method for problem solving

35 problem-solving techniques and methods for solving complex problems

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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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Problem-Solving Strategies and Obstacles

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

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

JGI / Jamie Grill / Getty Images

Application
Improvement

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

What Is Problem-Solving?

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

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

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

The problem-solving process involves:

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

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

Problem-Solving Mental Processes

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

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

Problem-Solving Strategies

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

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

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

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

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

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

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

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

Trial and Error

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

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

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

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

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

How to Apply Problem-Solving Strategies in Real Life

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

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

Obstacles to Problem-Solving

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

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

How to Improve Your Problem-Solving Skills

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

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

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

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

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

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

What Is Problem Solving?

Definition and importance.

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

Problem-Solving Steps

The problem-solving process typically includes the following steps:

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

Defining the Problem

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

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

Generating Solutions

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

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

Evaluating and Selecting Solutions

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

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

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

Implementing and Monitoring the Solution

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

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

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

Problem-Solving Techniques

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

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

Brainstorming

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

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

When brainstorming, remember to:

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

Root Cause Analysis

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

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

SWOT Analysis

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

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

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

Mind Mapping

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

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

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

Examples of Problem Solving in Various Contexts

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

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

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

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

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

Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
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The Ultimate Problem-Solving Process Guide: 31 Steps and Resources

Updated: Jan 24, 2023

GOT CHALLENGES WITH YOUR PROBLEM-SOLVING PROCESS? ARE YOU FRUSTRATED?

prob·lem-solv·ing noun -the process of finding solutions to difficult or complex issues. It sounds so simple, doesn’t it? But in reality problem-solving is hard. It's almost always more complex than it seems. That's why problem-solving can be so frustrating sometimes. You can feel like you’re spinning your wheels, arguing in circles, or just failing to find answers that actually work. And when you've got a group working on a problem, it can get even muddier …differences of opinions, viewpoints colored by different backgrounds, history, life experiences, you name it. We’re all looking at life and work from different angles, and that often means disagreement. Sometimes sharp disagreement. That human element, figuring out how to take ourselves out of the equation and make solid, fact-based decisions , is precisely why there’s been so much written on problem-solving. Which creates its own set of problems. Whose method is best? How can you possibly sift through them all? Are we to have one person complete the entire problem-solving process by themselves or rely on a larger team to find answers to our most vexing challenges in the workplace ? Today, we’re going to make sense of it all. We’ll take a close look at nine top problem-solving methods. Then we’ll grab the best elements of all of them to give you a process that will have your team solving problems faster, with better results , and maybe with less sharp disagreement. Ready to dive in? Let’s go!

9 PROFITABLE PROBLEM-SOLVING TECHNIQUES AND METHODS

While there are loads of methods to choose from, we are going to focus on nine of the more common ones. You can use some of these problem-solving techniques reactively to solve a known issue or proactively to find more efficient or effective ways of performing tasks. If you want to explore other methods, check out this resource here . A helpful bit of advice here is to reassure people that you aren’t here to identify the person that caused the problem . You’re working to surface the issue, solve it and make sure it doesn’t happen again, regardless of the person working on the process. It can’t be understated how important it is to continually reassure people of this so that you get unfiltered access to information. Without this, people will often hide things to protect themselves . After all, nobody wants to look bad, do they? With that said, let’s get started...

1. CREATIVE PROBLEM SOLVING (CPS)

Alex Osborn coined the term “Creative Problem Solving” in the 1940s with this simple four-step process:

Clarify : Explore the vision, gather data, and formulate questions.

Ideate : This stage should use brainstorming to generate divergent thinking and ideas rather than the random ideas normally associated with brainstorming.

Develop : Formulate solutions as part of an overall plan.

Implement : Put the plan into practice and communicate it to all parties.

2. APPRECIATIVE INQUIRY

Source: http://www.davidcooperrider.com/ai-process/ This method seeks, first and foremost, to identify the strengths in people and organizations and play to that “positive core” rather than focus our energies on improving weaknesses . It starts with an “affirmative topic,” followed by the “positive core (strengths).” Then this method delves into the following stages:

Discovery (fact-finding)

Dream (visioning the future)

Design (strategic purpose)

Destiny (continuous improvement)

3. “FIVE WHYS” METHOD

This method simply suggests that we ask “Why” at least five times during our review of the problem and in search of a fix. This helps us dig deeper to find the the true reason for the problem, or the root cause. Now, this doesn’t mean we just keeping asking the same question five times. Once we get an answer to our first “why”, we ask why to that answer until we get to five “whys”.

Using the “five whys” is part of the “Analyze” phase of Six Sigma but can be used with or without the full Six Sigma process.

Review this simple Wikipedia example of the 5 Whys in action:

The vehicle will not start. (the problem)

Why? - The battery is dead. (First why)

Why? - The alternator is not functioning. (Second why)

Why? - The alternator belt has broken. (Third why)

Why? - The alternator belt was well beyond its useful service life and not replaced. (Fourth why)

Why? - The vehicle was not maintained according to the recommended service schedule. (Fifth why, a root cause)

4. LEAN SIX SIGMA (DMAIC METHOD)

Define, Measure, Analyze, Design, Verify

While many people have at least heard of Lean or Six Sigma, do we know what it is? Like many problem-solving processes, it has five main steps to follow.

Define : Clearly laying out the problem and soliciting feedback from those who are customers of the process is necessary to starting off on the right foot.

Measure : Quantifying the current state of the problem is a key to measuring how well the fix performed once it was implemented.

Analyze : Finding out the root cause of the problem (see number 5 “Root Cause Analysis” below) is one of the hardest and least explored steps of Six Sigma.

Improve : Crafting, executing, and testing the solution for measureable improvement is key. What doesn’t get implemented and measured really won’t make a difference.

Control : Sustaining the fix through a monitoring plan will ensure things continue to stay on track rather than being a short-lived solution.

5. ROOT CAUSE ANALYSIS

Compared to other methods, you’ll more often find this technique in a reactive problem-solving mode, but it is helpful nonetheless. Put simply, it requires a persistent approach to finding the highest-level cause, since most reasons you’ll uncover for a problem don’t tell the whole story.

Most of the time, there are many factors that contributed to an issue. The main reason is often shrouded in either intentional or unintentional secrecy. Taking the time to drill down to the root of the issue is key to truly solving the problem.

6. DEMING-SHEWHART CYCLE: PLAN-DO-CHECK-ACT (PDCA)

Named for W. Edwards Deming and Walter A. Shewhart, this model follows a four-step process:

Plan: Establish goals and objectives at the outset to gain agreement. It’s best to start on a small scale in order to test results and get a quick win.

Do: This step is all about the implementation and execution of the solution.

Check: Study and compare actual to expected results. Chart this data to identify trends.

Act/Adjust: If the check phase showed different results, then adjust accordingly. If worse than expected, then try another fix. If the same or better than expected, then use that as the new baseline for future improvements.

7. 8D PROBLEM-SOLVING

While this is named “8D” for eight disciplines, there are actually nine , because the first is listed as step zero. Each of the disciplines represents a phase of this process. Its aim is to implement a quick fix in the short term while working on a more permanent solution with no recurring issues.

Prepare and Plan : Collecting initial information from the team and preparing your approach to the process is a necessary first step.

Form a Team : Select a cross-functional team of people, one leader to run meetings and the process, and one champion/sponsor who will be the final decision-maker.

Describe the Problem : Using inductive and deductive reasoning approaches, lay out the precise issue to be corrected.

