the actors to use those words, and the actors must find alternatives, such as using synonyms or taking the scene in a new direction.

Scenes from a chat : Audience gives a suggestion for a scene, and players act the scene out. Though it’s a fictional and often ridiculous scenario, actors must react to the situation and solve the problem in order for the scene to end.

Miracle cure : Miracle cure is a quick-moving exercise that follows a simple format. One player declares, “I have a problem.” Another player responds, “I have a….[random object.]” The first player then replies, “great! I can use the [random object] to….” and describes how they will solve the problem.

Check out more problem-solving improv games .

14. Spaghetti Tower

The spaghetti tower is a classic team building game. Participants gather uncooked spaghetti and marshmallows, and must construct the tallest freestanding tower.

During the in-person version, players must construct one tall freestanding tower. However, for the virtual version of the game, players construct individual towers. You can send groups to breakout rooms for the build, then reconvene in the main room for judging. Teams are judged on three main factors: number of towers, height, and uniformity.

This version of the game not only tests the structural integrity of the tower, but also consistency and quality control. This exercise teaches teams to align and collaborate remotely, and produce a consistent product even when far apart.

15. What Would You Do?

What Would You Do? is a simple situational game that challenges participants to react to different circumstances. To play this game, read prompts one by one, and then ask participants to respond with gameplans. You can use the polling or raise hand feature to vote for the best option.

Here are some problem solving scenarios for adults or kids to use in the game:

• Zombies attack and you have to find a place to hide.
• You are at the zoo and the animals escape. Which one do you try to corral back into the pen first?
• After waiting in line for hours, someone cuts in front of you last minute. The person appears to be visually and hearing impaired, and doesn’t notice your protests. An official announces that due to diminishing supply, this individual will be the last in line to be served.
• You are eating a meal with important clients and/or your partner’s parents, and you want to impress. The individuals make you a dish that does not fit within your dietary restrictions, but you do not speak the same language and cannot explain why you do not want to eat.
• An imposter has infiltrated the organization, who looks, speaks, and behaves exactly like you. How do you convince your peers that you are the original?

For similar dilemmas, check out this list of Would You Rather? questions.

16. Desert Island Survival

Desert Island Survival is a game that challenges players to prioritize. The premise is that players have been stranded on an island, and must decide what order to perform survival steps.

Here are the possible actions:

• Set up shelter
• Explore the island
• Try to signal for help
• Make weapons for self-defense
• Build a raft to escape the island
• Start a fire
• Choose a group leader
• Search for other survivors

All group members must agree on the order of the steps. Players should explain the reasoning for the order of each step while ranking the actions.

Another version of the game involves players receiving a list of 15 to 20 items, and selecting five or so to bring to the island. You can also vary the location of the game, substituting remote islands for destinations like outer space or the distant past.

17. Choose Your Own Adventure

Choose Your Own Adventure stories enable readers to determine the outcome of the story by making decisions. Each action has a consequence that takes the tale in a different direction. Participants can try to guess how the story may unfold by talking through the different choices. When completing the activity in a group setting, the majority of the team must agree on an action before moving forward in the story.

There are a few ways to facilitate these activities online:

• Play an online role playing video game
• Watch an interactive movie like Black Mirror: Bandersnatch
• Read from a Choose Your Own Adventure book on Zoom
• Click through a Choose Your Own Adventure platform
• Create your own story using a Google Form

Whichever way you choose to do the exercise, you can use the screen share feature in your virtual meeting software so that listeners can more easily follow along.

18. MacGyver

MacGyver is a show where the hero escapes sticky situations by improvising tools out of unlikely materials. For example, in one episode the hero makes a telescope out of a newspaper, magnifying lens, and a watch crystal.

To play MacGyver, you can either list three to five objects participants can use, or challenge players to use items that are within arms reach.

Simply state a desired end result, such as “a way to open a locked door,” or “a getaway vehicle,” and then ask teams to explain what they will build and how they will build it. To make the activity more collaborative, you can give teams five or ten minutes in breakout rooms to strategize and design a prototype.

19. Dungeons & Dragons

Dungeons & Dragons is a roleplaying game where players pretend to be magical figures and creatures. One player serves as the dungeon master, who guides the game, while the other players pick characters and make decisions to move the story forward. Upon choosing a course of action, players roll a twenty-sided die to determine whether or not the plan succeeds. The game is story-based, the possibilities are nearly limitless, and truly creative problem solving options arise. Also, since gameplay is mostly verbal, Dungeons & Dragons is an easy activity to do over Zoom.

Here are the basic rules for Dungeons & Dragons .

20. Pandemic

Pandemic is a game that pits players against the forces of nature in a race to contain and control disease outbreaks. At the beginning of the game, each player receives a role such as containment specialist or operations expert. Participants must carry out the duties of their roles by choosing appropriate actions. Pandemic is a great game for groups because each team member has a clear part to play, and players must collaborate and work together instead of competing against each other.

To play the game online, you can use a Pandemic game app , or talk through the exercise while one attendee moves and displays pieces on the board.

Note: The subject of this game might hit too close to home for some players, considering recent history. You can find games with similar mechanics that deal with different subject matter, such as Forbidden Island.

Check out more team building board games .

21. Model UN

Model UN is one of the best virtual problem solving activities for students. This exercise casts participants in the role of international diplomats who must negotiate to solve realistic problems. Each player assumes the role of a country ambassador and must form alliances and propose solutions to solve crises.

Here are some sample Model UN scenarios:

• Human rights violation by powerful country
• Food shortage
• Disease epidemic
• Technology privacy violations
• Civil war branching into surrounding countries
• Natural disasters

Depending on the size of the group, participants either take on the part of an entire government of a country, or play a certain role within the government. To carry out the activity on Zoom, players can take turns giving speeches, message other countries privately via the chat, meet in breakout rooms to form alliances or have more intimate discussions, and use the polling feature to vote on propositions.

If politics does not resonate with your group, then you can alter the exercise by applying the same activity structure to a different theme, such as the Justice League, movie characters, business board members, or reality TV stars.

The main purpose of the exercise is to research, talk through problems, and compromise. As long as these elements are present, then the specifics of the setup do not matter.

There are many types of problem solving activities for adults. You can do online problem solving games, which require a different skill set than in-person problem solving. For instance, communication must be much clearer and more abundant when group members are far apart and unable to demonstrate or pick up physical cues.

Though many problem solving games include props and in-person elements, there are many games you can play together online. These exercises work well as educational tools as well as team bonding accelerators. Upon completion, participants are likely to feel a sense of accomplishment and increased confidence. These games are also great practice for real life conflict resolution, creative thinking and team building.

Next check out this list of connection games , this collection of crime-solving games , and this post with conflict resolution games .

We also have a list of the best decision making books and a list of team building problems for work .

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FAQ: Problem solving activities

Here are common answers to questions about group problem solving activities.

What are problem solving games?

Problem solving games are challenges that ask players to think critically and use logic to overcome issues or answer riddles. Examples include sudoku, murder mysteries, and spaghetti towers. These games are also known as “problem solving exercises”, “problem and solution games” and “group problem solving activities.”

What are the best problem solving games for groups?

The best problem solving games for groups include online escape rooms, moral challenges, and improv games.

What are some good problem solving team building activities for students?

Some good problem solving activities for students include crossword puzzles, choose your own adventure stories, and model UN.

How do you play problem solving games online?

The best way to play problem solving games online is to join a video call meeting to talk through the issue. Using the screen sharing and digital whiteboard features helps participants visualize the problem more clearly. Breakout rooms give teams the chance to discuss the issue more intimately.

Author: Angela Robinson

Marketing Coordinator at teambuilding.com. Team building content expert. Angela has a Master of Fine Arts in Creative Writing and worked as a community manager with Yelp to plan events for businesses.

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Improve Your Problem-Solving Skills – Steps, Processes & Technique

When you are faced with a problem, how do you go about solving it? Do you let it overwhelm you, or do you flex your problem-solving muscles and figure out the best possible solution?

People who allow themselves to be overwhelmed or ignore complex problems often become frantic and confused. They usually take a haphazard approach to thinking, and then they are dismayed when they find themselves floundering and making no progress.

Luckily, there is a much better way.

I’d like to introduce you to a problem-solving process that can help you face and tackle any type of challenge. With these 10 problem-solving strategies, you will strengthen your ability to always find a solution while enabling yourself to see real progress.

Once you begin to execute these problem-solving  techniques, you will feel confident to face a problem right away.

What Are Problem-Solving Skills?

Problem-solving skills involve identifying a problem, coming up with possible solutions, choosing an appropriate solution, and then implementing it.

Often, there is more than one correct solution to a problem. But frequently, you are looking for the best solution that applies to your particular circumstance.

For instance, possible solutions to losing weight include eating less, adding healthier foods to your diet, walking 30 minutes a day, swimming three times a week, training for a 5K race, drinking more water, and many other effective solutions.

Your job is to find the solution that will work best for you and give you the most success.

Good problem-solving skills are essential in all areas of your life because we encounter problems to solve in one form or another nearly every day, from small things like getting stuck in traffic to major events like being diagnosed with a chronic illness.

A problem can be defined in one of two ways:

“Any question or matter involving doubt, uncertainty, or difficulty; a question proposed for solution or discussion.”

The Encyclopedia of the Sciences of Learning explains that a problem:

“…is generally considered to be a task, a situation, or person which is difficult to deal with or control due to complexity and transparency. In everyday language, a problem is a question proposed for a solution, a matter stated for examination or proof.”

In short, a problem is something that’s hard to deal with and needs to be solved.

Examples of common problems in the workplace might include:

• Lack of motivation or boredom
• Discrimination
• Conflict with a boss or coworkers
• Performance issues
• Burnout or stress
• Bad working conditions

Or maybe you’re dealing with problems in your personal life. For example:

• A strained marriage or divorce
• Financial worries
• Health issues
• Grief over the death of loved ones
• Issues your children are experiencing
• A decision to move, change jobs, or get an education

No matter what you’re facing, it’s important to actively cultivate your creative thinking and learn problem-solving techniques. 

When you’re able to solve problems effectively, you will enjoy greater satisfaction in life. Your relational skills will improve, and your problem-solving abilities will make you highly valuable in the workplace.

The Importance of Solving Problems

We solve problems daily in all aspects of life. People who are good problem solvers are more likely to be successful in getting around obstacles and achieving their desired end result.

What’s more, solving complex problems doesn’t only help change your external circumstances. You’ll also feel happier and more confident in yourself, knowing you can solve future problems.  

Problem-solving allows you to:

• Fix things that are broken
• Address risk
• Improve performance
• Seize opportunity
• Lower stress and anxiety
• Prevent more serious consequences

Having a problem-solving strategy will make you more attractive to hiring managers. In many cases, you might be asked in a job interview about your problem-solving skills. 

It’s smart to think of an example ahead of time–a problem that came up at your last job and how you solved it–so you’ll be prepared. You can also mention the soft skills listed above: 

“My communication skills, flexibility, and ability to think outside the box help me deal with problems in a timely manner.”

The more you practice effective problem-solving techniques, the better you will get at solving problems and the more reliable and trustworthy you will become in your field as well as in your personal life.

Understanding the Problem-Solving Process

When you’re setting out to solve a problem, what should you do first?

While there is no one-size-fits-all approach to problem-solving, there is a general framework that you can use to help solve problems.

The problem-solving process is often broken down into seven steps:

• Identify the issue and its root cause
• Understand every angle of the problem
• List possible solutions
• Evaluate the options
• Choose an option
• Evaluate the results

I’ll explain this process and each of these steps, plus a few bonus steps. I’ll also share some further problem-solving strategies so you are well-equipped with solution-finding techniques that you can apply to various situations.

The important thing to understand now, though, is that you can use a structured process to improve problem-solving skills. You don’t have to shoot in the dark–simply follow the steps listed in this process.

Problem-Solving Skills

What kind of skills should you cultivate to become a better problem-solver?

You can also work on things like your communication skills, analytical skills, and other key skills in life that will make you a better problem solver. These soft skills go hand in hand with being able to come up with solutions quickly.

Focus on the following:

Brainstorming

This is a method of free-thinking used to generate ideas that involve thinking of a long list of possible solutions without making an initial judgment about how effective they might be. You can brainstorm with a group of people or on your own.

Data gathering

Collecting information related to the issue is a vital problem-solving tool as the more information you have about the root cause and contributing factors to a problem, the easier it will be to find solutions that work. Fact-finding can come from interviewing people involved, researching related problems, reading documents, analyzing data, and more.

Creative thinking

When you’re a creative thinker, you’re able to look at a complex problem or an everyday problem and think of unique, original solutions. Your ability to come up with creative solutions will make you more marketable as well as more successful in meeting complex problems head-on.

Communication

Having communication skills is essential to work with others to solve problems. You need to not only be able to express your thoughts clearly and concisely without causing offense or contention, but you also need to be able to listen to others as they express their views until everyone is on the same page.

Like communication skills, teamwork involves being able to work collectively with others to apply problem-solving strategies. Often, two heads are better than one, and the wisdom you gain from collective intelligence will make identifying underlying causes and finding solutions much easier.

Analyzing involves being able to break up a complex problem into smaller parts so you can examine and evaluate it to understand the problem better. 

You may find the root cause of the problem as well as contributing factors. Ill-defined problems are difficult to solve, so it is important to be able to apply problem analysis to any issue you are dealing with.

Time management

Time-management skills help you avoid procrastination and spending time on unnecessary tasks. 

You can develop good time management skills by setting goals, making daily to-do lists, prioritizing your tasks, and reducing or eliminating distractions.

Troubleshooting

Troubleshooting is applying a step-by-step process to find the cause of a problem and then working your way to different solutions. 

Common, well-defined problems, such as those that occur in the computer science field or automotive industry, may have a preset list of troubleshooting steps to follow. 

Other problems will require you to develop a troubleshooting process as you go. Troubleshooting skills make you a valuable asset to any team.

When you take initiative, you do not wait for others to tell you what to do. You see a need and seek to fill that need. Often, by taking initiative, you can address an issue before a problem occurs. 

One example in the workplace would be to sign up for training that will keep you up to date on the newest developments in your industry.

Flexibility

Being flexible is an important tool you will use to solve problems. It’s an essential skill in all aspects of your life. When you are too rigid, you often are not able to see creative solutions and different strategies that can help make your life easier. 

There is often more than one good way to solve the same problem, and being open-minded will help you move from your existing beliefs to other effective ways of solving problems.

I know this is a long list, but you don’t have to do everything at once.

Even more, chances are you’ve already picked up some of these skills in your daily life without even realizing it. Keeping these skills in mind as you practice solving problems will help you become better at not only solution-finding but at everything you do.

10 Steps to Solving a Problem

In this 10-step problem-solving process, I’ll walk you through how to identify and implement the right solution to the problem at hand. In learning these steps, you will develop your critical thinking and elevate your problem-solving skills.

1. Take a Positive Approach

When a problem arises, it’s easy to enter panic mode or envision worst-case scenarios. Before you let your mind go there, take a step back and address every problem as simply another situation.

It is a challenge that you can handle, with the right approach. Part of that approach is thinking positively and creatively about the situation.

When figuring out ways to use creative thinking for problem-solving, I like to explore  how geniuses solve challenges . They think outside the box, keep an open mind, and take a systematic approach.

It all starts with thinking positively about the problem.

One problem-solving strategy I like to use is to think of it as a situation, not a problem.

Problems are a fact of life; you can’t control when or how they occur, but you can control your attitude. The more positive your language and mental process are, the more confident and optimistic you will be when approaching any complication.

How can you develop a more positive outlook on life? This mindset shift can take some time. 

You can’t snap your fingers and instantly become a more positive person overnight. However, there are actionable steps you can take to be more positive.

Start by focusing on the good things in your life. Yes, you have problems, but you have good things too. If you’re struggling to come up with anything that makes you smile, consider keeping a gratitude journal where you make an entry every day.

I also recommend positive affirmations and self-talk. Repeat phrases to yourself such as “There are good things in my life,” “I can come up with creative solutions,” or “I have good problem-solving skills.”

And of course, it’s important to surround yourself with people who are equally as positive and upbeat as you’re trying to be. The same applies to all aspects of your life. Read positive books, articles, and social media posts. Listen to uplifting music, and watch videos and movies that leave you feeling positive and optimistic.

Remember that every problem comes with a solution already custom-made for it. You just need to find it, and you can by maintaining a calm, positive attitude and steadily progressing through the different stages of the problem-solving process.