Interim Containment Action : Determine if an interim solution needs to be implemented or if it can wait until the final fix is firmed up. If necessary, the interim action is usually removed once the permanent solution is ready for implementation.

Root Cause Analysis and Escape Point : Finding the root of the issue and where in the process it could’ve been found but was not will help identify where and why the issue happened.

Permanent Corrective Action : Incorporating key criteria into the solution, including requirements and wants, will help ensure buy-in from the team and your champion.

Implement and Validate the Permanent Corrective Action : Measuring results from the fix implemented validates it or sends the team back to the drawing board to identity a more robust solution.

Prevent Recurrence : Updating work procedure documents and regular communication about the changes are important to keep old habits in check.

Closure and Team Celebration : Taking time to praise the team for their efforts in resolving the problem acknowledges the part each person played and offers a way to move forward.

8. ARMY PROBLEM SOLVING PROCESS

The US Army has been solving problems for more than a couple of centuries , so why not take a look at the problem-solving process they’ve refined over many years? They recommend this five step process:

Identify the Problem : Take time to understand the situation and define a scope and limitations before moving forward.

Gather Information : Uncover facts, assumptions, and opinions about the problem, and challenge them to get to the truth.

Develop Screening and Evaluation Criteria :

Five screening items should be questioned. Is it feasible, acceptable, distinguishable, and complete?

Evaluation criteria should have these 5 elements: short title, definition, unit of measure, benchmark, and formula.

Generate, Analyze, and Compare Possible Solutions : Most fixes are analyzed, but do you compare yours to one another as a final vetting method?

Choose a Solution and Implement : Put the fix into practice and follow up to ensure it is being followed consistently and having the desired effect.

9. HURSON'S PRODUCTIVE THINKING MODEL

Tim Hurson introduced this model in 2007 with his book, Think Better. It consists of the following six actions.

Ask "What is going on?" : Define the impact of the problem and the aim of its solution.

Ask "What is success?" : Spell out the expected outcome, what should not be in fix, values to be considered, and how things will be evaluated.

Ask "What is the question?" : Tailor questions to the problem type. Valuable resources can be wasted asking questions that aren’t truly relevant to the issue.

Generate answers : Prioritize answers that are the most relevant to solutions, without excluding any suggestion to present to the decision-makers.

Forge the solution : Refine the raw list of prioritized fixes, looking for ways to combine them for a more powerful solution or eliminate fixes that don’t fit the evaluation criteria.

Align resources: Identify resources, team, and stakeholders needed to implement and maintain the solution.

STEAL THIS THOROUGH 8-STEP PROBLEM-SOLVING PROCESS

Little Girl Reaching For Strawberries On The Counter

Now that we’ve reviewed a number of problem-solving methods, we’ve compiled the various steps into a straightforward, yet in-depth, s tep-by-step process to use the best of all methods.

1. DIG DEEP: IDENTIFY, DEFINE, AND CLARIFY THE ISSUE

“Elementary, my dear Watson,” you might say.

This is true, but we often forget the fundamentals before trying to solve a problem. So take some time to gain understanding of critical stakeholder’s viewpoints to clarify the problem and cement consensus behind what the issue really is.

Sometimes it feels like you’re on the same page, but minor misunderstandings mean you’re not really in full agreement.. It’s better to take the time to drill down on an issue before you get too far into solving a problem that may not be the exact problem . Which leads us to…

2. DIG DEEPER: ROOT CAUSE ANALYSIS

This part of the process involves identifying these three items :

What happened?

Why did it happen?

What process do we need to employ to significantly reduce the chances of it happening again ?

You’ll usually need to sort through a series of situations to find the primary cause. So be careful not to stop at the first cause you uncover . Dig further into the situation to expose the root of the issue. We don’t want to install a solution that only fixes a surface-level issue and not the root. T here are typically three types of causes :

Physical: Perhaps a part failed due to poor design or manufacturing.

Human error: A person either did something wrong or didn’t do what needed to be done.

Organizational: This one is mostly about a system, process, or policy that contributed to the error .

When searching for the root cause, it is important to ensure people that you aren’t there to assign blame to a person but rather identify the problem so a fix can prevent future issues.

3. PRODUCE A VARIETY OF SOLUTION OPTIONS

So far, you’ve approached the problem as a data scientist, searching for clues to the real issue. Now, it’s important to keep your eyes and ears open, in case you run across a fix suggested by one of those involved in the process failure. Because they are closest to the problem, they will often have an idea of how to fix things. In other cases, they may be too close, and unable to see how the process could change.

The bottom line is to solicit solution ideas from a variety of sources , both close to and far away from the process you’re trying to improve.

You just never know where the top fix might come from!

4. FULLY EVALUATE AND SELECT PLANNED FIX(ES)

"Time To Evaluate" Written on a Notepad with Pink Glasses & Pen

Evaluating solutions to a defined problem can be tricky since each one will have cost, political, or other factors associated with it. Running each fix through a filter of cost and impact is a vital step toward identifying a solid solution and hopefully settling on the one with the highest impact and low or acceptable cost.

Categorizing each solution in one of these four categoriescan help teams sift through them:

High Cost/Low Impact: Implement these last, if at all, since t hey are expensive and won’t move the needle much .

Low Cost/Low Impact: These are cheap, but you won’t get much impact.

High Cost/High Impact: These can be used but should be second to the next category.

Low Cost/High Impact: Getting a solid “bang for your buck” is what these fixes are all about. Start with these first .

5. DOCUMENT THE FINAL SOLUTION AND WHAT SUCCESS LOOKS LIKE

Formalize a document that all interested parties (front-line staff, supervisors, leadership, etc.) agree to follow. This will go a long way towards making sure everyone fully understands what the new process looks like, as well as what success will look like .

While it might seem tedious, try to be overly descriptive in the explanation of the solution and how success will be achieved. This is usually necessary to gain full buy-in and commitment to continually following the solution. We often assume certain things that others may not know unless we are more explicit with our communications.

6. SUCCESSFULLY SELL AND EXECUTE THE FIX

Arriving at this stage in the process only to forget to consistently apply the solution would be a waste of time, yet many organizations fall down in the execution phase . Part of making sure that doesn’t happen is to communicate the fix and ask for questions multiple times until all parties have a solid grasp on what is now required of them.

One often-overlooked element of this is the politics involved in gaining approval for your solution. Knowing and anticipating objections of those in senior or key leadership positions is central to gaining buy-in before fix implementation.

7. RINSE AND REPEAT: EVALUATE, MONITOR, AND FOLLOW UP

Next, doing check-ins with the new process will ensure that the solution is working (or identity if further reforms are necessary) . You’ll also see if the measure of predefined success has been attained (or is making progress in that regard).

Without regularly monitoring the fix, you can only gauge the success or failure of the solution by speculation and hearsay. And without hard data to review, most people will tell their own version of the story.

8. COLLABORATIVE CONTINGENCIES, ITERATION, AND COURSE CORRECTION

Going into any problem-solving process, we should take note that we will not be done once the solution is implemented (or even if it seems to be working better at the moment). Any part of any process will always be subject to the need for future iterations and course corrections . To think otherwise would be either foolish or naive.

There might need to be slight, moderate, or wholesale changes to the solution previously implemented as new information is gained, new technologies are discovered, etc.

14 FRUITFUL RESOURCES AND EXERCISES FOR YOUR PROBLEM-SOLVING JOURNEY

Resources | People Working Together At A Large Table With Laptops, Tablets & Paperwork Everywhere

Want to test your problem-solving skills?

Take a look at these twenty case study scenario exercises to see how well you can come up with solutions to these problems.