2. Define The Problem

Problem identification is a vital step in problem-solving processes so that you know exactly what you are dealing with. What might seem to be the root cause of your situation may be something entirely different.

Also, defining the problem will help you gather data, analyze the issues surrounding it, and find a potential solution.

What exactly is the challenge you are facing? What about this particular situation is causing you stress and anxiety? You must clearly define the problem to resolve it.

Not only should you clarify what the problem is, but you should also see what caused the problem. If you can’t conclude the cause of the problem, you may need to meet with other parties involved to determine the root before moving forward.

Sometimes a clear root cause cannot be determined, or there may be several factors that are causing the problem. In these cases, you can still move forward in finding solutions by defining what is currently hard to deal with and what needs to be changed or solved.

If you are working with a group, it’s important to write and rewrite the problem until everyone agrees that the problem is clearly and correctly defined. Each person will bring a unique perspective that will help clarify what the situation is.

Identify important details that define that problem, and weed out information that is extraneous or useless so that it doesn’t distract you from your ability to solve it or waste your time.

It can help to ask the following questions:

• Who is involved in the problem?
• What exactly is happening that is preventing forward progress?
• When did the problem occur and how often?
• Why is the problem happening?
• How is it affecting workflow or people?

Write out the problem so that it is easy for you and everyone else to see exactly what it is. It may help to draw a picture, diagram, or graph to fully visualize the problem.

When the issue is clearly defined, the solution may be obvious. But you may never find the solution at all if the problem isn’t defined.

3. Use Creative Thinking

As I mentioned in the first step, geniuses solve issues with out-of-the-box thinking. So you need to see the problem from every angle before you begin moving down solution paths.

You should think: Are there other problems that are affecting this obstacle? If so, you need to address it first.

It can be easy to have tunnel vision when you’re problem-solving, but there are usually multiple things at play with any dilemma. Zoom out from the situation at hand and see all contributing factors to the issue and listen to everyone’s point of view.

Meeting with others who may be involved in the process can offer you more brainpower to shed light on the problem. That’s why teamwork is so important. You can work together to look at what the issue is affecting, what is affecting it, and how to solve it.

It might feel as if you can work faster on your own. But when you collaborate with others, you’ll be able to come up with higher-quality solutions.

In fact, statistics show that 86% of employees and executives say lack of collaboration or ineffective communication causes workplace failures.

Don’t be afraid to sit down with people involved in the problem to work things out. People outside the problem can also offer a valuable third-party opinion. Their advice and ideas may actually be more helpful because they don’t have a personal stake in the issue.

When discussing the problem with others, replace “No, but” with “Yes, and.” For example, if someone says, “I think part of the problem stems from a lack of communication within the team.” Respond with, “Yes, and it can also come from people arriving late to meetings.”

This approach validates what the other person is saying so that all input is accepted as valuable and ideas are not negated. It also gives you an equal opportunity to add your ideas and input.

Think creatively by looking outside of your industry or situation for solutions. While it is helpful to analyze how others within your field or circumstances have solved a similar problem, you might find helpful insight in looking at how companies or individuals in other walks of life that have seemingly non-matching characteristics have approached related problems.

Ask “what if” questions. This can often help you think outside the box when solving problems creatively. As you look at potential solutions, ask,

“Why not?”

“What assumptions can we get rid of?”

“What can we add beyond the expected solutions?” and similar questions to take a broader view of the problem and possible solutions.

State the opposite of the problem to get a different perspective on it. For example, instead of asking, “How can we encourage our existing customers to buy more products?” ask, “How can we discourage our existing customers from buying more products.” This process can lead to surprisingly effective solutions.

4. Brainstorm Possible Solutions

Part of addressing the situation from different directions is to come up with not just one but several solutions. There are likely to be multiple solutions to any single problem.

The first conclusion that comes to mind may not be the best one, but the more you focus, the more solutions you will find. That’s why brainstorming all possible resolutions is an essential step to  problem-solving .

If you’re brainstorming together with a group of others, make sure to define a clear goal for the brainstorming session before you begin. Allow people time before the meeting to reflect on the problem. This will allow them to come prepared with ideas.

Throughout the session, record any suggestions that come up. You can write them on a physical whiteboard so that everyone can see them, or simply jot them down in a digital folder. Share these notes with attendees post-meeting and assign any follow-up tasks.

Reserve judgment until after your brainstorming session is complete. Some ideas may seem ridiculous or impractical, but say them and record them anyway. The goal is to move beyond existing ideas and look at the problem and possible solutions from every angle. Sometimes, an idea that seems far-flung can begin a conversation and flow of ideas that lead to the best solution.

Defining your end goal will help inspire unique ways you can get there. It can also help to pose the problem as a question and come up with conclusions to that question. Use the examples offered earlier of who, what, when, where, and how questions to get you started.

5. Find The Best Solution 

Now, not all possible solutions you outlined will be a good fit. You should be able to narrow down each method and see which is the most effective for your issue.

After brainstorming all potential solutions, ask yourself, “What solution will likely produce the best outcome?”

Do this by comparing each of the results with the one you believe to be the most ideal. Which one is the best under the current circumstances? What will successfully solve the problem? Which one will lead to a better outcome in the future? What will prevent further problems? Is there more than one solution that we should apply for the best results?

It might take some time to work through each of your potential solutions. Some will quickly weed themselves out. In other cases, though, don’t be afraid to spend some time thinking about how a given solution would work.

Identify the pros and cons or benefits and costs of each solution to help you determine which one or more is best.

After looking in-depth at the various approaches, decide on the best solution for the situation.

6. Expect the Best and Prepare for the Worst

Before you jump at the chance to solve your problem with the best-fit solution, consider the repercussions of the solution. 

Now is the time to jump to worst-case scenarios. What will happen if the solution fails? Knowing the answer to this will allow you to prepare if it doesn’t resolve your dilemma.

Even if at first you don’t succeed, you will learn something in the end. Don’t take it as a failure but as a learning opportunity.

Accept that it didn’t work and try something new. Determine what didn’t work and why to come up with additional possible strategies. Thankfully, you already have a list of alternative solutions that can help you find the right one.

Preparing for the worst is not about thinking negatively. Remember, the power of positive thinking will allow you to uncover more solutions. If you can train your mind to think this way, the more solution-oriented you will become.

Instead, thinking through worst-case scenarios is simply being realistic. This allows you to create a Plan B. 

If one solution doesn’t work, which solution will you try next? Come up with a backup plan. You might move on to the next solution on your shortlist, or you might tweak things and continue working with your #1 idea.

Preparing for the worst allows you to end up with the best possible solution.

7. Set a Deadline

The next of my 10 problem-solving strategies is to create a timeframe for your solution. Determine:

• When to implement the solution
• How long it will take to complete
• When you expect to see results

What actions are necessary to meet this deadline, and who will be accomplishing it? List out the tasks needed and assign each one to an appropriate person.

It’s important to not only set a deadline, but also place standards on how you will measure its success. How will you know that you’re making progress, or in other words, what will be your key performance indicators (KPIs)? How will you compare the success of this solution against the success of another?

Determine what key performance indicators will allow you to measure the success of your outcomes and set a series of short-term deadlines to report. Clearly communicate these benchmarks with everyone involved.

Make sure people understand how you’re choosing to measure success so they can be successful by your standards.

8. Take Responsibility

Now that you’ve found the solution to the problem that you want to implement, consider how it will impact the situation if it works or if it doesn’t.

If your outcome doesn’t work, that’s okay, but it is your job to accept responsibility. Be ready to admit any mistakes and continue working to make things right.

Some of the most creative ideas never transpire because no one is assigned the authority to carry out the decision.

Taking responsibility for your decision doesn’t necessarily mean you need to be the one to implement it. There may be various people involved in the problem and different jobs required to accomplish the solution.

By taking responsibility for the decision you make, you’ll ensure that everyone involved knows what job they need to do, when they need to do it, and how the successful or unsuccessful completion of that job is defined.

9. Solve the Problem

Now, it’s finally time to take action.

Execute your solution so you can reach your defined goals and learn what works best. Continue communicating with everyone on board as you all work together to solve the problem.

However, not every problem will be solved easily.

You may encounter additional obstacles as you attempt to solve the initial problem. You can overcome any drawback by tapping into your creative mind and taking action consistently and persistently until you reach your goal.

As you work hard, you can develop your capacity to achieve more in the future. Every time you successfully solve a problem, you are developing your analytical skills, communication skills, and problem-solving abilities. You’re also increasing your confidence.

Next time you need to solve a problem, you can look back on the successful jobs you’ve done before.

10. Track Your Results

The final step of my  problem-solving process is to track the results. Using the deadlines, KPIs, and scheduled reports you set in step seven will let you know immediately if you’re on track or falling behind.

When you reach your deadline, ask yourself if you met the goals you set out to achieve.

What worked and what didn’t work? Did you solve the problem? Did you solve it with the approach and timeframe you expected?

Answering these questions will allow you to understand if you need to take further action and help you improve your problem-solving methods for the future.

The best way to learn to problem solve is to simply do it. Jump in with both feet and start coming up with potential solutions to issues that need fixing. Over time, you’ll learn about problem-solving without even realizing it.

However, in addition to learning “on the job,” you can also take courses to help boost your skills. 

Studying subjects like project management or data analysis is a good way to help you succeed in identifying problems, thinking of better solutions, and leading others with good communication as you work together to put your solutions in place.

Bonus: Further Problem-Solving Strategies

More good news: The process outlined above isn’t the only way to solve complex problems. In fact, there are many strategies you can implement for solving a problem.

Here are summaries of a few more problem-solving methods that you can learn more about:

The IDEAL process of solving a problem can help you look at situations objectively and remove the emotional aspects that can arise when a problem occurs. It works especially well for problems that may not seem to have a clear cause or may need more than one solution. The steps involve:

• Identifying the problem
• Defining what the problem is and the desired outcome
• Exploring possible solutions
• Acting on a solution
• Looking back to evaluate the effectiveness of the solution

Root Cause Analysis

Root cause analysis is actually a set of various problem-solving processes that aim to identify the main cause of a problem so that you can find appropriate solutions. The purpose of root cause analysis is to get to the root of a problem and prevent further difficulties instead of treating the symptoms of a problem.

At the same time, this approach to solving complex problems recognizes that there is value in treating symptoms for short-term relief while the larger problem-finding process is going on.

It also assumes that there can be more than one root cause and focuses on how and why a problem occurs instead of who causes it.

This method provides a structured approach to solving a complex problem, especially those that do not have a clear solution. Simplex problem-solving involves eight steps:

• Problem finding: Identifying what the problem is
• Fact-finding: Collecting information and data about the problem
• Problem definition: Clearly define the complex problem so you know what you are solving
• Idea finding: Generating possible solutions to the problem
• Evaluation and Selection: Choosing the solution that seems to like it will best address the complex problem
• Planning: Deciding how you will implement the solution
• Sell the idea: Get stakeholders on board with implementing the solution
• Action: Carrying out the solution

Appreciative Inquiry

Appreciative inquiry looks at a problem from a different angle, or not at all. It focuses on what is going right instead of what is going wrong. It is often best applied when a change is needed within an organization or individual. This approach leans heavily on cognitive science and positive thinking.

It involves five steps:

• Define the desired outcome
• Discover what our strengths are
• Dream of what would work well in the future
• Design a plan to make it happen
• Deploy the action

Six Thinking Hats

This approach to solving a complex problem focuses on approaching solutions in a balanced way. Using the six thinking hats approach, you will ask yourself a series of questions based on six principles or divide your team into six different groups:

• The white hat will focus on facts and logic (objective)
• The red hat will focus on emotion and instinct (intuitive)
• The black hat will focus on predicting negative outcomes (cautious)
• The yellow hat will look for positive outcomes (optimistic)
• The green hat will focus on reducing criticism and increasing ideas (creative)
• The blue hat will focus on management and organization (control)

The 5 whys is an example of a root cause analysis tool. The purpose of using this problem-solving technique is to find the exact reason a problem is occurring by asking a series of “why” questions. After asking why five times, the cause of the problem and its accompanying solution should be clear.

Start Implementing Solutions to Problems Today

You don’t need to feel overwhelmed and confused when a problem arises anymore. Stress and unhappiness are simply byproducts of how you respond to those situations. Instead, you can look at each problem or difficulty by asking, “What is the opportunity in this?”

When you enhance your problem-solving skills, you will experience determination and a sense of calmness when the next difficult situation arises.

While you may not know how to resolve most issues right away, you will know the problem-solving steps to take to uncover the best response: Define the problem, determine the cause, discover the best problem-solving technique, take action, and analyze the outcome.

Follow this process over and over again and you will creatively solve your problems. After all, an effective way to solve problems is a skill that you can develop with practice.

To help you enhance your success, download my free  SMART Goals Template . This resource is a good fit for someone who wants to achieve their goals and optimize their success. I walk you through how to set goals and plan ahead the right way. As you advance your problem-solving skills, you will experience more success in your daily life—for big-picture items and small ones alike.

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About Brian Tracy — Brian is recognized as the top sales training and personal success authority in the world today. He has authored more than 60 books and has produced more than 500 audio and video learning programs on sales, management, business success and personal development, including worldwide bestseller The Psychology of Achievement. Brian's goal is to help you achieve your personal and business goals faster and easier than you ever imagined. You can follow him on Twitter , Facebook , Pinterest , Linkedin and Youtube .

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10 best AI math solver tools for math problem-solving

Homework AI makes it easier for students to learn difficult subjects. Boost your assignment and exam grades with these best AI homework helpers.

• March 18, 2024

The traditional approach to learning involves acquiring knowledge through listening and observation.

However, professionally trained AI can better accommodate different learning styles and enhance comprehension by offering tailored, on-demand learning assistance, especially in challenging subjects like mathematics.

As a subject many students struggle with, having access to a reliable AI math solver is invaluable. Math AI solvers can provide students and other learners with instant homework help outside the classroom at any time when needed.

They can also help improve students’ math test scores and build their mathematical skills over time. Let’s look at some of the best math AI tools for mathematical problem-solving:

Ten best AI math solver tools

1. Mathful – Best AI math solver overall

2. HIX Tutor – Best AI math solver for rapid homework response

3. AI Math – Best AI math solver for increasing math test scores

4. HomeworkAI – Best AI math solver for 24/7 math homework help

5. GeniusTutor – Best AI math solver for high-level learning 

6. Mathway – Best AI math solver for solving algebra problems

7. Air Math – Best AI math solver for mobile uses

8. StudyMonkey – Best AI math solver for in-depth explanations 

9. Interactive Mathematics – Best AI math solver for comprehensive chat support

10. Smodin – Best AI math solver for step-by-step solutions

Mathful – Best AI math solver overall

Mathful is an AI-powered math homework solver that provides step-by-step answers to all types of math questions.

The math AI tool uses a large language model and advanced algorithms to help students improve their math grades and prepare for exams.

Mathful has proven to be one of the most accurate AI math solvers, boasting a remarkable 98% accuracy rate across various mathematical disciplines, such as calculus, algebra, and geometry.

Mathful can also help students of all levels, from elementary school to university and beyond.

Mathful can help students improve their math grades in school by enforcing core math concepts and providing detailed explanations that promote comprehension.

Students can start using Mathful for free; low-cost subscription plans are available after the initial trial. 

• Able to provide highly accurate solutions and comprehensive explanations.
• Can process text and image files.
• Able to solve a variety of question types. 
• Available to use 24/7. 
• It cannot replace a real classroom education. 

Get instant answers to Math homework questions with Mathful AI math solver >>>

HIX Tutor – Best AI math solver for rapid homework response

HIX Tutor is a powerful AI homework helper that provides comprehensive support in many subjects, such as chemistry, biology, and physics.

It also serves as a personal AI math tutor, helping students boost their math grades and overall academic success. 

To use HIX Tutor’s advanced math AI, type in a math problem or upload an image or document of the question.

The tool instantly generates a detailed explanation for each problem step, helping students understand the underlying math concepts. 

HIX Tutor’s AI math problem solver can help save users time spent struggling with complicated math assignments.

Try the AI math solver at no cost. Once you’ve reached your question limit, upgrade to an affordable monthly or annual plan.

• Delivers step-by-step solutions to math questions.
• Trained on a large math knowledge dataset. 
• Reduces time spent on math homework. 
• Requires payment after the initial trial. 
• Some students may only use the tool to get answers without learning. 

Streamline the math learning experience with HIX Tutor’s math AI solver >>>

AI Math – Best AI math solver for increasing math test scores

How you prepare for a math test can significantly impact your performance.

AI math solvers like AI Math help take the frustration out of studying by providing thorough explanations that teach students how to tackle similar math problems. 

The AI math problem solver generates answers to questions in under 10 seconds with a 99% accuracy rate.

AI Math supports over 30 languages so that students can get responses in their native language for better understanding.

Students who use AI Math to supplement their classroom education experience an increase in their math test scores of up to 35%. Starting with AI Math is free; subscriptions cost just a few dollars a month.

• Covers most branches of math, such as arithmetic and trigonometry.
• Walks students through the solution to facilitate understanding. 
• Can solve simple to complex math problems.
• Does not currently offer advanced math features. 

Choose AI Math and study for math tests in a smarter way >>>

HomeworkAI – Best AI math solver for 24/7 math homework help

Students often need help with homework outside of traditional school hours. AI math solver tools like HomeworkAI allow students to get comprehensive support round-the-clock.

Much like a personal tutor, HomeworkAI focuses on teaching students how to solve homework problems instead of simply giving answers. 

HomeworkAI can handle math problems with multiple solution methods, meaning a primary solution and possible alternative approaches.

It can also analyze textbook material with practice math questions to aid students’ studies. 

While HomeworkAI excels in helping students complete math assignments with high precision, this AI homework tool can also help students in other school subjects, such as biology, physics, chemistry, literature, and history.

Try HomeworkAI for free, or choose from a low-cost subscription plan for unlimited uses. 

• Allows students to work at their own pace at home. 
• User-friendly platform is easy to navigate. 
• It can help students excel in many subjects, including math.
• This may cause students to rely too much on online math-solving platforms. 
• Rarely, solutions may be outdated or incorrect. 

Try HomeworkAI and get instant help for your math homework >>>

5. Genius Tutor – Best AI Math Solver for High-Level Learning

Genius Tutor is a versatile AI tutor and homework helper that can help students build their math skills and gain confidence in their academic abilities.

While the AI math solver is geared toward all types of learners, it is best suited for high school and college-level students.

The AI math problem solver provides a step-by-step breakdown for math questions of all types, showing the exact process of figuring out math problems and concepts.

Genius Tutor also highlights and explains important theorems, formulas, and rules so that students know when and how to use them.

Genius Tutor not only helps students complete math homework assignments in record time but can also help them prepare for exams.

No credit card is needed to try Genius Tutor, and budget-friendly paid subscriptions are available after the free trial.

• Can help students with all mathematical disciplines.
• Provides in-depth guides that foster lifelong learning. 
• Gives instant feedback on a variety of homework questions. 
• May not provide accurate solutions to highly complex math problems. 

Genius Tutor’s AI math solver can instantly elevate your math learning experience >>>

Mathway – Best AI math solver for solving algebra problems

Algebra is a complex branch of mathematics that many students struggle with in high school and college.

Mathway offers a sophisticated AI math solver designed to solve algebra homework questions, from word problems to complex mathematical operations that form meaningful expressions.

The math solver AI tool combines an algebra calculator with a conversational chatbot. Simply type in a math problem or upload a photo and get instant step-by-step solutions. 

Mathway also offers AI-driven math problem solvers for other branches of math, such as calculus, statistics, chemistry, and physics.

• The clean interface is easy to use. 
• You can upload documents on a computer or mobile device. 
• It makes it easy to master algebraic concepts. 
• Additional features require a paid upgrade. 
• Does not always provide detailed explanations. 

Air Math – Best AI math solver for mobile uses

Nowadays, many students rely on their smartphones or other mobile devices for homework help. Air Math is a smart AI math solver app available on Apple and Android devices.

Once installed, the Air Math app allows students to snap and solve math homework questions in under three seconds.

The innovative math AI solver can solve everything from geometry questions to word problems.

The 24/7 instant solutions include step-by-step solutions to teach students how to solve the problem independently. 

If you still have problems understanding the explanations, Air Math can connect you with professional math experts worldwide at any time. 

• Free to use.
• Offers support on mobile devices.
• You can ask expert math tutors for additional assistance. 
• Students can download the Chrome Extension on the web. 
• The app may not accurately read handwritten math questions. 

StudyMonkey – Best AI math solver for in-depth explanations 

StudyMonkey is a free AI homework helper that provides academic assistance in many areas, including mathematics.

The powerful AI math solver saves students time and headaches by instantly generating solutions to complex math problems, preventing long homework sessions. 

Type in the math problem, and StudyMonkey provides an accurate answer, detailed explanation, and steps to solve the problem to make it easier to understand.

This platform also retains a history of past questions asked, allowing students to review and revisit solutions anytime, aiding in effective long-term learning. 

• Can handle math problems from first grade to expert. 
• Offers a free plan. 
• Math features are limited.
• Can not upload images or documents. 
• You must pay for a subscription to ask more than three questions daily.

Interactive Mathematics – Best AI math solver for comprehensive chat support

Many students are familiar with chatbots, making Interactive Mathematics a popular option for homework help.

The state-of-the-art AI math problem solver claims to be more accurate than ChatGPT and more powerful than a math calculator. Its speed also surpasses human math tutors. 

Using Interactive Mathematics for homework help is also very simple.

You can type in your math question or upload an image, and the tool immediately sets to work, with the added benefit of offering solutions through a chatbot-style conversation that simulates a real-time, interactive math problem-solving session.

• You can help students improve their grades.
• Chat-based real-time problem-solving
• Offers bonuses like SAT/ACT prep courses. 
• Users can only ask three questions before reaching the free question limit.

Smodin – Best AI math solver for step-by-step solutions

The Smodin Math AI Homework Solver can help if you’re struggling with math homework.

This unique tool uses machine learning and AI algorithms to efficiently solve all types of math problems, from formulas to equations.

The tool also promises high accuracy, reducing the risk of submitting incorrect answers. 

Smodin doesn’t just provide a final answer to your query. It provides both brief answers and comprehensive explanations to help you better understand the concept.

It also shows a variety of relevant web answers and links to other resources, such as YouTube videos. 

• Users must make an account to start using Smodin.
• Step-by-step solutions are highly detailed and engaging. 
• Can help students ace their math exams. 
• Free users are limited to 3 daily credits. 
• Cannot upload images or documents. 

Final thoughts

Many students struggle with math, but that doesn’t mean they must settle for bad grades. With the right AI math solver, students can confidently develop their math skills and complete assignments and exams. 

Based on our assessments, Mathful easily stands out from the pack. It is a sophisticated AI math problem solver that offers enhanced problem-solving capabilities, accurate solutions, and affordable subscription plans.

Try Mathful for free and achieve greater academic success.

Have any thoughts on this? Drop us a line below in the comments, or carry the discussion to our  Twitter  or  Facebook .

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Problems with Solutions and Answers for Grade 10

Grade 10 math word problems with answers and solutions are presented.

A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?

• An airplane flies against the wind from A to B in 8 hours. The same airplane returns from B to A, in the same direction as the wind, in 7 hours. Find the ratio of the speed of the airplane (in still air) to the speed of the wind.

Solutions to the Above Problems

• 6% x = 8,880 : x = selling price of house. x = $148,000 : solve for x.
• 3000 revolutions / minute = 3000×360 degrees / 60 seconds = 18,000 degrees / second
• L × W = 300 : area , L is the length and W is the width. 2 L + 2 W = 70 : perimeter L = 35 - w : solve for L (35 - W) × W = 300 : substitute in the area equation W = 15 and L = 20 : solve for W and find L using L = 35 - w.
• Let h be the height of the trapezoid. area = (1/2) × h × (10 + 10 + 3 + 4) = 270 h = 20 : solve for h 20 2 + 3 2 = L 2 : Pythagora's theorem applied to the right triangle on the left. L = sqrt(409) 20 2 + 4 2 = R 2 : Pythagora's theorem applied to the right triangle on the right. R = sqrt(416) perimeter = sqrt(409) + 10 + sqrt(416) + 17 = 27 + sqrt(409) + sqrt(416)
• 400 rev / minute = 400 × 60 rev / 60 minutes = 24,000 rev / hour 24,000 × C = 72,000 m : C is the circumference C = 3 meters
• Let x be the price of one shirt, y be the price of one pair of trousers and z be the price of one hat. 4x + 4y + 2z = 560 : 9x + 9y + 6z = 1,290 3x + 3y + 2z = 430 : divide all terms of equation C by 3 x + y = 130 : subtract equation D from equation B 3(x + y) + 2z = 430 : equation D with factored terms. 3*130 + 2z = 430 z = 20 : solve for z x + y + z = 130 + 20 = $150
• x : the total number of toys x/10 : the number of toys for first child x/10 + 12 : the number of toys for second child x/10 + 1 : the number of toys for the third child 2(x/10 + 1) : the number of toys for the fourth child x/10 + x/10 + 12 + x/10 + 1 + 2(x/10 + 1) = x x = 30 toys : solve for x
• Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above. [sum(Xi) + sum(Yi)] / 20 = 70 : class average sum(Xi) / n = 50 : average for less that 60 sum(Yi) / N = 75 : average for 60 or more 50n + 75N = 1400 : combine the above equations n + N = 20 : total number of students n = 4 and N = 16 : solve the above system
• f(x) = -3(x - 10)(x - 4) = -3 x 2 + 42 x - 120 : expand and obtain a quadratic function h = -b/2a = - 42/(-6) = 7 : h is the value of x for which f has a maximum value f(h) = f(7) = 27 : maximum value of f.
• (1 - 1/10)(1 - 1/11)(1 - 1/12)...(1 - 1/99)(1 - 1/100) = (9/10)(10/11)(11/12)...(98/99)(99/100) = 9/100 : simplify
• Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B. d = 3(S + r) : boat travelling down river d = 5(S - r) : boat travelling up river 3(S + r) = 5(S - r) r = S / 4 : solve above equation for r d = 3(S + S/4) : substitute r by S/4 in equation B d / S = 3.75 hours = 3 hours and 45 minutes.
• Let: S be the speed of the airplane in still air, r be the speed of the wind and d the distance between A and B. d = 8(S - r) : airplane flies against the wind d = 7(S + r) : airplane flies in the same direction as the wind 8(S - r) = 7(S + r) S/r = 15

Links and References

Morning Carpool

21 Mental Shifts to Boost Problem-Solving Skills and Become More Strategic

Posted: February 10, 2024 | Last updated: February 10, 2024

Discover transformative mental shifts to supercharge your problem-solving skills. From embracing uncertainty to the power of daydreaming, prepare to change the way you tackle challenges forever!

Embrace Uncertainty

Accept that not all answers are immediately clear. Uncertainty can be a powerful motivator rather than a source of stress. By embracing the unknown, we open ourselves up to a broader range of possibilities and solutions.

Seek Diverse Perspectives

Look beyond your own experiences. Different perspectives can provide unique insights and spark innovative solutions. Engaging with people from various backgrounds allows you to see problems through a new lens and discover paths you might not have considered.

Simplify the Complex

Break down big problems into smaller, manageable parts. When faced with a complex issue, deconstruct it to understand its fundamental components. This approach makes the problem less daunting and easier to tackle, leading to clearer, more effective solutions.

Adopt a Growth Mindset

Believe in your ability to learn and grow. A growth mindset encourages resilience and the pursuit of knowledge. Challenges are just undiscovered opportunities with potential for personal and professional development.

Question Assumptions

Challenge the status quo. The barriers to solving a problem are often based on outdated or incorrect assumptions. By questioning the basis of your thinking, you can uncover new paths and innovative solutions.

Think in Reverse

Start with the desired outcome and work backward. This reverse-engineering approach forces you to think differently and can reveal insights you might have missed when approaching the problem linearly.

Embrace Failure as a Teacher

Learn from mistakes and change your perspective. Nobody likes to fail, but each failure provides valuable lessons that can guide future decisions and strategies. Failure isn’t the end but the beginning of understanding.

Harness the Power of Daydreaming

Let your mind wander. Sometimes, the best ideas come when you’re not actively trying to solve a problem. Allowing your mind to drift can lead to creative breakthroughs and unexpected solutions.

Practice Empathy

Understand others’ perspectives and needs. By putting yourself in someone else’s shoes, you can gain insights into the emotional and practical aspects of a problem, leading to more compassionate and effective solutions.

Set Clear Goals

Define what success looks like. Clear goals provide direction and focus, making identifying the steps needed to solve a problem easier. They also help measure progress and keep you motivated.

Stay Curious

Ask questions and seek knowledge. A curious mind is always looking for new information and ideas, which can lead to innovative problem-solving strategies. Curiosity is the engine of achievement.

Use Analogies

Draw parallels from different areas. Analogies can help clarify complex problems by relating them to something more familiar. This can simplify the problem-solving process and spark creative solutions.

Focus on the Process, Not Just the Outcome

Enjoy the journey of problem-solving. Focusing too much on the end result can lead to frustration and missed opportunities. By valuing the process, you can learn and adapt as you go, leading to more sustainable solutions.

Prioritize Effectively

Set deadlines for achieving your goals. Know what matters most. Not all aspects of a problem are equally important. By prioritizing the key factors, you can allocate your time and resources more effectively and achieve better results.

Build Resilience

Give yourself time to recover, then bounce back from setbacks. Resilience is crucial for problem-solving, as it allows you to keep going despite challenges and failures. Resilience turns problems into opportunities.

Cultivate Patience

Give solutions time to unfold. Sometimes, the best solutions emerge over time, and immediate answers aren’t always the best. Patience allows you to thoroughly explore options and make more considered decisions.

Practice Reflection

Don’t overlook the power of self-reflection. Take time to think about what you’ve learned. Reflecting on your experiences and the outcomes of your problem-solving efforts can provide valuable insights and improve future strategies.

Encourage Collaboration

Work with others to find solutions and share goals. Collaborating with a team can bring in a range of skills and perspectives that enhance the problem-solving process and lead to more effective solutions.

Visualize Success

Imagine the desired outcome. Visualization can be a powerful motivator to enhance your performance and guide your actions toward achieving your goals. Focusing on the end result in your mind’s eye can make it a reality.

Adapt and Evolve

Be willing to change your approach. The most effective problem-solvers are flexible and open to new methods and ideas. Adapting your strategy in response to new information or challenges can lead to better solutions.

Maintain a Positive Attitude

Stay optimistic and focused. A positive outlook can keep you motivated and open to new ideas. An optimistic mindset can also make the problem-solving process more enjoyable and less daunting.

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Shocked and honored, Randall McMurray receives Officer of the Year at 2024 SBPD awards

SOUTH BEND — Randall McMurray wears many hats in the South Bend Police Department , serving on the honor guard, pension board, peer support team, critical incidents stress management team, FACT team, rapid response team and as an emergency vehicle operations instructor. 

McMurray, a first class patrolman currently serving as a crime scene technician, was shocked to receive a new role Wednesday night: South Bend's Officer of the Year.

“I’m very honored,” he said during the ceremony at the Four Winds Casino ballroom. “I’ve been here for 10 years, so it feels good to get recognized and know that my work is being seen by others.” 

McMurray has "teched" 80 scenes while completing 202 reports, “treating each one with equal regard,” South Bend Police Chief Scott Ruszkowski said in his speech announcing McMurray's honor.

McMurray, who sat at a table near the front, said he had no idea he would be receiving Officer of the Year. In fact, his family picked the spot, he said. 

“There’s a lot of people in the department who deserve this award just as much,” he said. For him, the awards are an opportunity to come together and “see the work everyone has done over the year and get recognized for it,” McMurray said. 

This award won’t change McMurray's work ethic. “I’m going to continue to do what I do, working to the best of my ability and try to make citizens, my family and everyone proud,” he said. 

Department presents Community Problem Solving Award and more

The department honored officers, police department personnel and community members throughout the evening, including the Community Problem Solving Award to Christine Karsten and Officer Brian Meador. 

The award is given to anyone who shows an exemplary effort to identify, analyze and successfully respond to causes, conditions and problems that may lead to crime and neighborhood disorder. 

Chief Scott Ruszkowski called recipient WNDU Morning News Anchor Christine Karsten the “voice and hope to the victims of unsolved crimes. She is a true ambassador of the message of ‘See something, say something, so we can do something,'" he said.

In Karsten’s segment, Michiana Unsolved, “she brings awareness to the unsolved cases in a way the community can empathize with and offers another way to make a difference,” Ruszkowski said. 

Officer honored for saving baby's life

Community Resource Officer Brian Meador also received the Community Problem Solving Award, but before he could take his seat, Ruszkowski called state legislators to the stage.