Still have a desire to discover more about solving problems?

Check out these 14 articles and books...

1. THE LEAN SIX SIGMA POCKET TOOLBOOK: A QUICK REFERENCE GUIDE TO NEARLY 100 TOOLS FOR IMPROVING QUALITY AND SPEED

This book is like a Bible for Lean Six Sigma , all in a pocket-sized package.

2. SOME SAGE PROBLEM SOLVING ADVICE

Hands Holding Up a Comment Bubble That Says "Advice"

The American Society for Quality has a short article on how it’s important to focus on the problem before searching for a solution.

3. THE SECRET TO BETTER PROBLEM SOLVING: HARVARD BUSINESS REVIEW

Wondering if you are solving the right problems? Check out this Harvard Business Review article.

4. PROBLEM SOLVING 101 : A SIMPLE BOOK FOR SMART PEOPLE

Looking for a fun and easy problem-solving book that was written by a McKinsey consultant? Take a look!

5. THE BASICS OF CREATIVE PROBLEM SOLVING – CPS

A Drawn Lightbulb Where The Lightbulb is a Crumbled Piece Of Yellow Paper

If you want a deeper dive into the seven steps of Creative Problem Solving , see this article.

6. APPRECIATIVE INQUIRY : A POSITIVE REVOLUTION IN CHANGE

Appreciative Inquiry has been proven effective in organizations ranging from Roadway Express and British Airways to the United Nations and the United States Navy. Review this book to join the positive revolution.

7. PROBLEM SOLVING: NINE CASE STUDIES AND LESSONS LEARNED

The Seattle Police Department has put together nine case studies that you can practice solving . While they are about police work, they have practical application in the sleuthing of work-related problems.

8. ROOT CAUSE ANALYSIS : THE CORE OF PROBLEM SOLVING AND CORRECTIVE ACTION

Need a resource to delve further into Root Cause Analysis? Look no further than this book for answers to your most vexing questions .

9. SOLVING BUSINESS PROBLEMS : THE CASE OF POOR FRANK

Business Team Looking At Multi-Colored Sticky Notes On A Wall

This solid case study illustrates the complexities of solving problems in business.

10. THE 8-DISCIPLINES PROBLEM SOLVING METHODOLOGY

Learn all about the “8Ds” with this concise primer.

11. THE PROBLEM-SOLVING PROCESS THAT PREVENTS GROUPTHINK HBR

Need to reduce groupthink in your organization’s problem-solving process ? Check out this article from the Harvard Business Review.

12. THINK BETTER : AN INNOVATOR'S GUIDE TO PRODUCTIVE THINKING

Tim Hurson details his own Productive Thinking Model at great length in this book from the author.

13. 5 STEPS TO SOLVING THE PROBLEMS WITH YOUR PROBLEM SOLVING INC MAGAZINE

This simple five-step process will help you break down the problem, analyze it, prioritize solutions, and sell them internally.

14. CRITICAL THINKING : A BEGINNER'S GUIDE TO CRITICAL THINKING, BETTER DECISION MAKING, AND PROBLEM SOLVING!

LOOKING FOR ASSISTANCE WITH YOUR PROBLEM-SOLVING PROCESS?

There's a lot to take in here, but following some of these methods are sure to improve your problem-solving process. However, if you really want to take problem-solving to the next level, InitiativeOne can come alongside your team to help you solve problems much faster than you ever have before.

There are several parts to this leadership transformation process provided by InitiativeOne, including a personal profile assessment, cognitive learning, group sessions with real-world challenges, personal discovery, and a toolkit to empower leaders to perform at their best.

There are really only two things stopping good teams from being great. One is how they make decisions and two is how they solve problems. Contact us today to grow your team’s leadership performance by making decisions and solving problems more swiftly than ever before!

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The Basics of Structured Problem-Solving Methodologies: DMAIC & 8D

Topics: Minitab Engage

When it comes to solving a problem, organizations want to get to the root cause of the problem, as quickly as possible. They also want to ensure that they find the most effective solution to that problem, make sure the solution is implemented fully, and is sustained into the future so that the problem no longer occurs. The best way to do this is by implementing structured problem-solving. In this blog post, we’ll briefly cover structured problem-solving and the best improvement methodologies to achieve operational excellence. Before we dive into ways Minitab can help, let’s first cover the basics of problem-solving.

WHAT IS STRUCTURED PROBLEM-SOLVING?

Structured problem-solving is a disciplined approach that breaks down the problem-solving process into discrete steps with clear objectives. This method enables you to tackle complex problems, while ensuring you’re resolving the right ones. It also ensures that you fully understand those problems, you've considered the reasonable solutions, and are effectively implementing and sustaining them.

WHAT IS A STRUCTURED PROBLEM-SOLVING METHODOLOGY?

A structured problem-solving methodology is a technique that consists of a series of phases that a project must pass through before it gets completed. The goal of a methodology is to highlight the intention behind solving a particular problem and offers a strategic way to resolve it. WHAT ARE THE BEST PROBLEM-SOLVING METHODOLOGIES?

That depends on the problem you’re trying to solve for your improvement initiative. The structure and discipline of completing all the steps in each methodology is more important than the specific methodology chosen. To help you easily visualize these methodologies, we’ve created the Periodic Table of Problem-Solving Methodologies. Now let’s cover two important methodologies for successful process improvement and problem prevention: DMAIC and 8D .

8D is known as the Eight Disciplines of problem-solving. It consists of eight steps to solve difficult, recurring, or critical problems. The methodology consists of problem-solving tools to help you identify, correct, and eliminate the source of problems within your organization. If the problem you’re trying to solve is complex and needs to be resolved quickly, 8D might be the right methodology to implement for your organization. Each methodology could be supported with a project template, where its roadmap corresponds to the set of phases in that methodology. It is a best practice to complete each step of a given methodology, before moving on to the next one.

MINITAB ENGAGE, YOUR SOLUTION TO EFFECTIVE PROBLEM-SOLVING

Minitab Engage TM was built to help organizations drive innovation and improvement initiatives. What makes our solution unique is that it combines structured problem-solving methodologies with tools and dashboards to help you plan, execute, and measure your innovation initiatives! There are many problem-solving methodologies and tools to help you get started. We have the ultimate end-to-end improvement solution to help you reach innovation success.

Ready to explore structured problem-solving?

Download our free eBook to discover the top methodologies and tools to help you accelerate your innovation programs.

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A Step-by-Step Guide to A3 Problem Solving Methodology
Learn Lean Sigma
Problem Solving

Problem-solving is an important component of any business or organization. It entails identifying, analyzing, and resolving problems in order to improve processes, drive results, and foster a culture of continuous improvement. A3 Problem solving is one of the most effective problem-solving methodologies.

A3 Problem solving is a structured and systematic approach to problem-solving that originated with the lean manufacturing methodology. It visualizes the problem-solving process using a one-page document known as an A3 report. The A3 report provides an overview of the problem, data analysis, root causes, solutions, and results in a clear and concise manner.

A3 Problem Solving has numerous advantages, including improved communication, better decision-making, increased efficiency, and reduced waste. It is a powerful tool for businesses of all sizes and industries, and it is especially useful for solving complex and multi-faceted problems.

In this blog post, we will walk you through the A3 Problem Solving methodology step by step. Whether you are new to A3 Problem Solving or simply want to improve your skills, this guide will help you understand and apply the process in your workplace.

What is a3 problem solving.