In a surprise to Meador, Rep. Maureen Bauer, D-South Bend and state Sen. David Niezgodski, D-South Bend took the podium to announce the passing of House Concurrent Resolution 8 , in recognition of Meador’s heroic efforts on Dec. 12 in the police department’s lobby. 

On the evening of Dec. 12, a couple was taking their child to the hospital when their child became unresponsive in the car. They entered the police station for help. Officer Meador, upon hearing the commotion, began performing chest compressions until medics arrived. 

Niezgodski and Bauer credited Meador’s quick thinking, composure and training to save the child’s life, and it wasn’t the first time he’d done so.

Meador said he and two other officers previously saved a baby with special needs, winning a life-saving award previously.

He recalled the events leading up to the Dec. 12 incident. 

“I thought it was a fight at first,” he said. After hearing the words, “He’s not breathing,” Meador said he started running. 

“I didn’t know it was a baby (at first) either. All the training kicked in,” he said. He said he thinks all officers have a versatile training equipped to assist in any situation. 

“If I hadn’t been there any of the other officers would have jumped in,” he said. “I just happened to be the guy that was there.” 

Niezgodski and Bauer both presented House Concurrent Resolution 8 in their respective chambers, but Niezgodski credited Bauer for reaching out to him and beginning the resolution in the House. 

“This is a way for us as legislators to recognize Officer Meador for his heroic actions,” Bauer told The Tribune. Having “the entire Indiana General Assembly come together and recognize his efforts, so many of my colleagues in the House were impressed by his actions.” 

“It’s one of the most special things we can do as legislators to honor those back home,” Niezgodski said. 

The department distributed 10 other awards, including:

Chief’s Award of Merit

Commander’s Award

Jose Aguilar, Tyler Donlon, Rodolfo Espraza, Sgt. Kevin Gibbons, Jen Jozwiak, Detective Chris Kozora, Officer Aaron Omanson and Officer Bradley Sadilek.

Department Commendation

Detective Kyle Bilinski, Officer Chris Brady, Detective Bruno Martinsky, Officer Hunter Miller, Rose Thompson, Chris Rajski, Officer Antonio Rodriguez, Detective Tim Taylor

Crime Prevention Special Commendation

Jarveair Bourn

Unit Meritorious Performance Award

SBPD Crime Lab: Charlie Eakins, Sierra Halstead, Ronald Kaszas, Lacie Klosinski, Aaron McCray, Ronald Wilson and Ray Wolfenbarger

Life Saving Award

Devonte Spratt, Jeffrey Veal, Zachery Wells, Brian Meador, Bradley Sadilek, Joseph Slabach, Jerrid Arnold, Maranda Baker and John Bies

Community Oriented Policing Special Partnership Award

Lynn Coleman, Tina Thompson, Charlotte Williams

Business Appreciation Award

Palmer Funeral Home and South Bend Cubs

Dortha Paxton Award

Tony Salazar

Patty Derue Nemeth Humanitarian Award

Crystal Hutchens

In a special recognition, Chief Dan Skibins recognized the efforts of field training officers who trained over 70 new recruits in 2022 and 2023 combined. "Without the dedication of our field training officers, we would not have been successful in building back our department to full staffing," he said in his speech. The department recognized Anne Hayes, Jeffery Vance, Travis Kukla, Tyler Donlon, Trent Mamazza, Timmy Buckingham, Sean Ryan, Joseph Carey, Reid Spitaels, Tony Dawson, Michael Stuk, Brandon Martin, Mollie Anton, Robert Anton and Tyler Jackey.

Email Tribune staff writer Camille Sarabia at  [email protected] .

About iOS 17 Updates

iOS 17 brings big updates to Phone, Messages, and FaceTime that give you new ways to express yourself as you communicate. StandBy delivers a new full-screen experience with glanceable information designed to view from a distance when you turn iPhone on its side while charging. AirDrop makes it easier to share and connect with those around you and adds NameDrop for contact sharing. Enhancements to the keyboard make entering text faster and easier than ever before. iOS 17 also includes updates to Widgets, Safari, Music, AirPlay, and more.

For information on the security content of Apple software updates, please visit this website: https://support.apple.com/kb/HT201222

This update provides important bug fixes and security updates and is recommended for all users.

For information on the security content of Apple software updates, please visit this website:

https://support.apple.com/kb/HT201222

This update introduces new emoji, transcripts in Apple Podcasts and includes other features, bug fixes, and security updates for your iPhone.

New mushroom, phoenix, lime, broken chain, and shaking heads emoji are now available in the emoji keyboard

18 people and body emoji add the option to face them in either direction

Apple Podcasts

Transcripts let you follow an episode with text that highlights in sync with the audio in English, Spanish, French and German

Episode text can be read in full, searched for a word or phrase, tapped to play from a specific point and used with accessibility features such as Text Size, Increase Contrast, and VoiceOver

This update includes the following enhancements and bug fixes:

Music recognition lets you add songs you have identified to your Apple Music Playlists and Library, as well as Apple Music Classical

Siri has a new option to announce messages you receive in any supported language

Stolen Device Protection supports the option for increased security in all locations

Battery Health in Settings shows battery cycle count, manufacture date, and first use on iPhone 15 and iPhone 15 Pro models

Call Identification displays Apple-verified business name, logo, and department name when available

Business updates in Messages for Business provide trusted information for order status, flight notifications, fraud alerts or other transactions you opt into

Apple Cash virtual card numbers enable you to pay with Apple Cash at merchants that don’t yet accept Apple Pay by typing in your number from Wallet or using Safari AutoFill

Fixes an issue where contact pictures are blank in Find My

Fixes an issue for Dual SIM users where the phone number changes from primary to secondary and is visible to a group they have messaged

Some features may not be available for all regions or on all Apple devices. For information on the security content of Apple software updates, please visit this website:

This update provides bug fixes for your iPhone including:

Text may unexpectedly duplicate or overlap while typing

This update introduces additional security measures with Stolen Device Protection. This release also includes a new Unity wallpaper to honor Black history and culture in celebration of Black History Month, as well as other features, bug fixes, and security updates for your iPhone.

Stolen Device Protection

Stolen Device Protection increases security of iPhone and Apple ID by requiring Face ID or Touch ID with no passcode fallback to perform certain actions

Security Delay requires Face ID or Touch ID, an hour wait, and then an additional successful biometric authentication before sensitive operations like changing device passcode or Apple ID password can be performed

Lock Screen

New Unity wallpaper honors Black history and culture in celebration of Black History Month

Collaborate on playlists allows you to invite friends to join your playlist and everyone can add, reorder, and remove songs

Emoji reactions can be added to any track in a collaborative playlist

This update also includes the following improvements:

AirPlay hotel support lets you stream content directly to the TV in your room in select hotels

AppleCare & Warranty in Settings shows your coverage for all devices signed in with your Apple ID

Crash detection optimizations (all iPhone 14 and iPhone 15 models)

This update provides important bug fixes and is recommended for all users.

This update introduces Journal, an all-new way to reflect on life’s moments and preserve your memories. This release also includes Action button and Camera enhancements, as well as other features, bug fixes, and security updates for your iPhone.

Journal is a new app that lets you write about the small moments and big events in your life so you can practice gratitude and improve your wellbeing

Journaling suggestions make it easy to remember your experiences by intelligently grouping your outings, photos, workouts, and more into moments you can add to your journal

Filters let you quickly find bookmarked entries or show entries with attachments so you can revisit and reflect on key moments in your life

Scheduled notifications help you keep a consistent journaling practice by reminding you to write on the days and time you choose

Option to lock your journal using Touch ID or Face ID

iCloud sync keeps your journal entries safe and encrypted on iCloud

Action Button

Translate option for the Action button on iPhone 15 Pro and iPhone 15 Pro Max to quickly translate phrases or have a conversation with someone in another language

Spatial video lets you capture video on iPhone 15 Pro and iPhone 15 Pro Max so you can relive your memories in three dimensions on Apple Vision Pro

Improved Telephoto camera focusing speed when capturing small faraway objects on iPhone 15 Pro and iPhone 15 Pro Max

Catch-up arrow lets you easily jump to your first unread message in a conversation by tapping the arrow visible in the top-right corner

Add sticker option in the context menu lets you add a sticker directly to a bubble

Memoji updates include the ability to adjust the body shape of any Memoji

Contact Key Verification provides automatic alerts and Contact Verification Codes to help verify people facing extraordinary digital threats are messaging only with the people they intend

Precipitation amounts help you stay on top of rain and snow conditions for a given day over the next 10 days

New widgets let you choose from next-hour precipitation, daily forecast, sunrise and sunset times, and current conditions such as Air Quality, Feels Like, and wind speed

Wind map snapshot helps you quickly assess wind patterns and access the animated wind map overlay to prepare for forecasted wind conditions for the next 24 hours

Interactive moon calendar lets you easily visualize the phase of the moon on any day for the next month

This update also includes the following improvements and bug fixes:

Siri support for privately accessing and logging Health app data using your voice

AirDrop improvements including expanded contact sharing options and the ability to share boarding passes, movie tickets, and other eligible passes by bringing two iPhones together

Favorite Songs Playlist in Apple Music lets you quickly get back to the songs you mark as favorites

Use Listening History in Apple Music can be disabled in a Focus so music you listen to does not appear in Recently Played or influence your recommendations

A new Digital Clock Widget lets you quickly catch a glimpse of the time on your Home Screen and while in StandBy

Enhanced AutoFill identifies fields in PDFs and other forms enabling you to populate them with information such as names and addresses from your contacts

New keyboard layouts provide support for 8 Sámi languages

Sensitive Content Warning for stickers in Messages prevents you from being unexpectedly shown a sticker containing nudity

Qi2 charger support for all iPhone 13 models and iPhone 14 models

Fixes an issue that may prevent wireless charging in certain vehicles

This update provides important security fixes and is recommended for all users.

In rare circumstances, Apple Pay and other NFC features may become unavailable on iPhone 15 models after wireless charging in certain cars

Weather Lock Screen widget may not correctly display snow

This update introduces the ability for AirDrop transfers to continue over the internet when you step out of AirDrop range. This release also includes enhancements to StandBy and Apple Music, as well as other features, bug fixes, and security updates for your iPhone.

Content continues to transfer over the internet when you step out of AirDrop range

New options to control when the display turns off (iPhone 14 Pro, iPhone 14 Pro Max, iPhone 15 Pro, and iPhone 15 Pro Max)

Favorites expanded to include songs, albums, and playlists, and you can filter to display your favorites in the library

New cover art collection offers designs that change colors to reflect the music in your playlist

Song suggestions appear at the bottom of every playlist, making it easy to add music that matches the vibe of your playlist

Option to choose a specific album to use with Photo Shuffle on the Lock Screen

Home key support for Matter locks

Improved reliability of Screen Time settings syncing across devices

Fixes an issue that may cause the Significant Location privacy setting to reset when transferring an Apple Watch or pairing it for the first time

Resolves an issue where the names of incoming callers may not appear when you are on another call

Addresses an issue where custom and purchased ringtones may not appear as options for your text tone

Fixes an issue that may cause the keyboard to be less responsive

Fixes an issue that may cause display image persistence

https://support.apple.com/HT201222

This update provides important bug fixes, security updates, and addresses an issue that may cause iPhone to run warmer than expected.

This update provides important bug fixes, security updates, and fixes an issue that may prevent transferring data directly from another iPhone during setup.

Contact Posters let you customize how you appear on other people’s devices when you call them with a customized poster

Live Voicemail displays a live transcription as someone leaves a message and allows you to pick up the call

Stickers iMessage app brings all your stickers into one place including Live Stickers, Memoji, Animoji, emoji stickers, and your third party sticker packs

Live Stickers can be created by lifting the subject from photos or videos and stylizing them with effects like Shiny, Puffy, Comic, and Outline

Check In automatically notifies a family member or friend when you arrive at a destination safely and can share helpful information with them in case of a delay

Audio message transcription is available for audio messages you receive so you can read them in the moment and listen later

Search improvements help you find messages faster by allowing you to combine search filters such as people, keywords, and content types like photos or links to find exactly what you are looking for

Swipe to reply to a message inline by swiping to the right on any bubble

One-time verification code cleanup automatically deletes verification codes from the Messages app after using them with AutoFill in other apps

Leave a video or audio message to capture exactly what you want to say when someone does not pick up your FaceTime call

Enjoy FaceTime calls on Apple TV by using your iPhone as a camera (Apple TV 4K 2nd generation and later)

Reactions layer 3D effects like hearts, balloons, confetti, and more around you in video calls and can be triggered with gestures

Video effects allow you to adjust the intensity of Studio Lighting and Portrait mode

Full-screen experience with glanceable information like clocks, photos, and widgets designed to view from a distance when iPhone is on its side and charging in places such as your nightstand, kitchen counter, or desk

Clocks are available in a variety of styles including Digital, Analog, Solar, Float, and World Clock, with elements you can personalize like the accent color

Photos automatically shuffle through your best shots or showcase a specific album you choose

Widgets give you access to information at a distance and appear in Smart Stacks that deliver the right information at the right time

Night Mode lets clocks, photos, and widgets take on a red tone in low light

Preferred view per MagSafe charger remembers your preference for each place you charge with MagSafe, whether that’s a clock, photos, or widgets

Interactive widgets let you take actions, like mark a reminder as complete, directly from the widget by tapping it on the Home Screen, Lock Screen, or in StandBy

iPhone widgets on Mac enable you to add widgets from your iPhone to your Mac desktop

NameDrop lets you exchange contact information with someone new by bringing your iPhones close together

New way to initiate AirDrop allows you to share content or start a SharePlay session over AirDrop by bringing your iPhones close together

Improved autocorrect accuracy makes typing even easier by leveraging a powerful transformer-based language model (iPhone 12 and later)

Easier autocorrect editing temporarily underlines corrected words and lets you revert back to what you originally typed with just a tap

Enhanced sentence corrections can correct more types of grammatical mistakes when you finish sentences (iPhone 12 and later)

Inline predictive text shows single and multi-word predictions as you type that can be added by tapping space bar (iPhone 12 and later)

Safari and Passwords

Profiles keep your browsing separate for topics like work and personal, separating your history, cookies, extensions, Tab Groups, and favorites

Private Browsing enhancements include locking your private browsing windows when you’re not using them, blocking known trackers from loading, and removing identifying tracking from URLs

Password and passkey sharing lets you create a group of passwords to share with trusted contacts that stays up to date as members of the group make changes

One-time verification code AutoFill from Mail autofill in Safari so you can log in without leaving the browser

SharePlay makes it easy for everyone to control and play Apple Music in the car

Crossfade smoothly transitions between songs by fading out the currently playing song while fading in the next so the music never stops

Intelligent AirPlay device list makes finding the right AirPlay-compatible TV or speaker even easier by showing your devices in order of relevance, based on your preferences

Suggested AirPlay device connections are proactively shown to you as a notification to make it even more seamless to connect to your preferred AirPlay devices

Automatic AirPlay device connections are made between your iPhone and the most relevant AirPlay-compatible device so all you have to do is tap “Play” to begin enjoying your content

Adaptive Audio delivers a new listening mode that dynamically blends Active Noise Cancellation and Transparency to tailor the noise control experience based on the conditions of your environment (AirPods Pro (2nd generation) with firmware version 6A300 or later)

Personalized Volume adjusts the volume of your media in response to your environment and listening preferences over time (AirPods Pro (2nd generation) with firmware version 6A300 or later)

Conversation Awareness lowers your media volume and enhances the voices of the people in front of the user, all while reducing background noise (AirPods Pro (2nd generation) with firmware version 6A300 or later)

Press to mute and unmute your microphone by pressing the AirPods stem or the Digital Crown on AirPods Max when on a call (AirPods (3rd generation), AirPods Pro (1st and 2nd generation), or AirPods Max with firmware version 6A300 or later)

Offline Maps allow you to select an area you want to access, search, and explore rich information for places to download for use when your iPhone doesn’t have a Wi-Fi or cellular signal

EV routing improvements give you routes based on real-time EV charger availability for supported chargers

Option to say “Siri” in addition to “Hey Siri” for an even more natural way to make requests

Back-to-back requests can be issued without needing to reactivate Siri in between commands (iPhone 11 and later)

Visual Look Up

Expanded domains in Visual Look Up help you discover similar recipes from photos of food, Maps information from photos of storefronts, and the meaning of signs and symbols on things like laundry tags

Multiple or single subjects can be lifted from the background of photos and videos and placed into apps like Messages

Visual Look Up in Video helps you learn about objects that appear in paused video frames