A3 Problem Solving is a structured and systematic approach to problem-solving that makes use of a one-page document called an A3 report to visually represent the process. The A3 report provides an overview of the problem, data analysis, root causes, solutions, and results in a clear and concise manner. The method was created within the framework of the Lean manufacturing methodology and is based on the principles of continuous improvement and visual management.

Looking for a A3 Problem solving template? Click here

Origin and History of A3 Problem Solving

A3 Problem Solving was developed by Toyota Motor Corporation and was first used in the manufacture of automobiles. The term “A3” refers to the size of the paper used to create the report, which is an ISO standard known as “A3”. The goal of the A3 report is to provide a visual representation of the problem-solving process that all members of the organisation can easily understand and share. A3 Problem Solving has been adopted by organisations in a variety of industries over the years, and it has become a widely used and recognised method for problem-solving.

Key Principles of A3 Problem Solving

The following are the key principles of A3 Problem Solving:

Define the problem clearly and concisely
Gather and analyze data to gain a deep understanding of the problem
Identify the root causes of the problem
Develop and implement effective solutions
Evaluate results and continuously improve

These principles serve as the foundation of the A3 Problem Solving methodology and are intended to assist organisations in continuously improving and achieving their objectives. Organizations can effectively solve problems, identify areas for improvement, and drive results by adhering to these principles.

Step 1: Define the Problem

Importance of clearly defining the problem.

The first step in the A3 Problem Solving process is critical because it lays the groundwork for the remaining steps. To define the problem clearly and accurately, you must first understand the problem and identify the underlying root cause. This step is critical because if the problem is not correctly defined, the rest of the process will be based on incorrect information, and the solution developed may not address the issue effectively.

The significance of defining the problem clearly cannot be overstated. It aids in the collection and analysis of relevant data, which is critical for developing effective solutions. When the problem is clearly defined, the data gathered is more relevant and targeted, resulting in a more comprehensive understanding of the issue. This will enable the development of solutions that are more likely to be effective because they are founded on a thorough and accurate understanding of the problem.

However, if the problem is not clearly defined, the data gathered may be irrelevant or incorrect, resulting in incorrect conclusions and ineffective solutions. Furthermore, the process of collecting and analysing data can become time-consuming and inefficient, resulting in resource waste. Furthermore, if the problem is not accurately defined, the solutions developed may fail to address the root cause of the problem, resulting in ongoing issues and a lack of improvement.

Techniques for Defining the Problem

The first step in the A3 Problem Solving process is to clearly and accurately define the problem. This is an important step because a clearly defined problem will help to ensure that the appropriate data is collected and solutions are developed. If the problem is not clearly defined, incorrect data may be collected, solutions that do not address the root cause of the problem, and time and resources may be wasted.

A problem can be defined using a variety of techniques, including brainstorming , root cause analysis , process mapping , and Ishikawa diagrams . Each of these techniques has its own advantages and disadvantages and can be used in a variety of situations depending on the nature of the problem.

Best Practice for Defining the Problem

In addition to brainstorming, root cause analysis, process mapping, and Ishikawa diagram s, best practices should be followed when defining a problem in A3 Problem Solving. Among these best practices are:

Define the issue in a specific and quantifiable way: It is critical to be specific and concise when defining the problem, as well as to quantify the problem in terms of its impact. This will help to ensure that all stakeholders understand the problem and that data collection is focused on the right areas.
Focus on the problem’s root cause: The A3 Problem Solving methodology is intended to assist organisations in identifying and addressing the root cause of a problem, rather than just the symptoms. Organizations can ensure that their solutions are effective and long-lasting by focusing on the root cause of the problem.
Ascertain that all stakeholders agree on the problem’s definition: All stakeholders must agree on the definition of the problem for the A3 Problem Solving process to be effective. This ensures that everyone is working towards the same goal and that the solutions developed are relevant and appropriate.
Consider the problem’s impact on the organisation and its stakeholders: It is critical to consider the impact of the problem on the organisation and its stakeholders when defining it. This will assist in ensuring that the appropriate data is gathered and that the solutions developed are relevant and appropriate.

Organizations can ensure that their problem is defined in a way that allows for effective data collection, analysis, and solution development by following these best practices. This will aid in the development of appropriate solutions and the effective resolution of the problem, resulting in improvements in the organization’s processes and outcomes.

Step 2: Gather Data

Gathering data in a3 problem solving.

Data collection is an important step in the A3 Problem Solving process because it allows organisations to gain a thorough understanding of the problem they are attempting to solve. This step entails gathering pertinent information about the problem, such as data on its origin, impact, and any related factors. This information is then used to help identify root causes and develop effective solutions.

One of the most important advantages of data collection in A3 Problem Solving is that it allows organisations to identify patterns and trends in data, which can be useful in determining the root cause of the problem. This information can then be used to create effective solutions that address the problem’s root cause rather than just its symptoms.

In A3 Problem Solving, data collection is a collaborative effort involving all stakeholders, including those directly impacted by the problem and those with relevant expertise or experience. Stakeholders can ensure that all relevant information is collected and that the data is accurate and complete by working together.

Overall, data collection is an important step in the A3 Problem Solving process because it serves as the foundation for effective problem-solving. Organizations can gain a deep understanding of the problem they are attempting to solve and develop effective solutions that address its root cause by collecting and analysing relevant data.

Data Collection Methods

In A3 Problem Solving, several data collection methods are available, including:

Observations
Process diagrams

The best data collection method will be determined by the problem being solved and the type of data required. To gain a complete understanding of the problem, it is critical to use multiple data collection methods.

Tools for Data Analysis and Visualization

Once the data has been collected, it must be analysed and visualised in order to gain insights into the problem. This process can be aided by the following tools:

Excel Spreadsheets
Flow diagrams
Pareto diagrams
Scatter Plots
Control diagrams

These tools can assist in organising data and making it easier to understand. They can also be used to generate visual representations of data, such as graphs and charts, to communicate the findings to others.

Finally, the data collection and analysis step is an important part of the A3 Problem Solving process. Organizations can gain a better understanding of the problem and develop effective solutions by collecting and analysing relevant data.

Step 3: Identify Root Causes

Identifying the root causes of the problem is the third step in the A3 Problem Solving process. This step is critical because it assists organisations in understanding the root causes of a problem rather than just its symptoms. Once the underlying cause of the problem is identified, it can be addressed more effectively, leading to more long-term solutions.

Overview of the Root Cause Analysis Process

The process of determining the underlying causes of a problem is known as root cause analysis. This process can assist organisations in determining why a problem is occurring and what can be done to prevent it from recurring in the future. The goal of root cause analysis is to identify the underlying cause of a problem rather than just its symptoms, allowing it to be addressed more effectively.

To understand Root cause analysis in more detail check out RCA in our Lean Six Sigma Yellow Belt Course Root Cause Analysis section

Techniques for Identifying Root Causes

There are several techniques for determining the root causes of a problem, including:

Brainstorming
Ishikawa diagrams (also known as fishbone diagrams)
Root Cause Tree Analysis

These methods can be used to investigate the issue in-depth and identify potential root causes. Organizations can gain a deeper understanding of the problem and identify the underlying causes that must be addressed by using these techniques.

Best Practices for Conducting Root Cause Analysis

It is critical to follow these best practices when conducting root cause analysis in A3 Problem Solving:

Make certain that all stakeholders participate in the root cause analysis process.
Concentrate on determining the root cause of the problem rather than just its symptoms.
Take into account all potential root causes, not just the most obvious ones.
To identify root causes, use a systematic approach, such as the 5 Whys or root cause tree analysis.

Organizations can ensure that root cause analysis is carried out effectively and that the root cause of the problem is identified by adhering to these best practises. This will aid in the development of appropriate solutions and the effective resolution of the problem.

Step 4: Develop Solutions

Developing solutions is the fourth step in the A3 Problem Solving process. This entails generating ideas and options for dealing with the problem, followed by selecting the best solution. The goal is to develop a solution that addresses the root cause of the problem and prevents it from recurring.

Solution Development in A3 Problem Solving

A3 solution development Problem solving is an iterative process in which options are generated and evaluated. The data gathered in the previous steps, as well as the insights and understanding gained from the root cause analysis, guide this process. The solution should be based on a thorough understanding of the problem and address the underlying cause.

Techniques for Developing Solutions

There are several techniques that can be used to develop solutions in A3 Problem Solving, including:

Brainwriting
Solution matrix
Multi voting
Force field analysis

These techniques can help to generate a range of options and to select the best solution.

Best Practice for Developing Solutions

It is critical to follow the following best practices when developing solutions in A3 Problem Solving:

Participate in the solution development process with all stakeholders.
Make certain that the solution addresses the underlying cause of the problem.
Make certain that the solution is feasible and achievable.
Consider the solution’s impact on the organisation and its stakeholders.

Organizations can ensure that the solutions they develop are effective and sustainable by adhering to these best practises. This will help to ensure that the problem is addressed effectively and that it does not reoccur.

Step 5: Implement Solutions

The final and most important step in the A3 Problem Solving methodology is solution implementation. This is the stage at which the identified and developed solutions are put into action to address the problem. This step’s goal is to ensure that the solutions are effective, efficient, and long-lasting.

The implementation Process

The implementation process entails putting the solutions developed in the previous step into action. This could include changes to processes, procedures, and systems, as well as employee training and education. To ensure that the solutions are effective, the implementation process should be well-planned and meticulously executed.

Techniques for Implementing Solutions

A3 Problem Solving solutions can be implemented using a variety of techniques, including:

Piloting the solution on a small scale before broadening its application
Participating in the implementation process with all relevant stakeholders
ensuring that the solution is in line with the goals and objectives of the organisation
Monitoring the solution to determine its effectiveness and make any necessary changes

Best Practice for Implementing Solutions

It is critical to follow these best practices when implementing solutions in A3 Problem Solving:

Make certain that all relevant stakeholders are involved and supportive of the solution. Have a clear implementation plan that outlines the steps, timeline, and resources required. Continuously monitor and evaluate the solution to determine its efficacy and make any necessary changes. Encourage all stakeholders to communicate and collaborate openly. Organizations can ensure that solutions are effectively implemented and problems are effectively addressed by adhering to these best practices. The ultimate goal is to find a long-term solution to the problem and improve the organization’s overall performance.

In conclusion, A3 Problem Solving is a comprehensive and structured methodology for problem-solving that can be applied in various industries and organisations. The A3 Problem Solving process’s five steps – Define the Problem, Gather Data, Identify Root Causes, Develop Solutions, and Implement Solutions – provide a road map for effectively addressing problems and making long-term improvements.

Organizations can improve their problem-solving skills and achieve better results by following the key principles, techniques, and best practices outlined in this guide. As a result, both the organisation and its stakeholders will benefit from increased efficiency, effectiveness, and satisfaction. So, whether you’re an experienced problem solver or just getting started, consider incorporating the A3 Problem Solving methodology into your work and start reaping the benefits right away.

Daniel Croft

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

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Adopting the right problem-solving approach

May 4, 2023 You’ve defined your problem, ensured stakeholders are aligned, and are ready to bring the right problem-solving approach and focus to the situation to find an optimal solution. But what is the right problem-solving approach? And what if there is no single ideal course of action? In our 2013 classic from the Quarterly , senior partner Olivier Leclerc highlights the value of taking a number of different approaches simultaneously to solve difficult problems. Read on to discover the five flexons, or problem-solving languages, that can be applied to the same problem to generate richer insights and more innovative solutions. Then check out more insights on problem-solving approaches, and dive into examples of pressing challenges organizations are contending with now.

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The six thinking hats method: how to use it for effective brainstorming

August 10, 2023 by MindManager Blog

Learn how to effectively use the six thinking hats method to foster diverse perspectives and improve decision-making. Discover practical tips and techniques to promote more productive and collaborative thinking in your team!

What is Edward De Bono’s six thinking hats brainstorming method?

Edward De Bono’s six thinking hats is a decision-making and problem-solving method that encourages parallel thinking and creativity.

Parallel thinking is a term coined by De Bono. It’s a collaborative thought process where people explore different perspectives on a topic, enabling a balanced and productive brainstorming environment.

The six thinking hats process involves a facilitator guiding participants through different thinking styles by symbolically wearing different hats. Using these hats, participants explore a topic, one perspective at a time, giving everyone an equal chance to contribute without debate or criticism.

We’ll dive deeper into this later, but for now, here’s a quick breakdown of what each hat represents and its related thinking style:

White hat: Objective data analysis.
Red hat: Emotional and intuitive responses.
Black hat: Critical judgment for identifying risks and flaws.
Yellow hat: Positive thinking for exploring benefits.
Green hat: Creative and innovative ideas.
Blue hat: Facilitation and process control.

In all, the six thinking hats process provides a framework that improves collaboration, decision-making, and problem-solving by leveraging the power of parallel thinking and tapping into group intellect.

The 6 benefits of six thinking hats

There are many benefits of the six thinking hats brainstorming technique that may be of interest when problem-solving and decision-making. Some of these include:

1. Enhanced creativity

The six thinking hats method stimulates creative thinking by encouraging participants to explore various perspectives, generate new ideas, and think outside the box.

By wearing different hats, individuals are encouraged to step out of their comfort zones and explore uncommon ideas. Overall, the method promotes nontraditional thinking and unlocks fresh ideas and possibilities.

2. Balanced thinking

Each of the six hats ensures balanced thinking by considering all angles of a topic, including:

Facts
Emotion
Critical judgments
Positive thinking
Creativity
Process control

When all of these factors are considered, the results are more balanced and fairer. This allows participants to see the topic, idea, or problem comprehensively.

3. Improved collaboration

The structured framework of the six thinking hats facilitates effective collaboration by ensuring that all participants can contribute to the discussion. Furthermore, they have the opportunity to share their viewpoints without conflicts or interruptions.

4. Efficient decision-making

The method enables faster and more efficient decision-making by systematically analyzing different aspects, risks, benefits, and alternative possibilities.

By doing so, the method helps streamline the decision-making process, reducing the time spent on deliberation and enabling timely outcomes. Moreover, the approach minimizes the risk of overlooking important factors, which helps to create solid solutions.

5. Reduced bias and subjectivity

The six thinking hats technique asks participants to temporarily set aside their personal biases and judgments and focus on the specific thinking style that their appointed hat represents.

By encouraging a temporary shift in thinking, individuals can approach a problem or idea with an objective mindset. This enables them to consider perspectives based on logical reasoning rather than personal biases.

6. Increased productivity

The six hats process provides a structured and organized approach to brainstorming , ideation, and planning, which increases productivity.

During a session, discussions remain concentrated on the overall goal. By channeling efforts towards a common objective, participants can streamline their thought processes, eliminate distractions, and maintain focus throughout the session.

This increased clarity contributes to heightened productivity as team members use their collective intelligence to achieve outcomes quickly.

The six thinking hats step-by-step process

The six thinking hats process, developed by Edward De Bono, is a structured method for brainstorming, problem-solving , and decision-making.