Visual Look Up for subjects in photos enables you to look up information about objects you lift from photos directly from the callout bar

State of Mind reflection allows you to log your momentary emotion and daily mood, choose what factors are having the biggest impact on you, and describe your feelings

Interactive charts give you insights into your state of mind, how it has changed over time, and what factors may have influence such as exercise, sleep, and mindful minutes

Mental health assessments help you understand your current risk for depression and anxiety and if you might benefit from getting support

Screen Distance leverages the TrueDepth camera that powers Face ID to encourage you to increase the distance you view your device to reduce digital eye strain and can help reduce the risk of myopia in children

Sensitive Content Warnings can be enabled to prevent users from unexpectedly being shown images containing nudity in Messages, AirDrop, Contact Posters in the Phone app, and FaceTime messages

Expanded Communication Safety protections for children now detect videos containing nudity in addition to photos that children may receive or attempt to send in Messages, AirDrop, Contact Posters in the Phone app, FaceTime messages, and the system Photo picker

Improved sharing permissions give you even more control over what you share with apps, with an embedded photo picker and an add-only Calendar permission

Link tracking protection removes extra information from links shared in Messages, Mail, and Safari Private Browsing that some websites use in their URLs to track you across other websites, and links still work as expected

Accessibility

Assistive Access distills apps and experiences to their essential features in Phone and FaceTime, Messages, Camera, Photos, and Music, including large text, visual alternatives, and focused choices to lighten cognitive load

Live Speech lets you type what you want to say and have it be spoken out loud in phone calls, FaceTime calls, and for in-person conversations

Personal Voice enables users who are at risk of losing their voice to privately and securely create a voice that sounds like them on iPhone, and use it with Live Speech in phone and FaceTime calls

Point and Speak in Magnifier Detection Mode uses iPhone to read text out loud on physical objects with small text labels, such as keypads on doors and buttons on appliances

This release also includes other features and improvements:

Roadside Assistance via satellite lets you contact AAA to help you with vehicle issues when out of Wi-Fi or cellular range (iPhone 14, iPhone 14 Plus, iPhone 14 Pro, iPhone 14 Pro Max)

Pets in the People album in Photos surfaces individual pets in the album just like friends or family members

Photos Album widget lets you select a specific album from the Photos app to appear in the widget

Item sharing in Find My allows you to share an AirTag or Find My network accessory with up to five other people

Activity History in Home displays a recent history of events for door locks, garage doors, security systems, and contact sensors

Grid Forecast in Home shows when your electrical grid has cleaner energy sources available (Contiguous US only)

Grocery Lists in Reminders automatically group related items into sections as you add them

Inline PDFs and document scans in Notes are presented full-width, making them easy to view and mark them up

New Memoji stickers in Keyboard include Halo, Smirk, and Peekaboo

App Shortcuts in Spotlight Top Hit offer you app shortcuts to your next action when you search for an app

Redesigned Sharing tab in Fitness provides highlights of your friends’ activity like workout streaks and awards

Email or phone number sign-in lets you sign into your iPhone with any email address or phone number listed in your Apple ID account

New drawing tools in Freeform include a fountain pen, watercolor brush, ruler and more to create expressive boards

Crash Detection optimizations (iPhone 14, iPhone 14 Plus, iPhone 14 Pro, iPhone 14 Pro Max)

Some features may not be available for all regions or on all Apple devices. For more information, please visit this website:

https://www.apple.com/ios/ios-17

Some features may not be available for all regions or on all iPhone models. For information on the security content of Apple software updates, please visit this website:

Black-winged kite algorithm: a nature-inspired meta-heuristic for solving benchmark functions and engineering problems

• Open access
• Published: 23 March 2024
• Volume 57 , article number  98 , ( 2024 )

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• Jun Wang 1 ,
• Wen-chuan Wang   ORCID: orcid.org/0000-0003-1367-5886 1 ,
• Xiao-xue Hu 1 ,
• Lin Qiu 1 &
• Hong-fei Zang 1  

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This paper innovatively proposes the Black Kite Algorithm (BKA), a meta-heuristic optimization algorithm inspired by the migratory and predatory behavior of the black kite. The BKA integrates the Cauchy mutation strategy and the Leader strategy to enhance the global search capability and the convergence speed of the algorithm. This novel combination achieves a good balance between exploring global solutions and utilizing local information. Against the standard test function sets of CEC-2022 and CEC-2017, as well as other complex functions, BKA attained the best performance in 66.7, 72.4 and 77.8% of the cases, respectively. The effectiveness of the algorithm is validated through detailed convergence analysis and statistical comparisons. Moreover, its application in solving five practical engineering design problems demonstrates its practical potential in addressing constrained challenges in the real world and indicates that it has significant competitive strength in comparison with existing optimization techniques. In summary, the BKA has proven its practical value and advantages in solving a variety of complex optimization problems due to its excellent performance. The source code of BKA is publicly available at https://www.mathworks.com/matlabcentral/fileexchange/161401-black-winged-kite-algorithm-bka .

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1 Introduction

In recent years, due to resource scarcity and increasing demand from people (Feng et al. 2024 ), improving production efficiency has become a research hotspot (Zhao et al. 2023a , b ). As technology advances and problems become more complex, optimization tasks frequently exhibit multi-objective, large-scale, uncertain, and complicated traits to parse (Wan et al. 2023 ). In the real world, many problems have multiple optimization objectives and constraints, while traditional optimization algorithms (Inceyol and Cay 2022 ; Wang et al. 2022 ) are mainly designed for a single objective or a small number of objective issues (Atban et al. 2023 ; Hu et al. 2023 ; Wang et al. 2023a , b ). Traditional algorithms may not be able to accurately find the optimal solution when faced with these challenging optimization tasks, or the solving procedure may be overly complicated and time-consuming. Secondly, the search space for some problems is vast, and traditional optimization algorithms find it challenging to efficiently search for the optimal solution in this situation. In addition, once the problem involves uncertainty and fuzziness (Berger and Bosetti 2020 ), traditional optimization algorithms cannot handle it well. This is because conventional optimization algorithms are mainly based on deterministic assumptions and constraints. At the same time, there are always uncertainties and randomness in areas such as venture capital (Xu et al. 2023a , b ), supply chain management (Zaman et al. 2023 ), and resource scheduling (Al-Masri et al. 2023 ). Finally, traditional optimization algorithms typically rely on the analytical form of the problem, which requires the problem to be clearly defined and described in mathematical form (Kumar et al. 2023 ). In practical situations, it is often difficult to express the problem analytically, or the problem's objective function and constraint conditions are intricate (Wang et al. 2020 ). In summary, traditional optimization algorithms often cannot meet the needs and challenges of current optimization tasks.

In this context, meta-heuristic optimization algorithms (Fan and Zhou 2023 ) have rapidly developed due to their flexibility and gradient-free mechanisms. They have become essential tools for solving production efficiency improvement problems. The flexibility of meta-heuristic optimization algorithms enables them to adapt to diverse production environments and problem scenarios (Melman and Evsutin 2023 ). Meta-heuristic optimization algorithms can search and explore the problem space based on the characteristics of specific problems to find the best solution or a solution that comes close to the best one (Abdel-Basset et al. 2023a , b , c ). Whether facing problems such as product design, production planning, resource allocation, or supply chain management, meta-heuristic optimization algorithms can flexibly adjust and optimize according to actual situations.

Meanwhile, the meta-heuristic optimization algorithm also has the characteristic of no gradient mechanism (Liu and Xu 2023 ), which allows it to deal with problems without explicit gradient information or continuous derivatives. In many production environments, obtaining gradient information on the issues through analytical methods using traditional optimization methods is difficult. The meta-heuristic optimization algorithm utilizes local knowledge about the problem for optimization through heuristic search and random exploration. In addition to high-dimensional and nonlinear problems, this gradient-free optimization method is also appropriate for discrete and constraint-based problems (Boulkroune et al. 2023 ).

1.1 Meta-heuristic methods

An optimization algorithm based on a heuristic search is called a meta-heuristic optimization algorithm (Wang et al. 2023a , b ). They usually do not have any special requirements for the objective function but instead search by simulating intelligent behavior in nature (Chen et al. 2023 ) or other phenomena. They are more likely to find a globally optimal solution with a broader range of applications and a certain probability of escaping the local optimum. The characteristic of meta-heuristic optimization algorithms is their global solid search ability and robustness (Xu 2023a , b ; Zhao et al.  2023a , b ), which can find optimal solutions in large-scale, high-dimensional problems and quickly solve problems that do not exist or have not yet found polynomial time-solving algorithms. The classification diagram for the meta-heuristic optimization algorithm is shown in Fig. 1 . Meta-heuristic algorithms, which combine random algorithms with local algorithms to solve challenging optimization problems, are inspired by random phenomena in nature (Bingi, et al. 2023 ). They can be broadly classified into the following four types based on their various sources of inspiration:

Classification of metaheuristic algorithms

The algorithm is designed based on the behavioral characteristics of biological populations. These models simulate organisms' collective intelligence and collaborative strategies, enabling the rapid search of problem space and finding global optimal or better approximate solutions. Biologically inspired optimization models perform well in handling continuous and global search problems. Zamani et al. ( 2022 ) present a novel bio-inspired algorithm inspired by starlings’ behaviors during their stunning murmuration named Starling Murmuration Optimizer (SMO) to solve complex and engineering optimization problems as the most appropriate application of metaheuristic algorithms. The SMO introduces a dynamic multi-flock construction and three new search strategies: separating, diving, and whirling. Sand Cat Swarm Optimization (Seyyedabbasi and Kiani 2023 ) is a meta-heuristic algorithm based on sand cats' natural behavior. This algorithm was influenced by sand cats' capacity to recognize low-frequency noise. Due to its unique traits, the sand cat can find prey above and below ground. The Squirrel Search Algorithm (SSA) (Jain et al. 2019 ) is a single-objective optimization problem-solving heuristic algorithm based on the feeding habits of wild squirrels. This algorithm simulates the search strategy of squirrels when searching for food, gradually approaching the optimal solution by continuously adjusting the search position and range. To achieve the goal of optimization, Aquila Optimizer (AO) (Abualigah et al. 2021 ) primarily mimics eagles' behavior while capturing prey. It has strong optimization ability and fast convergence speed. The inspiration for the Sea Horse Optimizer (SHO) (Zhao et al. 2023a , b ) comes from the hippocampus's movement, predation, and reproductive behavior in nature. The foraging and navigational habits of African vultures served as the basis for the African Vultures Optimization Algorithm (AVOA) (Abdollahzadeh et al. 2021 ). Particle Swarm Optimization (PSO) (Kennedy and Eberhart 1995 ) is a search algorithm developed based on group collaboration by simulating the foraging behavior of bird flocks. The Chameleon Swarm Algorithm (CSA) (Braik 2021 ) models the chameleons' dynamic foraging behavior in and around trees, deserts, and swamps. The Mayfly Algorithm (MA) (Zervoudakis and Tsafarakis 2020 ) is inspired by the mayflies' flight behavior and mating process. Wild horses' lives and behaviors inspired the Wild Horse Optimizer (WHO) (Naruei and Keynia 2022 ). Spider Wasp Optimizer (SWO) (Abdel-Basset et al. 2023b ) is proposed based on female spider wasps' hunting, nesting, and mating behavior. The Coati Optimization Algorithm (COA) (Dehghani et al. 2022 ) is inspired by coatis. The grey wolf's social structure and hunting strategies served as the basis for the Grey Wolf Optimization (GWO) algorithm (Mirjalili et al. 2014 ). The Marine Predators Algorithm (MPA) (Faramarzi et al. 2020a , b ) draws inspiration from the prey-hunting Brownian and Lévy movements of marine predators. The Ant Lion Optimizer (ALO) (Mirjalili 2015 ) is modeled after how ants navigate between their nests and food in their natural behavior. The humpback whales' bubble net hunting techniques and natural behavior served as the basis for the Whale Optimization Algorithm (WOA) (Mirjalili and Lewis 2016 ). The Dandelion Optimizer (DO) (Zhao et al. 2022 ) was proposed to simulate the process of dandelion seeds flying over long distances by wind. This algorithm considers two main factors, wind speed, and weather, and introduces Brownian motion and Levi flight to describe the seed's motion trajectory. Golden Jackal Optimization (GJO) (Chopra and Ansari 2022 ) is inspired by the cooperative hunting behavior of golden jackals in nature.

Algorithms abstracted from human behavior or social phenomena. These models have strong learning ability and adaptability and have demonstrated excellent performance in image recognition and natural language processing fields. The Volleyball Premier League (VPL) (Moghdani and Salimifard 2018 ) is inspired by the rivalry and interaction between various volleyball teams throughout the season. The social learning behavior of humans arranged in families in the social environment is the basis for the Social Evolution and Learning Optimization (SELO) (Kumar et al. 2018 ) algorithm. The inspiration for Social Group Optimization (SGO) (Satapathy and Naik 2016 ) comes from social group learning. The inspiration for the Cultural Revolution Algorithm (CEA) (Kuo and Lin 2013 ) comes from the process of social transformation. Hunter Prey Optimization (HPO) (Naruei et al. 2021 ) is inspired by the process of animal hunting. The inspiration for the IbI Logic Algorithm (Azizi et al.) (Mirrashid and Naderpour 2023 ) comes from thinking about brain logic.

Inspired by genetic evolution algorithms. These models can handle discrete and multi-objective optimization problems and have strong robustness and global search ability for complex issues. Gene Expression Programming (GEP) (Sharma 2015 ) aims to use gene expression programming to simulate the mathematical expression relationship between data points in a set of data points based on the laws of genetic inheritance, the idea of natural selection, survival of the fittest, and elimination of the best. The population is constantly evolving to find the most suitable chromosome. The processes of how species move from one island to another, how new species appear, and how species go extinct are the inspirations for Biogeography-Based Optimization (BBO) (Simon 2008 ) and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) (Hansen and Kern 2004 ). The inspiration for Symbiotic Organisms Search (SOS) (Cheng and Prayogo 2014 ) comes from symbiotic phenomena in biology. The inspiration for Evolution Strategies (ES) (Beyer and Schwefel 2002 ) comes from biological evolution. Genetic programming is inspired by natural selection (GP) (Koza 1992 ).

Algorithms abstracted from physical properties or chemical reactions as inspiration. These models can jump between multiple local optimal solutions and find global optimal solutions by simulating the characteristics of physical phenomena and optimizing search strategies. The Kepler Optimization Algorithm (KOA) (Abdel-Basset et al. 2023a , b , c ) is a physics-based meta-heuristic algorithm that predicts the position and motion of planets at any given time by Kepler's laws of planetary motion. Energy Valley Optimizer (EVO) (Azizi et al. 2023 ) is a brand-new meta-heuristic algorithm that draws inspiration from physical theory's various particle decay modes and stability laws. Light Spectrum Optimizer (LSO) (Abdel-Basset et al. 2022 ) is a new physics-inspired meta-heuristic algorithm that generates meteorological phenomena of colored rainbow spectra inspired by the dispersion of light at different angles when passing through raindrops. Rime Optimization Algorithm (RIME) (Su et al. 2023 ), which constructs a soft time search strategy and a hard time puncture mechanism, simulates ice's soft time and hard time growth processes and achieves exploration and development behavior in optimization methods. Multi-verse Optimization (MVO) (Mirjalili et al. 2016 ) is inspired by the fact that the universe has an expansion rate, utilizing the principle that white holes have higher and black holes have a lower expansion rate. The particles in the universe search through the principle of transferring from white spots to black holes through wormholes. The control volume mass balance model, used to estimate dynamic and equilibrium states, is the primary source of inspiration for the Equilibrium Optimizer (EO) (Faramarzi et al. 2020a , b ).

1.2 Related work

In this section, we discussed some recent work.