The process involves the following steps, participants, facilitation, and tools:

Define the focus. The session begins by clearly defining the problem, idea, or topic of discussion that requires brainstorming and decision-making.
Select participants. Select a diverse group of individuals who bring different perspectives, expertise, and roles to the discussion.
Introduce the six hats. The chosen facilitator introduces the concept of the six thinking hats and explains the meaning and role of each hat color. Participants are briefed on the thinking styles associated with each hat and the purpose they serve during the session.
Assign hat roles. The facilitator assigns specific hat roles to participants. Each person is responsible for wearing a particular hat for a given period.
Hat rotation. The session progresses with hat rotation, where participants switch roles by changing hats at designated intervals. This rotation ensures that every participant has the chance to contribute from different perspectives and prevents individuals from becoming fixated on a single thinking style.
Hat exploration. While wearing a specific hat, participants share their thoughts, ideas, observations, or questions related to the topic. The facilitator guides the discussion, ensuring that the focus remains on the thinking style represented by the current hat.
Facilitator’s role. The facilitator plays a crucial role in managing the session. They guide the flow of the discussion, enforce hat rotation, encourage active participation, and maintain a balanced and inclusive environment. The facilitator also ensures that all participants have an opportunity to express their views and that the session stays on track.
Tools and visual aids. The brainstorming process can be supported by visual aids so that participants can jot down key points, ideas, or observations associated with their hat. Visual representations help in organizing thoughts and summarizing outcomes.
Summarize and analyze. At the end of the session, the facilitator summarizes the key insights, observations, ideas, and conclusions from each thinking style. This summary helps to consolidate the collective understanding, identify patterns, and inform subsequent decision-making processes.

The six thinking hats colors and what they represent

Each hat in the six thinking hats method represents a distinct thinking style. The collective use of these hats during a brainstorming session facilitates the evaluation of ideas and well-rounded decision-making.

Red hat

The red hat represents emotions and intuition. When wearing the red hat, participants can express their feelings, gut instincts, and subjective opinions without the need for justification.

This hat encourages the open sharing of personal perspectives and taps into the intuitive and emotional aspects of decision-making. It helps to foster a more holistic understanding of the topic at hand.

Green hat

The green hat symbolizes creativity and new ideas. Participants wearing the green hat are encouraged to think innovatively, develop fresh ideas, and explore alternative possibilities.

This hat promotes divergent thinking, encourages brainstorming, and stimulates creative solutions. It adds a spark of inventiveness to the session.

Blue hat

The blue hat represents process control and organization. It plays the role of a facilitator in the brainstorming session.

The blue hat wearer manages the overall thinking process, guides the discussion, and ensures the session stays on track. They summarize outcomes, coordinate the contributions of different hats, and keep the session focused and productive.

Yellow hat

The yellow hat signifies positive thinking. Participants wearing the yellow hat focus on exploring the benefits, advantages, and positive aspects of the ideas or proposal.

Yellow hat wearers look for value, prospects, and optimistic perspectives. In addition, they help to create a constructive and forward-thinking atmosphere.

White hat

The white hat is associated with facts and information. It represents a logical and objective thinking style.

Participants wearing the white hat gather and analyze data, facts, and information relevant to the topic. They provide an objective foundation and add evidence-based insights, helping the group make well-informed decisions.

Black hat

The black hat embodies critical judgment. Participants wearing the black hat take a cautious and critical approach.

They identify potential risks, flaws, and negative aspects of ideas or proposals. The black hat thinking style aims to identify pitfalls, challenge assumptions, and encourage careful evaluation.

When to use the six thinking hats method

The six thinking hats method provides a framework for collaborative brainstorming that maximizes the potential of a team’s collective intelligence. As a result, sessions may be more creative and effective.

The six hats thinking method is particularly useful in situations where:

A team needs to generate new ideas or solutions.
There are diverse opinions or conflicts among team members.
A comprehensive evaluation of ideas is required.
Emotional or intuitive aspects need to be considered alongside logical reasoning.
The decision-making process needs to be more objective and rational.

Six thinking hats example

To understand the six thinking hats method more fully, here’s an example of how the process may play out in a real-life scenario:

Team : The marketing team at a tech company.
Objective : Generate innovative marketing campaign ideas for a new product launch.
Process : The team leader introduces the six thinking hats method and assigns specific hat roles to each team member.
Red hat (emotions and intuition): The individual wearing the red hat openly expresses their gut feelings and emotional responses towards the marketing campaign ideas at hand. They discuss their personal inclinations and share their enthusiasm or concerns about specific campaign concepts.
Green hat (creativity) : The green hat team member freely shares creative marketing campaign ideas without criticism. They generate diverse ideas, such as viral videos, interactive social media campaigns, and experiential events.
White hat (facts and information): The team transitions to the person wearing the white hat. Here, the individual analyzes the feasibility and gathers data on the market campaign ideas. They consider budget constraints, target audience demographics, and competitor analysis.
Black hat (critical judgment): Moving to the black hat, this individual critically evaluates the ideas on the table. They identify potential risks, such as legal implications, negative public perception, or budget overruns. They weigh the pros and cons of each idea and highlight any drawbacks or challenges.
Yellow hat (positive thinking): The person wearing the yellow hat focuses on the positive aspects of the campaign ideas. They discuss potential benefits, advantages, and opportunities for each concept. They also highlight the possible impact on brand awareness, customer engagement, and market differentiation
Blue hat (process control): This team member takes on the role of session manager. They summarize the key insights and guide the discussion toward the most promising ideas. They also highlight the most feasible concepts from the overall hat discussion.
Results : The brainstorming session allowed the marketing team to explore various creative marketing campaign ideas. The team considered diverse perspectives, backed by data and discussion.

The session facilitated inclusive participation and balanced the exploration of ideas. As a result, the team identified three promising campaign concepts:

A gamified social media contest.
An influencer-driven product launch event.
An interactive augmented reality experience.

The team left the session with a clear direction for further developing and refining these ideas. This led to a more informed and effective marketing strategy for the new product launch.

Unleash the power of the six thinking hats method for brainstorming and take your ideation sessions to new heights!

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Six thinking hats frequently asked questions (FAQ)

Below are a few commonly asked questions about the six thinking hats brainstorming method:

What is six thinking hats?

The six thinking hats is a method developed by Edward De Bono for structured thinking and decision-making. It involves wearing six metaphorical hats, each representing a specific thinking style.

This technique explores ideas, analyzes information, considers emotions, and facilitates well-rounded and effective discussions.

How do teams use six thinking hats?

Teams use the six thinking hats to develop unique perspectives and ideas. By assigning different hats to each participant, teams can work together to think outside the box and enjoy efficient and productive brainstorming, problem-solving, and decision-making.

What are the benefits of six thinking hats?

The benefits of six thinking hats include:

Enhanced creativity
Balanced perspectives
Improved decision-making
Efficient collaboration
Effective problem-solving
Increased productivity

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

Business team using creative problem-solving

01 Feb 2022

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

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

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

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What Is Creative Problem-Solving?

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

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

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

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

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

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

1. Balance Divergent and Convergent Thinking

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

2. Reframe Problems as Questions

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

3. Defer Judgment of Ideas

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

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

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

Creative Problem-Solving and Design Thinking

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

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

The four stages are:

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

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

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

Creative Problem-Solving Tools

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

Creating a Problem Story

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

1. Identify a UDP

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

2. Move Forward in Time

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

3. Move Backward in Time

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

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

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

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

4. Break the Chains

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

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

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

Brainstorming

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

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

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

Alternate Worlds

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

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

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

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

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

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Using the Scientific Method to Solve Problems

How the scientific method and reasoning can help simplify processes and solve problems.