Banaie-Dezfouli et al. ( 2023 ) introduce an improved binary GWO algorithm called the extreme value-based GWO (BE-GWO) algorithm. This algorithm proposes a new cosine transfer function (CTF) to convert continuous GWO into binary form. Then, it introduces an extreme value (Ex) search strategy to improve the efficiency of converting binary solutions. Nama et al. ( 2023 ) propose a new ensemble algorithm called e-mPSOBSA with the reformed Backtracking Search Algorithm (BSA) and PSO. Chakraborty et al. ( 2022 ) suggest an enhanced SOS algorithm called nwSOS to resolve higher dimensional optimization issues. Nama and Saha ( 2022 ) introduce an improved BSA (ImBSA) based on multi-group methods and modified control parameter settings to understand the collection of various mutation strategies. Nama ( 2021 ) proposes an improved form of SOS to establish an increasingly stable balance between discovery and activity cores. This technology uses three unique programs: adjusting benefit factors, changing parasitic stages, and searching based on random weights. To achieve the best DE efficiency, Nama and Saha ( 2020 ) proposed a new version of the DE algorithm to control parameters and mutation operators, making appropriate adjustments to time-consuming control parameters. Nama ( 2022 ) offers a new quasi-reflective slime mold (QRSMA) method that combines the SMA algorithm with a reflective learning mechanism (QRBL) to improve the performance of SMA. Nama, Sharma et al. ( 2022a , b ) proposed an improved BSA framework called gQR-BSA, which is based on quasi-reflection initialization, quantum Gaussian mutation, adaptive parameter execution, and quasi-reflection hopping to change the coordinate structure of BSA. This algorithm adopts adaptive parameter settings, Lagrange interpolation formulas, and a new local search strategy embedded in Levy flight search to enhance search capabilities and better balance exploration and development. Nadimi-Shahraki et al. ( 2023a , b ) wrote a review of Whale optimization algorithms, systematically explaining the theoretical basis, improvement, and mixing of WOA algorithms. Sharma et al. ( 2022a , b ) proposed a new variant of BOA, mLBOA, to improve its performance. Sahoo et al. ( 2023 ) propose an improved dynamic reverse learning-based MFO algorithm (m-DMFO) combined with an enhanced emotional reverse learning (DOL) strategy. Sharma et al. ( 2022a , b ) propose a hybrid sine cosine butterfly optimization algorithm (m-SCBOA), which combines the improved butterfly optimization algorithm with the sine cosine algorithm to achieve excellent exploratory and developmental search capabilities. Chakraborty et al. ( 2023 ) have proposed a hybrid slime mold algorithm (SMA) to address the issues above and accelerate the exploration of natural slime molds. Nadimi-Shahraki et al. ( 2023b ) have developed an enhanced moth flame optimization algorithm called MFO-SFR to solve global optimization problems. Zamani et al. ( 2021 ) propose a novel DE algorithm named Quantum-based Avian Navigation Optimizer Algorithm (QANA) inspired by the extraordinary precision navigation of migratory birds during long-distance aerial paths. In the QANA, the population is distributed by partitioning into multiple flocks to explore the search space effectively using proposed self-adaptive quantum orientation and quantum-based navigation consisting of two mutation strategies, DE/quantum/I and DE/quantum/II. Nama et al. ( 2022a , b ) proposes a new integrated technology called e-SOSBSA to completely change the degree of intensification and diversification, thereby striving to eliminate the shortcomings of (Wolpert and Macready 1997 )traditional SOS.

1.3 Motivation of the work

It should be noted that no algorithm can find comprehensive solutions for every problem. As the 'No Free Lunch' (NFL) theorem reasonably indicates, no meta-heuristic algorithm is superior in solving every optimization problem. In other words, a specific meta-heuristic algorithm may achieve excellent results on particular issues but may not perform as well on other types of problems. With the continuous progress of technology and the increasing complexity of problems, some traditional algorithms cannot effectively solve these problems. After reviewing relevant literature, we found that many algorithms have limitations, including insufficient search ability, difficulty in converging to the global optimal solution, etc. These shortcomings have had a certain impact on the performance of the algorithm. We have been prompted to propose an updated and more powerful algorithm to overcome these limitations of existing algorithms and seek more effective solutions. After careful consideration, we have introduced an intelligent optimization algorithm inspired by the black-winged kite. We chose black-winged kites as our source of inspiration because they exhibit high adaptability and intelligent behavior in attack and migration. This inspired us to develop an algorithm to better cope with complex problems. Therefore, the above reasons have become the main driving force behind our research.

1.4 Contribution and innovation to the work

The contribution and innovation of this article are as follows:

The proposed Black Winged Kite Algorithm (BKA) lies in its unique biological heuristic features, which not only capture the flight and predatory behavior of black winged kites in nature, but also deeply simulate their high adaptability to environmental changes and target positions. The imitation of this biological mechanism provides the algorithm with robust dynamic search capabilities, enabling it to effectively cope with changing optimization environments.

In the black winged kite algorithm, we first introduced the Cauchy mutation strategy, which is a probability distribution strategy that helps the algorithm jump out of local optima and increases the probability of discovering better solutions in the global search space. This strategy improves the performance of the algorithm in discovering global optimal solutions and provides new solutions for high-dimensional complex optimization problems.

We have integrated a leadership strategy that mimics the leadership role of leaders in the kite community, ensuring that the algorithm can effectively utilize the current best solution and guide the search direction. This method not only helps to enhance the efficiency of the algorithm in utilizing the current search area, but also effectively balances the dynamics between exploration and utilization, ensuring that potential competitive new areas are not overlooked in the pursuit of optimal solutions.

The remainder of this research is structured as follows: The second section introduces the Black-winged kite's attack strategy and migration behavior (Wu et al. 2023 ) and develops a mathematical model based on them. The third section analyzes 59 benchmark functions and the test results. Five real-world engineering cases are presented in the fourth section, and the outcomes are examined. This article is summarized, and prospects are suggested in the fifth section.

2 The black-winged kite algorithm (BKA)

In this section, a naturally inspired algorithm called the BKA is proposed.

2.1 Inspiration and behavior of black-winged kites

The black-winged kite is a small bird with a blue gray upper body and a white lower body. Their notable features include migration and predatory behavior (Ramli and Fauzi 2018 ). They feed on small mammals, reptiles, birds, and insects, possess strong hovering abilities, and can achieve extraordinary hunting success(Wu et al. 2023 ). Inspired by their hunting skills and migration habits, we established an algorithm model based on black-winged kites.

2.2 Mathematical model and algorithm

The development of the BKA algorithm as a simple and effective meta-heuristic optimization method is illustrated in this section. We modeled the migration and attack stages of the proposed BKA based on the Black-winged kite's attack strategy and migration behavior. In Fig. 2 , the pseudo-code of BKA is presented. This pseudocode clearly describes the execution process of the BKA algorithm. It provides steps and operations to solve specific problems and optimizes the results through iteration and adjustment.

Pseudocode of BKA

a Black-winged kite hovering in the air, b The Black-winged kite rushed towards its prey at great speed

2.2.1 Initialization phase

In BKA, creating a set of random solutions is the first step in initializing the population. The following matrix can be used to represent the location of every Black-winged kite (BK):

where pop is the number of potential solutions, dim is the size of the given problem's dimension, and BK ij is the j th dimension of the i th Black-winged kite. We are distributing the position of each Black-winged kite uniformly.

where i is an integer between 1 and pop, where BK lb and BK ub are the lower and upper bounds of i th Black-winged kites in the j th dimension, respectively, and the rand is a value chosen at random between [0, 1].

In the initialization process, BKA selects the individual with the best fitness value as the leader X L in the initial population, which is considered the optimal location of the Black-winged kites. Here is the mathematical representation of the initial leader X L using the minimum value as an example.

2.2.2 Attacking behavior

As a predator of small grassland mammals and insects, black-winged kites adjust their wings and tail angles according to wind speed during flight, hover quietly to observe prey, and then quickly dive and attack. This strategy includes different attack behaviors for global exploration and search. Figure 3 a shows a scene of a black-winged kite hovering in the air, spreading its wings and maintaining balance. Figure 3 b shows the scene of the black-winged kite rushing towards its prey at an extremely fast speed. Figure 4 a shows the attack state of the black-winged kite as it hovers in the air, while Fig. 4 b shows the state of the black-winged kite as it hovers in the air. The following is a mathematical model for the attack behavior of black-winged kites:

Two attack strategies of Black-winged kites are a hovering in the air, waiting for attack, and b hovering in the air, searching for prey

The following is a definition of the characteristics of Eqs. ( 5 ) and ( 6 ):

y i, j t and y i, j t + 1 represent the position of the i th Black-winged kites in the j th dimension in the t and ( t  + 1) th iteration steps, respectively.

r is a random number that ranges from 0 to 1, and p is a constant value of 0.9.

T is the total number of iterations, and t is the number of iterations that have been completed so far.

2.2.3 Migration behavior

Bird migration is a complex behavior influenced by environmental factors such as climate and food supply (Flack, et al. 2022 ). Bird migration is to adapt to seasonal changes, and many birds migrate south in winter from the north to obtain better living conditions and resources (Lees and Gilroy 2021 ). Migration is usually led by leaders, and their navigation skills are crucial to the success of the team. We propose a hypothesis based on bird migration: if the fitness value of the current population is less than that of the random population, the leader will give up leadership and join the migratory population, indicating that it is not suitable to lead the population forward (Cheng, et al. 2022 ). On the contrary, if the fitness value of the current population is greater than that of the random population, it will guide the population until it reaches its destination. This strategy can dynamically select excellent leaders to ensure a successful migration. Figure 5 shows the changes in the leading bird in the migration process of black-winged kites. The following is a mathematical model for the migration behavior of black-winged kites:

The strategic changes of Black-winged kites during migration Pseudocode of BKA

The attributes of Eqs. ( 7 ) and ( 8 ) are defined as follows:

L j t represents the leading scorer of the Black-winged kites in the j th dimension of the t th iteration so far.

F i represents the current position in the j th dimension obtained by any Black-winged kite in the t iteration.

F ri represents the fitness value of the random position in the j th dimension obtained from any Black-winged kites in the t iteration.

C (0,1) represents the Cauchy mutation (Jiang, et al. 2023 ). The definition is as follows:

A one-dimensional Cauchy distribution is a continuous probability distribution with two parameters. The following equation illustrates the probability density function of the one-dimensional Cauchy distribution:

When δ  = 1, μ  =  0, its probability density function will become the standard form. The following is the precise formula:

2.3 The balance and diversity analyses

Maintaining a good balance between global and local search is an important factor in optimizing algorithms to find the optimal solution, which involves exploring and developing the search space. In this process, it is necessary to balance the proportion of global search and local search to ensure that the algorithm does not prematurely mature and can find the best solution. To better balance these issues, this algorithm uses parameter p to control different attack behaviors. At the same time, the variable n set in this article will decrease nonlinearly with the increase of iteration times, which can control the algorithm to shift from a global search algorithm to a local search, enabling it to find the optimal solution faster and avoid falling into local optimal solution, to better solve practical problems.

Diversity is very important in intelligent optimization algorithms, as it helps to avoid the population falling into local optima and provides a wide search range, increasing the chances of the algorithm discovering global optima. Like most intelligent optimization algorithms, the individuals in the initial population of this article are randomly generated within a given range, which results in certain differences in the positions and eigenvalues of each individual, thus giving the individuals in the population a certain degree of diversity and better exploration of the solution space. Meanwhile, during the iteration process of the algorithm, the application of the Cauchy strategy and the reasonable setting of parameters improve the diversity of the algorithm, improve its global search ability, and avoid falling into local optima.

2.4 Computational complexity

We can assess the time and space resources needed for algorithms to handle large-scale problems using computational complexity, a crucial indicator of algorithm efficiency. To better understand the effectiveness and viability of the proposed BKA algorithm, we will conduct a thorough analysis of the time and spatial complexity of the algorithm in this section.

2.4.1 Time complexity

The BKA algorithm initializes a set of potential solutions during initialization, which will be used for further search and optimization. The initialization method selected, as well as the size of the problem, typically determine how time-consuming the initialization process is. The number of candidate solutions or the size of the problem, denoted by M , determines the computational complexity of the initialization procedure in this article, which is O  ( M ). This process involves generating initial solutions, determining parameter settings, and initializing other necessary operations. This initialization process needs to be executed once before starting the algorithm. Second, one of the crucial components of the BKA algorithm, which is used to assess the effectiveness and quality of potential solutions, is fitness evaluation. The issues considered and the particular evaluation method determine how complicated the fitness assessment process is. For specific problems, fitness assessment involves complex computational or simulation techniques with a time complexity of O  ( T  ×  M ) +  O  ( T  ×  M  ×  D ), where T is the maximum number of iterations and D is the specific problem's dimension. Finally, updating the Black-winged kite is a critical step in the BKA algorithm, which generates new candidate solutions based on the current key and neighborhood search. The neighborhood search difficulty and the update strategy employed determine the difficulty of updating Black-winged kites. Therefore, the runtime complexity of the BKA is O ( M  × ( T  +  T  ×  D  + 1)).

2.4.2 Space complexity

The spatial complexity of the BKA algorithm refers to the additional storage space required during algorithm operation. Let's analyze the spatial complexity of the BKA algorithm. The spatial complexity of the BKA algorithm is relatively low. The primary space consumption comes from storing candidate solutions and related intermediate results and temporary variables. Specifically, BKA algorithms typically only need to store the current best solution, candidate solutions, and some data structures related to the search and optimization process. In the most straightforward implementation, the spatial complexity of the BKA algorithm is approximately O  ( M ), where M represents the number of candidate solutions or the size of the problem. This is because the algorithm needs to allocate storage space for each candidate solution and update and compare it during iteration. In addition, additional storage space is needed to store other auxiliary variables and intermediate results. It should be noted that the BKA algorithm's spatial complexity can change depending on the particulars of the problem and its implementation. The spatial complexity may increase if more complex data structures or intermediate result storage are used in the algorithm.

3 Experimental results and discussion

This section conducts simulation studies and assesses the effectiveness of BKA in optimization. The experiments are conducted on MATLAB R2022b with a 3.20 GHz 64 bit Core i9 processor and 16 GB of main memory.

3.1 The benchmark set and compared algorithms

The ability of BKA to handle a variety of objective functions is tested in this article using 59 standard benchmark functions, including 18 benchmark functions, the CEC-2017 test set (Wu et al. 2016 ), and the CEC-2022 test set (Yazdani et al.  2021 ). The test results are compared with those of well-known algorithms like MVO, SCA, GWO, MPA, RIME, ALO, WOA, STOA, DO, GJO, PSO, AVOA, SHO, SCSO, SSA, AO, COA, etc. to assess the quality of the best solution offered by BKA. These algorithms' control parameters are all set to the values the algorithm proposer suggested. Three evaluation functions are also mentioned to analyze the algorithm's performance thoroughly: average (Avg), standard deviation (Std), and ranking.

(1) The definition of standard deviation is as follows:

(2) Ranking: ranking depends on the average fitness value of the algorithm. The algorithm is ranked higher when the average value is lower.

3.2 Sensitivity analysis

In this section, experiments and analysis are conducted based on the algorithm's internal parameters. The key internal parameters of the BKA algorithm are discussed and analyzed to determine the optimality and rationality of the key parameters of the proposed algorithm. In this section, when the attack mechanism takes effect, we will change the parameter p in Sect. 2.2.2 . This parameter is used to control the switching between two attack behaviors and is an important parameter that affects the overall accuracy and stability of the algorithm. Set the parameter p to 0.3, 0.5, and 0.7 for experiments and compare it with the original parameter p  = 0.9 to show the impact of parameter changes on BKA performance in the mechanism. The comparative experiment was conducted within a unified evaluation framework, with the same number of 30 populations and 30 independent runs. The experimental results are shown in Tables 1 and 2 .

From Table 1 , we can see that for the CEC-2017 test set, BKA achieved the best results among 21 functions at parameter p  = 0.9, achieved the same optimal results as p  = 0.7 on F23, and did not achieve the best results on only 7 functions. From Table 2 , we can see that for the CEC-2022 test set, BKA achieved the best results among 7 functions at parameter p  = 0.9, achieved the same optimal results as p  = 0.5 on the F3 function, achieved the same optimal results as p  = 0.7 on the F4 function, and achieved the same optimal results as p  = 0.5 and p  = 0.3 on the F12 function. Only two functions did not achieve the optimal results. Through a comprehensive analysis of Tables  1 and 2 , we believe that the BKA algorithm can achieve better results in processing optimization when the parameter p  = 0.9.

3.3 The results of the algorithm on different test sets

This section used several test sets to gauge how well the recently created meta-heuristic algorithm BKA handled global optimization issues.

3.3.1 Evaluation of 18 functions and qualitative analysis

This test set includes both unimodal and multimodal functions to thoroughly assess the performance of the BKA algorithm (Xie and Huang 2021 ). The unimodal function (F1–F9) in this test set is a function with a globally optimal solution used to verify the efficacy of the optimization algorithm. Multimodal functions (F10–F18) have many local extremum values used to assess the algorithm's exploratory power. Tables 3 and 4 provide detailed information on 18 test functions. The results of all algorithms were obtained using 30 search agents with 500 iterations and 10 independent runs.