By the Mind Tools Content Team

The processes of problem-solving and decision-making can be complicated and drawn out. In this article we look at how the scientific method, along with deductive and inductive reasoning can help simplify these processes.

‘It is a capital mistake to theorize before one has information. Insensibly one begins to twist facts to suit our theories, instead of theories to suit facts.’ Sherlock Holmes

The Scientific Method

The scientific method is a process used to explore observations and answer questions. Originally used by scientists looking to prove new theories, its use has spread into many other areas, including that of problem-solving and decision-making.

The scientific method is designed to eliminate the influences of bias, prejudice and personal beliefs when testing a hypothesis or theory. It has developed alongside science itself, with origins going back to the 13th century. The scientific method is generally described as a series of steps.

observations/theory
explanation/conclusion

The first step is to develop a theory about the particular area of interest. A theory, in the context of logic or problem-solving, is a conjecture or speculation about something that is not necessarily fact, often based on a series of observations.

Once a theory has been devised, it can be questioned and refined into more specific hypotheses that can be tested. The hypotheses are potential explanations for the theory.

The testing, and subsequent analysis, of these hypotheses will eventually lead to a conclus ion which can prove or disprove the original theory.

Applying the Scientific Method to Problem-Solving

How can the scientific method be used to solve a problem, such as the color printer is not working?

1. Use observations to develop a theory.

In order to solve the problem, it must first be clear what the problem is. Observations made about the problem should be used to develop a theory. In this particular problem the theory might be that the color printer has run out of ink. This theory is developed as the result of observing the increasingly faded output from the printer.

2. Form a hypothesis.

Note down all the possible reasons for the problem. In this situation they might include:

The printer is set up as the default printer for all 40 people in the department and so is used more frequently than necessary.
There has been increased usage of the printer due to non-work related printing.
In an attempt to reduce costs, poor quality ink cartridges with limited amounts of ink in them have been purchased.
The printer is faulty.

All these possible reasons are hypotheses.

3. Test the hypothesis.

Once as many hypotheses (or reasons) as possible have been thought of, then each one can be tested to discern if it is the cause of the problem. An appropriate test needs to be devised for each hypothesis. For example, it is fairly quick to ask everyone to check the default settings of the printer on each PC, or to check if the cartridge supplier has changed.

4. Analyze the test results.

Once all the hypotheses have been tested, the results can be analyzed. The type and depth of analysis will be dependant on each individual problem, and the tests appropriate to it. In many cases the analysis will be a very quick thought process. In others, where considerable information has been collated, a more structured approach, such as the use of graphs, tables or spreadsheets, may be required.

5. Draw a conclusion.

Based on the results of the tests, a conclusion can then be drawn about exactly what is causing the problem. The appropriate remedial action can then be taken, such as asking everyone to amend their default print settings, or changing the cartridge supplier.

Inductive and Deductive Reasoning

The scientific method involves the use of two basic types of reasoning, inductive and deductive.

Inductive reasoning makes a conclusion based on a set of empirical results. Empirical results are the product of the collection of evidence from observations. For example:

‘Every time it rains the pavement gets wet, therefore rain must be water’.

There has been no scientific determination in the hypothesis that rain is water, it is purely based on observation. The formation of a hypothesis in this manner is sometimes referred to as an educated guess. An educated guess, whilst not based on hard facts, must still be plausible, and consistent with what we already know, in order to present a reasonable argument.

Deductive reasoning can be thought of most simply in terms of ‘If A and B, then C’. For example:

if the window is above the desk, and
the desk is above the floor, then
the window must be above the floor

It works by building on a series of conclusions, which results in one final answer.

Social Sciences and the Scientific Method

The scientific method can be used to address any situation or problem where a theory can be developed. Although more often associated with natural sciences, it can also be used to develop theories in social sciences (such as psychology, sociology and linguistics), using both quantitative and qualitative methods.

Quantitative information is information that can be measured, and tends to focus on numbers and frequencies. Typically quantitative information might be gathered by experiments, questionnaires or psychometric tests. Qualitative information, on the other hand, is based on information describing meaning, such as human behavior, and the reasons behind it. Qualitative information is gathered by way of interviews and case studies, which are possibly not as statistically accurate as quantitative methods, but provide a more in-depth and rich description.

The resultant information can then be used to prove, or disprove, a hypothesis. Using a mix of quantitative and qualitative information is more likely to produce a rounded result based on the factual, quantitative information enriched and backed up by actual experience and qualitative information.

In terms of problem-solving or decision-making, for example, the qualitative information is that gained by looking at the ‘how’ and ‘why’ , whereas quantitative information would come from the ‘where’, ‘what’ and ‘when’.

It may seem easy to come up with a brilliant idea, or to suspect what the cause of a problem may be. However things can get more complicated when the idea needs to be evaluated, or when there may be more than one potential cause of a problem. In these situations, the use of the scientific method, and its associated reasoning, can help the user come to a decision, or reach a solution, secure in the knowledge that all options have been considered.

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Published: 10 April 2024

A hybrid particle swarm optimization algorithm for solving engineering problem

Jinwei Qiao 1 , 2 ,
Guangyuan Wang 1 , 2 ,
Zhi Yang 1 , 2 ,
Xiaochuan Luo 3 ,
Jun Chen 1 , 2 ,
Kan Li 4 &
Pengbo Liu 1 , 2

Scientific Reports volume 14 , Article number: 8357 ( 2024 ) Cite this article

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Computational science
Mechanical engineering

To overcome the disadvantages of premature convergence and easy trapping into local optimum solutions, this paper proposes an improved particle swarm optimization algorithm (named NDWPSO algorithm) based on multiple hybrid strategies. Firstly, the elite opposition-based learning method is utilized to initialize the particle position matrix. Secondly, the dynamic inertial weight parameters are given to improve the global search speed in the early iterative phase. Thirdly, a new local optimal jump-out strategy is proposed to overcome the "premature" problem. Finally, the algorithm applies the spiral shrinkage search strategy from the whale optimization algorithm (WOA) and the Differential Evolution (DE) mutation strategy in the later iteration to accelerate the convergence speed. The NDWPSO is further compared with other 8 well-known nature-inspired algorithms (3 PSO variants and 5 other intelligent algorithms) on 23 benchmark test functions and three practical engineering problems. Simulation results prove that the NDWPSO algorithm obtains better results for all 49 sets of data than the other 3 PSO variants. Compared with 5 other intelligent algorithms, the NDWPSO obtains 69.2%, 84.6%, and 84.6% of the best results for the benchmark function ( ${f}_{1}-{f}_{13}$ ) with 3 kinds of dimensional spaces (Dim = 30,50,100) and 80% of the best optimal solutions for 10 fixed-multimodal benchmark functions. Also, the best design solutions are obtained by NDWPSO for all 3 classical practical engineering problems.

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Introduction

In the ever-changing society, new optimization problems arise every moment, and they are distributed in various fields, such as automation control 1 , statistical physics 2 , security prevention and temperature prediction 3 , artificial intelligence 4 , and telecommunication technology 5 . Faced with a constant stream of practical engineering optimization problems, traditional solution methods gradually lose their efficiency and convenience, making it more and more expensive to solve the problems. Therefore, researchers have developed many metaheuristic algorithms and successfully applied them to the solution of optimization problems. Among them, Particle swarm optimization (PSO) algorithm 6 is one of the most widely used swarm intelligence algorithms.