Table 5 shows the results of BKA and the comparison algorithm on 18 test functions. The value of Avg determines the ranking in Table 5 ; the lower the value, the higher the ranking. In Figs. 6 and 7 , where the vertical axis denotes the fitness value and the horizontal axis the number of iterations, the convergence curves of BKA and other optimization algorithms at dimension 10 are contrasted. In unimodal functions, BKA exhibits an advantage over other F1, F3, and F4 algorithms, even surpassing other algorithms by tens of orders of magnitude. However, in F2, F5, and F9, the advantage of BKA is not as apparent as before. In F6, the RIME algorithm has a weak advantage over BKA; in F7 and F8, the WOA algorithm is slightly better than BKA. Although BKA did not achieve the optimal value on all unimodal functions, compared to the optimal algorithm, the difference between BKA and the optimal algorithm is minimal in those functions where BKA did not achieve the optimal solution. It should be emphasized that although BKA has significant advantages in some unimodal functions, its performance is not entirely dominant compared to other algorithms. This means that in specific problem domains and function types, other algorithms still have competitiveness and similar performance. The BKA algorithm achieved the theoretical optimal value of 0 on F10, F11, F13, F15, and F17 in multimodal functions. On F12 and F18, the BKA algorithm achieved results similar to those of other algorithms. While other algorithms are stuck in local optima for F14 and F16, the BKA algorithm still achieves excellent results. These findings show that the BKA algorithm performs well regarding global search and optimization when dealing with multimodal functions. In most multimodal functions, the BKA algorithm can accurately find the theoretical optimal value, demonstrating its powerful effect in global optimization. The BKA algorithm's results in functions F12 and F18 are comparable to those of other algorithms, but they still exhibit the BKA algorithm's effectiveness and robustness in handling complex problems. In contrast to other algorithms, the BKA algorithm can avoid hitting local optima and produce results close to the ideal outcome.

Convergence analysis of the proposed BKA and competitor algorithms in unimodal functions in dimension 10

Convergence analysis of the proposed BKA and competitor algorithms in multimodal functions in dimension 10

Figure 8 shows the search surface graph of the benchmark function, the historical search process of BKA, the average convergence curve of fitness values, and the average convergence curve. The first column displays the search space of each algorithm, and observing the search surface of the search space can provide a more precise and intuitive understanding of the characteristics of the function. The graph shows that F1, F2, and F8 have only one extreme value, while F12, F13, and F17 have multiple extreme values. The second column depicts the historical search process of BKA on a global scale, where the red dots represent the positions of the optimal individuals in each generation of BKA, and the blue dots represent the positions of ordinary individuals. Observing the images of the historical search process makes it possible to gain a more intuitive understanding of the distribution of BKA and the changes in individual positions during the iteration process. The intermediate fitness image of BKA represents the average target optimal values of all dimensions during each iteration process in the third column, which also shows the average trend of the population's evolution. The average fitness value of the BKA algorithm exhibits strong oscillations in the early iterations, which gradually weaken and tend to flatten out, as seen in the images. This reveals that the BKA algorithm has been fully explored in its early stages and extensively searched and optimized globally.

Search space , search history, average fitness, and convergence curve of BKA algorithm

Meanwhile, in the later stages of the iteration, we can also observe significant short-term oscillations. This reflects the BKA algorithm's continuous attempts to jump out of the local optimal value in the later stage to find higher accuracy and better solutions. This short-term oscillation indicates that the BKA algorithm has a certain degree of convergence and continuously strives to improve the quality of the key in the later stages. Overall, the BKA algorithm exhibits a strategy of exploration before development during the optimization process. The algorithm uses large oscillation amplitudes in the early stages to identify potential optimization directions. In the later stage, the BKA algorithm focuses more on fine-tuning and optimization, constantly trying to jump out of the local optimal solution to converge to higher accuracy and better results. The fourth column displays an image of the average convergence curve, which shows the optimal solution obtained by the BKA algorithm throughout the entire iteration process. The multimodal function curve decreases gradually during convergence, while the unimodal function curve rapidly decreases as the number of iterations rises. The ability of the BKA algorithm to quickly exit the local extremum and gradually inch closer to the global optimal value during the optimization process is reflected in this trend.

3.3.2 Evaluation of the CEC-2017 suite test

The CEC-2017 suite is chosen as the testing project in this experiment to gauge BKA's effectiveness in resolving optimization issues. The CEC-2017 set contains four different kinds of benchmark functions. It should be noted that the instability of the F2 function may lead to unpredictable optimization results, resulting in uncertain and inconsistent results when evaluating algorithm performance. The decision-maker decides to eliminate the F2 function from the CEC-2017 test suite to guarantee the test set's validity and consistency. The search domain for all functions in this test suite is [− 100, 100], and each test function has ten dimensions. The simulation results of all algorithms are obtained using 30 search agents with 1000 iterations and 10 independent runs.

In calculating the CEC-2017 test set, the outcomes of our algorithm and the comparison algorithm are shown in Table 6 , with the best effect denoted in bold. From the data in Table 6 , it can be concluded that in the 29 test functions of CEC-2017, the BKA algorithm achieved 21 optimal results, accounting for 72.4%, surpassing the other eight algorithms. A typical statistical chart in the field of statistics is the box plot. Its resemblance to a box's shape led to its name. The box chart can calculate the degree of dispersion of univariate data and clearly and intuitively display the degree of dispersion and distribution interval while highlighting abnormal data values. The box's upper and lower boundaries correspond to the upper and lower quartiles of the data, respectively, and the box's median represents the middle point of the data. The shorter the length of the box, the more concentrated the data. The longer the box length, the more scattered the data, and the worse the stability. Figure 9 shows the box plots of the BKA algorithm and its comparison algorithm on F3, F8, F9, F10, F14, F15, F20, and F26. By observing the chart, we can draw some conclusions. Firstly, the box plot shows that BKA, GJO, PSO, AVOA, and SHO algorithms have almost no outliers, indicating their high stability. This means that on these benchmark functions, the performance of these algorithms is relatively consistent, without significant performance fluctuations or anomalies. Secondly, by observing the box length, we can see that the box length of the BKA algorithm is shorter and at a lower position. This means that the BKA algorithm has a slight difference in the solution set on these benchmark functions, which means its solution accuracy is relatively high. Firstly, the box plot shows that BKA, GJO, PSO, AVOA, and SHO algorithms have almost no outliers, indicating their high stability. This means that on these benchmark functions, the performance of these algorithms is relatively consistent, without significant performance fluctuations or anomalies. Secondly, by observing the box length, we can see that the box length of the BKA algorithm is shorter and at a lower position. As a result, the BKA algorithm's solution set difference for these benchmark functions is minimal, demonstrating a high level of solution accuracy.

Boxplot of different algorithms on partial functions of CEC-2017 in dimension 10

The heat map is a graphical representation based on color coding, which represents the size of data through the strength, depth, and different colors of colors, allowing readers to have a more intuitive understanding of the correlations and trends between data. In Fig. 10 , the darker the color, the greater the error of the algorithm. The figure indicates that all algorithms perform poorly for functions F1, F2, F12, F13, F15, F18, F19, and F30, indicating that these functions are relatively difficult. In addition, the SSA algorithm has significant errors in most functions, proving that its performance is weak and cannot effectively solve these problems. Figure 11 shows the total running time of each algorithm on the CEC-2017 test set. Observing the graph, it can be seen that the running time of the BKA algorithm is at a relatively high level, with a difference of no more than 20 s compared to the PSO with the shortest running time. However, it is encouraging to note that in this test set, the performance of the BKA algorithm is significantly better than that of PSO and GJO. This indicates that although the BKA algorithm has a slightly longer runtime, it performs well.

The error performance of different algorithms on the CEC-2017 test set

The total running time of BKA and its comparison algorithm on CEC-2017

3.3.3 Evaluation of the CEC-2022 objective functions

This section further conducts experiments on the algorithm using the most recent CEC-2022 test set to highlight the uniqueness and superiority of the BKA algorithm. The CEC-2022 set includes four different kinds of benchmark functions. In the CEC-2022 test suite, the search domain for all functions is [− 100, 100]. The CEC-2022 test set provides an updated test set and evaluation metrics aimed at comprehensively evaluating the performance of optimization algorithms. We can better understand its performance in the latest environment by comparing the BKA algorithm with the previously mentioned algorithms. The simulation results of all algorithms are obtained using 30 search agents with 1000 iterations and 10 independent runs.

Table 7 shows that the BKA algorithm outperformed the other eight algorithms by achieving 8 out of the 12 test functions with the best results, or 66.7% of the total. Figure 12 shows that the results of BKA, GJO, PSO, and AVOA perform well on F1, but all have outliers, indicating that the performance of these algorithms is relatively high but not stable enough. Other algorithms perform very well in functions F2 and F6 except for SSA. In Fig. 13 , it can be seen that BKA performs stably on all functions, proving that BKA is robust. However, SSA performs poorly in various functions and cannot handle these challenging tasks. According to the results shown in Fig. 14 , we can observe the error situation of different algorithms. We can see large areas of high error, especially in the color distribution of heat maps for F1 and F6 functions. This indicates that these algorithms typically perform poorly on these specific functions. This indicates that these two functions pose substantial challenges for algorithms, and optimizing these functions is a relatively complex task for most algorithms. The graph shows that, aside from the SSA and COA algorithms, the performance of other algorithms is generally reasonable. They can achieve lower error levels when processing F1 and F6 functions, demonstrating relatively good performance. Figure 15 shows the total running time of each algorithm on the CEC-2022 test set. Observing the graph, it can be seen that the running time of the BKA algorithm is at a relatively high level, with a difference of no more than 10 s compared to the PSO with the shortest running time. This indicates that although the BKA algorithm has a slightly longer runtime, it performs well.

Box plots of different algorithms on the CEC-2022 test set (F1–F6)

Box plots of different algorithms on the CEC-2022 test set (F7–F12)

The error performance of different algorithms on the CEC–2022 test set

The total running time of BKA and its comparison algorithm on CEC–2022

In summary, the reasons why the BKA algorithm can achieve the best results are as follows: The BKA algorithm adopts the Cauchy distribution strategy and has a strong global search ability. Through the global search strategy, the BKA algorithm is highly likely to discover the global optimal solution. The BKA algorithm introduces a leader strategy. By selecting individuals with high fitness values as leaders, others learn and improve the solution through interaction with the leader.

3.4 Nonparametric statistical analysis

To comprehensively evaluate the performance of BKA, we chose to use the Wilcoxon sign rank test and Friedman test to test BKA and its comparison algorithm. Wilcoxon signed-rank test is a non-parametric test method used to compare two sets of related samples. Its main function is to determine whether there is a significant difference in the median between two related samples. This method can be used to test whether the difference in the median between two sets of related samples is significant. The Friedman test is a non-parametric test used to compare multiple sets of related samples. Its main function is to determine whether there is a significant difference in the median of multiple sets of related samples, which can be used to test whether there is a significant difference in the median of multiple sets of related samples.

Tables 8 and 9 list the results of Wilcoxon testing for different algorithms on different test sets, all of which are based on a 95% significance level (α = 0.05). In Tables 8 and 9 , the symbol " + " indicates that the reference algorithm performs better than the comparison algorithm, the symbol "−" indicates that the reference algorithm is not as good as the comparison algorithm. The symbol " = " indicates no difference in significance between the reference and comparison algorithms. By observing the last row in the table, we can conclude that the BKA algorithm has a smaller number of '-,' while there are more ' + ' and ' = '. This indicates that, in most cases, the performance of the BKA algorithm is not weaker than that of the comparison algorithm. Tables 10 and 11 list the Friedman test rankings and average rankings of different algorithms on different test sets. By observing Tables  10 and 11 , we can see that the BKA algorithm ranks first in most benchmark functions and first in average rankings. These statistical data demonstrate the BKA algorithm's excellent performance on a single benchmark function but, more importantly, by evaluating its overall performance, its practicality in multiple optimization problems can be more reliably evaluated.

3.5 Effectiveness analysis

The overall effectiveness (OE) of the BKA algorithm and other contender algorithms are computed by Eq. ( 12 ) and reported in Table 12 , where the parameter N is the total number of test functions, and L i is the number of test functions in which the i -th algorithm is a loser (Nadimi-Shahraki and Zamani 2022 ). From Table 12 , it can be seen that BKA demonstrated its effectiveness with 70.7% excellent results on the CEC-2017 and CEC-2022 test sets, far surpassing other comparative algorithms.

3.6 Limitation analysis

Although BKA has achieved good results in dealing with optimization problems, it cannot be ignored that this algorithm still has some shortcomings, which can be summarized as follows: this algorithm has not achieved optimal results in solving specific types of optimization problems and has shown insufficient stability in multiple runs. Specifically, the insufficient stability of the algorithm may be due to the uneven distribution of initial parameters, resulting in the search strategy exhibiting variation in multiple runs. In addition, when dealing with complex problems with high-dimensional search spaces, the algorithm may experience premature convergence or repeated convergence during the iteration process, reducing the consistency of the results. Meanwhile, although slightly superior in performance, BKA's running speed is relatively low, which may become a disadvantage in application scenarios that require fast iteration. To improve these limitations, it is recommended to further adjust the initial value distribution, optimize the exploration and utilization mechanism, and consider algorithm acceleration strategies in subsequent research in order to improve the stability and efficiency of the algorithm and better adapt to various complex optimization problems.

4 BKA for solving engineering problems

This section evaluates how well BKA performed in resolving five elaborate engineering design issues: the design of a tension/compression spring, a pressure vessel, a welded beam, a speed reducer, and a three-bar truss design issue. These well-known engineering problems contain numerous equality and inequality constraints, and the ability of BKA to optimize real-world and constrained problems is evaluated from the perspective of constraint processing. Here, the constrained issues are transformed into unconstrained problems using a straightforward method of the death penalty.

Solving constrained optimization problems is a crucial task in both optimization theory and applications. There are numerous methods for processing constraints, including operators, decoder functions, representations that preserve feasibility, repair algorithms, and penalty functions. Constrained optimization issues are typically solved using the penalty function method, a popular technique from optimization theory. The objective of the penalty function approach is to introduce a penalty function that transforms the constraint conditions into a component of the objective function, thereby changing the original constraint problem into an unconstrained one. Without considering constraints, the ideal answer to the original issue can be found by modifying the shape and parameters of the penalty function. This study resolves these practical engineering issues using the penalty function method.

4.1 Pressure vessel design

This engineering challenge aims to reduce the cost of producing cylindrical pressure vessels while meeting four constraints. This problem's resolution can be mathematically stated as follows:

Consider variable \(H = [h_{1} ,h_{2} ,h_{3} ,h_{4} ] = [T_{s} ,T_{h} ,R,L]\)

Variables range \(0 \le h_{j} \le 100,j = 1,2\) ,  \(10 \le h_{j} \le 200,j = 3,4\)

BKA has optimized this issue. BKA can obtain the optimal function value \(f(H) = 5887.364927\) with the structure variables \(H \, = \, (0.778433,0.384690,40.319619,200)\) . Table 13 displays the optimal values and variables that BKA and its comparison algorithm arrived at, demonstrating how well the algorithm resolved this issue. The algorithm performs better when the numerical value is lower. The results indicate that BKA has discovered a new structure that can achieve lower manufacturing costs than other structures.

4.2 Design issue with tension/compression springs

This engineering challenge aims to reduce the coil's weight while meeting three criteria. These limitations ensure the coil design adheres to certain engineering limitations and requirements. We can use the following mathematical expression to explain this issue:

Consider variable \(H = [h_{1} ,h_{2} ,h_{3} ] = [d,D,N]\)

Variables range  \(0.05 \le h_{1} \le 2,0.25 \le h_{2} \le 1.3,2 \le h_{3} \le 15\)  

Table 14 displays the optimal values and variables that BKA and its comparison algorithm arrived at, illustrating how well the algorithm resolved this issue. BKA can obtain the optimal function value \(f(H) = 0.01267027\) with the structure variables \(H \, = \, (0.051173,0.344426,12.047782)\) . The experiments and comparative analysis results demonstrate that the BKA algorithm can produce better solutions when tackling these issues. This discovery provides engineers and decision-makers with a reliable tool and method to improve the design, planning, and decision-making processes and achieve higher-quality engineering solutions.

4.3 Welded beam design

This engineering challenge aims to minimize the welded beam's weight while satisfying the four constraints. The welding thickness, rod connection length, rod height, and rod thickness are the four decision variables that we must optimize to describe this issue. For this engineering problem, we can define an objective function to represent the weight of the welded beam, namely:

Consider variable \(H = [h_{1} ,h_{2} ,h_{3} ,h_{4} ] = [h,l,t,b]\)

Minimize: \( (H) = 1.10471h_{2} h_{1}^{2} + \left( {14 + h_{2} } \right) \times 0.04811h_{3} h_{4} \)

Variables range \(P = 6,000lb,{\text{ }}L = 14in,E = 30e6psi,{\text{ }}G = 12e6psi,\) , \(\begin{gathered} \tau _{{\max }} = 13,000{\text{psi}},\sigma _{{\max }} = 30,000{\text{psi}},\delta _{{\max }} = 0.25{\text{in}},0.1 \le h_{1} \le 2,0.1 \le h_{2} \le 10, \hfill \\ 0.1 \le h_{3} \le 10,0.1 \le h_{4} \le 2. \hfill \\ \end{gathered}\)  

BKA can obtain the optimal function value \(f(H) = 1.724853\) with the structure variables \(H{\text{ }} = {\text{ }}(0.205730,3.470488,\begin{array}{*{20}l} {9.036622} \hfill \\ \end{array} ,0.205730)\) . The results in Table 15 indicate that BKA can bring better solutions to solving such problems. After analysis and comparison, the BKA algorithm can obtain better solutions under given constraints through flexible heuristic search methods and optimization mechanisms. It can adapt to different problem characteristics and solving requirements and has a high success rate and accuracy. This discovery gives engineers and decision-makers a reliable tool and method to improve the design and decision-making process and achieve higher-quality engineering solutions.

4.4 Speed reducer design problem

This issue aims to reduce the reducer device's weight while meeting 11 constraints. To describe this problem, we can use the following mathematical expression:

Consider variable \(H = [h_{1} ,h_{2} ,h_{3} ,h_{4} ,h_{5} ,h_{6} ,h_{7} ] = [b,m,p,l_{1} ,l_{2} ,d_{1} ,d_{2} ]\)

Variable range \(2.6 \le h_{1} \le 3.6,0.7 \le h_{2} \le 0.8,17 \le h_{3} \le 28,7.3 \le h_{4} \le 8.3\)

The optimal values and corresponding optimal variables that the BKA algorithm and its comparison algorithm arrived at are listed in Table 16 . These values offer a simple way to compare how well various algorithms perform when solving problems. BKA can obtain the optimal function value \(f(H) = 2994.47107\) with the structure variables \(H \, = \, (3.5,\begin{array}{*{20}l} {0.7} \hfill \\ \end{array} ,\begin{array}{*{20}l} {17} \hfill \\ \end{array} ,\begin{array}{*{20}l} {7.3} \hfill \\ \end{array} ,7.71532,\begin{array}{*{20}c} {3.350215} \\ \end{array} ,5.286654)\) . We can see from comparing the BKA algorithm's results to those of other algorithms that it solves problems more efficiently and produces better optimal values. This suggests that the BKA algorithm does a better job locating the optimal solution and may be closer to the problem's overall optimal solution. These optimal variables serve as crucial guides and references for a deeper comprehension of the problem's solution space and the viability of obtaining optimization results.

4.5 Three-bar truss design problem

This problem aims to reduce the member structure's weight while maintaining a constant total load. To achieve this goal, we need to consider three constraint conditions: the stress, buckling, and deflection constraints of each steel bar. Firstly, the stress constraint of each steel bar is to ensure that under the design working load, the stress borne by the steel bars in the member will not exceed the limit of their bearing capacity. This is to ensure the safety and reliability of the structure. The limitation of steel bar stress is determined by calculating the strength of the material and the force borne by the steel bar. Secondly, buckling constraint ensures that the member will not experience buckling under stress. Buckling refers to the instability phenomenon of a member under pressure, which may lead to structural failure. To avoid buckling, we need to limit the members' length, cross-sectional shape, and material selection to ensure that the structure can withstand the design load. Finally, deflection constraints ensure the member has sufficient stiffness and stability under stress. Deflection refers to the bending and deformation of a member under external forces. To control deflection, we need to limit the rod's geometric shape, the material's stiffness, and the design conditions' requirements. By simultaneously satisfying these three constraints, engineers can achieve maximum weight reduction in the member structure while maintaining the total load unchanged. This optimization design can reasonably utilize materials and reduce engineering costs while ensuring structural safety and performance. The following is the mathematical expression:

Table 17 , which compares the BKA algorithm to other algorithms, shows the optimal values and corresponding optimal variables. This table offers comparative analysis information that will allow us to assess how well various algorithms perform when solving problems. BKA can obtain the optimal function value \(f(H) = \begin{array}{*{20}c} {263.895843} \\ \end{array}\) with the structure variables \(H \, = (\begin{array}{*{20}c} {0.788675} \\ \end{array} ,\begin{array}{*{20}c} {0.408248} \\ \end{array} )\) . By analyzing the data, it can be deduced that the BKA algorithm offers a superior solution to these engineering problems.

4.6 Analysis of the results of engineering design problems

By observing the results of the five different types of constrained engineering design problems mentioned above, BKA achieved the optimal results. Below is an analysis of the reasons why BKA achieved optimal results in constraint design problems:

Advantages of swarm intelligence: The BKA algorithm is based on swarm intelligence, which enables interaction and information exchange between individuals in a group. The swarm intelligence algorithm can search for the optimal solution through individual cooperation and collaboration and has strong robustness and global search ability. Therefore, individuals in the BKA algorithm can better explore the solution space and find optimal results through the collaborative effect of swarm intelligence.

Parameter optimization and adjustment: The BKA algorithm includes some parameters, such as Cauchy distribution's control parameters and individual leaders' selection strategy. The BKA algorithm can better adapt to different engineering examples by optimizing and adjusting reasonable parameters. Reasonably setting parameters can improve the performance and effectiveness of the algorithm in specific problems, thus achieving optimal results.

The BKA algorithm adopts the Cauchy distribution strategy, which gives the algorithm a strong global search ability. The Cauchy distribution has a relatively wide tail, which allows for a wider search of the solution space and avoids falling into local optima. Therefore, BKA can traverse more solution spaces in different engineering examples and has a greater probability of finding the global optimal solution.

The BKA algorithm introduces a leader strategy to guide the algorithm's entire optimization process. By selecting individuals with high fitness values as leaders, other individuals learn and improve solutions through interaction with the leader. Leaders usually have relatively good solutions; through their guidance, the entire group can evolve toward a more optimal solution. Therefore, BKA can accelerate convergence and achieve optimal results through leader strategy in different engineering examples.

5 Conclusion and future works

This article presents the Black Kite Algorithm (BKA), a new swarm intelligence optimization algorithm inspired by the attack and migration behaviors of Black-winged kites. The algorithm mimics the Black-winged kites' high predatory skills and integrates a migratory strategy to enhance search capabilities, striking a balance between local and global optima. The study's main contents are:

Evaluate the performance of BKA using the CEC-2017 test set, CEC-2022 test set, and 18 complex functions, demonstrating superior results across various characteristics and complexities.

Statistical validation using the Friedman and Wilson sign rank tests, with BKA securing first place, confirming its effectiveness and scientific reliability.

Practical application of BKA in five engineering cases involving challenging conditions and constrained search spaces, where it shows significant superiority by quickly converging to high-quality solutions and exhibiting excellent performance.

In future research, BKA can be integrated with other well-known strategies, such as adversarial learning mechanisms (Lian et al. 2023 ) and chaotic mapping (Liu et al. 2023 ), to further enhance the optimization performance of the algorithm. BKA can also be used to optimize various engineering problems in the future, such as multi-disc clutch brake design problems (Yu et al. 2020 ), step cone pulley problems (Nematollahi et al. 2021 ), etc.

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Acknowledgements

The authors are grateful for supporting the special project for collaborative science and technology innovation in 2021 (No: 202121206) and Henan Province University Scientific and Technological Innovation Team (No: 18IRTSTHN009).

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Jun Wang: conceptualization, methodology, data curation, writing—original draft. Wen-chuan Wang: conceptualization, methodology, writing—original draft, formal analysis, data curation. Xiao-xue Hu: writing—original draft, preparing figures. Lin Qiu: investigation, formal analysis. Hong-fei Zang: writing—original draft, formal analysis.

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Wang, J., Wang, Wc., Hu, Xx. et al. Black-winged kite algorithm: a nature-inspired meta-heuristic for solving benchmark functions and engineering problems. Artif Intell Rev 57 , 98 (2024). https://doi.org/10.1007/s10462-024-10723-4

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Screen Rant

10 dead games that have the best chance for a comeback in 2024.

Even with a disastrous launch, it is sometimes possible for a game that flopped to come back from the dead with enough dedication and passion.

• Games like Cyberpunk 2077 and No Man's Sky have shown that hard work and community feedback can turn around disastrous launches.
• Initial launches can make or break a game's success, but continued communication with fans and hard work by developers can lead to redemption.
• Games like Overwatch 2 , Skull and Bones , and Diablo 4 are examples of titles that are working to improve content and address player feedback to make a comeback.

Over the past few years, there have been a few examples of video games with disastrous launches managing to make a comeback after putting in a lot of work and listening to the feedback of the gaming community. Games like Cyberpunk 2077 and No Man's Sky are examples of this, where, after a disappointing release, the developers did not give up and were able to turn things around and craft incredible experiences. Now, these games are known not only for their success story but are incredibly popular and fun forms of entertainment.

For most games, suffering setbacks from glitches, server overloads, or other issues at the initial launch of a game can prove to be an insurmountable problem. These first few days and weeks can make or break a game's success , particularly because the time when a game hits the market is when the most excitement is. Yet, in some cases, developers can take the feedback gained during these struggling starts and, with hard work and clear communication with fans, turn the game into a success after all. The following are games that could still turn things around in the next few months.

FFXIV or No Man's Sky: Which Comeback Was More Impressive

10 overwatch 2 (blizzard entertainment, 2022), free, but needing more content, modes, & polish.

Overwatch 2 was struggling before it even reached its release date, with years of delays and many large issues behind the scenes at Blizzard going on throughout its development. As the original Overwatch game was a massive success, the sequel had a lot of potential, but ultimately kept dropping aspects that were originally announced and simply did not have enough content available at launch. The free-to-play game is not giving up quietly, however, with the development team planning to continue to add content in addition to its regular nine-week seasons .

Overwatch 2 Review: Missing More Than An Extra Tank

9 suicide squad: kill the justice league (rocksteady studios, 2024), developers adding a larger, proper ending & more updates.

Suicide Squad: Kill The Justice League has a good cast of characters, a promising story, and more going for it, but ultimately failed to become what players were hoping for. In Screen Rant 's review of Suicide Squad: Kill The Justice League , it is noted that the combat felt underwhelming and the ending of the game was a bit disjointed. The development team at Rocksteady has said it is working on creating a larger, proper ending, more difficult missions, new weapons, and even more playable characters for the game, including Joker, who is scheduled to arrive on March 28, 2024.

Joker Is Coming To Suicide Squad: Kill The Justice League, But It’ll Already Be Too Late

8 redfall (arkane studios, 2023), repetitive gameplay & not enough playable characters.

The premise of shooting vampires and human cultists in Redfall was one that many looked forward to for quite some time before the official release of the game on May 2, 2023, but ultimately many players felt let down by the experience. There are many multiplayer co-op shooters on the market currently, which meant that to stand out, Redfall needed to have a lot more variation and enemies to stand out . Developers at Arkane have stated that they are going to continue working on the game to improve things, but they haven't provided a clear look at what is coming or when.

7 Skull And Bones (Ubisoft, 2024)

Promised premium content could solve issues.

Skull and Bones offers a beautiful stylized look at pirate games with a lot going for it, but its recent launch suffered from feeling as though the game wasn't completed. It has been criticized as having long loading times, poor character models with little customization, and too much of a focus on microtransactions and live-service aspects. The game is said to have many plans for content to be added and is frequently applying updates, which could create a much better experience for players in time.

Skull and Bones Review: "This Boat Is Visibly Sinking"

6 multiversus (player first games, 2024), expected to make a comeback in a big way this may.

Developers for the WB brawling game MultiVersus have already proven they are giving the game everything they can to make it a success. When MultiVersus launched in open beta, it initially was met with a lot of excitement but quickly began to receive a lot of negative feedback from players. Rather than simply releasing the game, or leaving it in an infinite early access period, the game was pulled from servers in June 2023 so that the team could give it a complete overhaul.

Using the feedback they had gotten, developers rebuilt the game using a new engine, updated netcode, and more to make it better and will release it in full on May 28, 2024 , as a free-to-play game with live-service elements. In their dev blogs, the team says they will continue to pay close attention to responses from players and have said they will continue to make adjustments.

5 Payday 3 (Starbreeze Studios, 2023)

Server overloads, but positive communication from developers.

Despite having many features that could make the game a fun experience, Payday 3 suffered one of the worst launches of 2023 , particularly from the server issues the online-only game faced. This caused many players to not even be able to get past the opening menus and lobbies to see what the game had to offer, and then if they made it in, they saw glitched character movements and frequent crashes.

This caused a lot of frustrated players to post negative reviews, but devs at Starbreeze have been listening to players, and have been making plans to improve the game based on the feedback received, as was stated on the Payday website's News page recently:

In order to turn your feedback into action, we’ve put together a strike team of veteran developers from the design, community, communication and production teams with the focus on bringing PAYDAY 3 up to where it will meet your expectations.

Payday 3 has also released a roadmap of future updates and DLC plans that will continue to address some of the feedback that the community has given on the current state of the game.

4 Nightingale (Inflexion Games, 2024)

Early access title with a chance to change.

Like MultiVersus , Nightingale is in a good position to be able to hear what the community is saying and make significant changes before the game releases in full. Currently, Nightingale is an Early Access title on Steam, and although the open-world survival crafting game has many good qualities, it has more to do to become a true success.

"The presentation and implementation of how people are introduced to these concepts need to be done in a more engaging way, one that's paced out better so people can get to the more interesting portions of the title, like more interesting enemy creatures, elaborate lore, and magic-infused weapons and gear. If this can be accomplished, then Nightingale may shed its lukewarm initial reception." - Screen Rant 's Nightingale preview

Nightingale does not have a full release date planned yet, which gives developers time to make changes to the game based on the information they are getting from players during Early Access.

3 Ark: Survival Ascended (Studio Wildcard, 2023)

Technical problems & crashes are hurting the game.

Ark: Survival Ascended has received many negative reviews since its Steam Early Access release in October 2023, with most issues being related to technical problems. The remastered version of 2015's Ark: Survival Evolved has had server issues disconnecting players, frequent bugs and glitches, game crashes, and more that have rendered it nearly unplayable for many . Hopefully, as it is still in Early Access, these technical problems will have time to be ironed out before a full launch.

Ark: Survival Ascended DLC Roadmap - All Planned Expansions & Updates

2 diablo 4 (blizzard entertainment, 2023), a good foundation that needs much more work.

As part of the franchise that was among the first true dungeon-crawling experiences, Diablo 4 had a big legacy to live up to and ultimately did not meet expectations for players at launch. The ARPG received criticism for not offering enough story, character options that don't feel exciting, and a railroaded skill tree that does not allow for enough customization.

Over the months since launch, developers at Blizzard have tried to be very receptive to the feedback they are getting and have been making many significant changes that are added in with each new season of content. Regular Campfire Chat livestreams with devs have also helped to give a transparent feeling of communication with the players. If this level of improvement and discussion continues, eventually Diablo 4 could still have a comeback.

Could Diablo 4's Newest Season Save The Game From Total Disaster?

1 cities: skylines 2 (colossal order, 2023), performance-heavy requirements led to serious technical issues.

Cities: Skylines 2 is in the best spot to truly make a comeback in 2024 after a disastrous launch in 2023. Developers for the game were perhaps a bit too ambitious in designing this intricate city-planning game that features many complex details, leading to performance issues because of the amount of processing power needed to run the game.

Immediately upon getting feedback, Paradox Interactive and Colossal Order directly addressed the issues and pulled back all other projects to focus on making a roadmap of fixes and updates for Cities: Skylines 2 . Already there has been a noticeable difference, with many more major patches on the horizon. If it continues to be handled correctly, Cities: Skylines 2 has the foundation laid to easily make one of the biggest comebacks in video game releases, similar to the turnarounds seen with Cyberpunk 2077 and No Man's Sky .

Source: Payday