However, the basic PSO has a simple operating principle and solves problems with high efficiency and good computational performance, but it suffers from the disadvantages of easily trapping in local optima and premature convergence. To improve the overall performance of the particle swarm algorithm, an improved particle swarm optimization algorithm is proposed by the multiple hybrid strategy in this paper. The improved PSO incorporates the search ideas of other intelligent algorithms (DE, WOA), so the improved algorithm proposed in this paper is named NDWPSO. The main improvement schemes are divided into the following 4 points: Firstly, a strategy of elite opposition-based learning is introduced into the particle population position initialization. A high-quality initialization matrix of population position can improve the convergence speed of the algorithm. Secondly, a dynamic weight methodology is adopted for the acceleration coefficients by combining the iterative map and linearly transformed method. This method utilizes the chaotic nature of the mapping function, the fast convergence capability of the dynamic weighting scheme, and the time-varying property of the acceleration coefficients. Thus, the global search and local search of the algorithm are balanced and the global search speed of the population is improved. Thirdly, a determination mechanism is set up to detect whether the algorithm falls into a local optimum. When the algorithm is “premature”, the population resets 40% of the position information to overcome the local optimum. Finally, the spiral shrinking mechanism combined with the DE/best/2 position mutation is used in the later iteration, which further improves the solution accuracy.

The structure of the paper is given as follows: Sect. “ Particle swarm optimization (PSO) ” describes the principle of the particle swarm algorithm. Section “ Improved particle swarm optimization algorithm ” shows the detailed improvement strategy and a comparison experiment of inertia weight is set up for the proposed NDWPSO. Section “ Experiment and discussion ” includes the experimental and result discussion sections on the performance of the improved algorithm. Section “ Conclusions and future works ” summarizes the main findings of this study.

Literature review

This section reviews some metaheuristic algorithms and other improved PSO algorithms. A simple discussion about recently proposed research studies is given.

Metaheuristic algorithms

A series of metaheuristic algorithms have been proposed in recent years by using various innovative approaches. For instance, Lin et al. 7 proposed a novel artificial bee colony algorithm (ABCLGII) in 2018 and compared ABCLGII with other outstanding ABC variants on 52 frequently used test functions. Abed-alguni et al. 8 proposed an exploratory cuckoo search (ECS) algorithm in 2021 and carried out several experiments to investigate the performance of ECS by 14 benchmark functions. Brajević 9 presented a novel shuffle-based artificial bee colony (SB-ABC) algorithm for solving integer programming and minimax problems in 2021. The experiments are tested on 7 integer programming problems and 10 minimax problems. In 2022, Khan et al. 10 proposed a non-deterministic meta-heuristic algorithm called Non-linear Activated Beetle Antennae Search (NABAS) for a non-convex tax-aware portfolio selection problem. Brajević et al. 11 proposed a hybridization of the sine cosine algorithm (HSCA) in 2022 to solve 15 complex structural and mechanical engineering design optimization problems. Abed-Alguni et al. 12 proposed an improved Salp Swarm Algorithm (ISSA) in 2022 for single-objective continuous optimization problems. A set of 14 standard benchmark functions was used to evaluate the performance of ISSA. In 2023, Nadimi et al. 13 proposed a binary starling murmuration optimization (BSMO) to select the effective features from different important diseases. In the same year, Nadimi et al. 14 systematically reviewed the last 5 years' developments of WOA and made a critical analysis of those WOA variants. In 2024, Fatahi et al. 15 proposed an Improved Binary Quantum-based Avian Navigation Optimizer Algorithm (IBQANA) for the Feature Subset Selection problem in the medical area. Experimental evaluation on 12 medical datasets demonstrates that IBQANA outperforms 7 established algorithms. Abed-alguni et al. 16 proposed an Improved Binary DJaya Algorithm (IBJA) to solve the Feature Selection problem in 2024. The IBJA’s performance was compared against 4 ML classifiers and 10 efficient optimization algorithms.

Improved PSO algorithms

Many researchers have constantly proposed some improved PSO algorithms to solve engineering problems in different fields. For instance, Yeh 17 proposed an improved particle swarm algorithm, which combines a new self-boundary search and a bivariate update mechanism, to solve the reliability redundancy allocation problem (RRAP) problem. Solomon et al. 18 designed a collaborative multi-group particle swarm algorithm with high parallelism that was used to test the adaptability of Graphics Processing Units (GPUs) in distributed computing environments. Mukhopadhyay and Banerjee 19 proposed a chaotic multi-group particle swarm optimization (CMS-PSO) to estimate the unknown parameters of an autonomous chaotic laser system. Duan et al. 20 designed an improved particle swarm algorithm with nonlinear adjustment of inertia weights to improve the coupling accuracy between laser diodes and single-mode fibers. Sun et al. 21 proposed a particle swarm optimization algorithm combined with non-Gaussian stochastic distribution for the optimal design of wind turbine blades. Based on a multiple swarm scheme, Liu et al. 22 proposed an improved particle swarm optimization algorithm to predict the temperatures of steel billets for the reheating furnace. In 2022, Gad 23 analyzed the existing 2140 papers on Swarm Intelligence between 2017 and 2019 and pointed out that the PSO algorithm still needs further research. In general, the improved methods can be classified into four categories:

Adjusting the distribution of algorithm parameters. Feng et al. 24 used a nonlinear adaptive method on inertia weights to balance local and global search and introduced asynchronously varying acceleration coefficients.

Changing the updating formula of the particle swarm position. Both papers 25 and 26 used chaotic mapping functions to update the inertia weight parameters and combined them with a dynamic weighting strategy to update the particle swarm positions. This improved approach enables the particle swarm algorithm to be equipped with fast convergence of performance.

The initialization of the swarm. Alsaidy and Abbood proposed 27 a hybrid task scheduling algorithm that replaced the random initialization of the meta-heuristic algorithm with the heuristic algorithms MCT-PSO and LJFP-PSO.

Combining with other intelligent algorithms: Liu et al. 28 introduced the differential evolution (DE) algorithm into PSO to increase the particle swarm as diversity and reduce the probability of the population falling into local optimum.

Particle swarm optimization (PSO)

The particle swarm optimization algorithm is a population intelligence algorithm for solving continuous and discrete optimization problems. It originated from the social behavior of individuals in bird and fish flocks 6 . The core of the PSO algorithm is that an individual particle identifies potential solutions by flight in a defined constraint space adjusts its exploration direction to approach the global optimal solution based on the shared information among the group, and finally solves the optimization problem. Each particle $i$ includes two attributes: velocity vector ${V}_{i}=\left[{v}_{i1},{v}_{i2},{v}_{i3},{...,v}_{ij},{...,v}_{iD},\right]$ and position vector ${X}_{i}=[{x}_{i1},{x}_{i2},{x}_{i3},...,{x}_{ij},...,{x}_{iD}]$ . The velocity vector is used to modify the motion path of the swarm; the position vector represents a potential solution for the optimization problem. Here, $j=\mathrm{1,2},\dots ,D$ , $D$ represents the dimension of the constraint space. The equations for updating the velocity and position of the particle swarm are shown in Eqs. ( 1 ) and ( 2 ).

Here ${Pbest}_{i}^{k}$ represents the previous optimal position of the particle $i$ , and ${Gbest}$ is the optimal position discovered by the whole population. $i=\mathrm{1,2},\dots ,n$ , $n$ denotes the size of the particle swarm. ${c}_{1}$ and ${c}_{2}$ are the acceleration constants, which are used to adjust the search step of the particle 29 . ${r}_{1}$ and ${r}_{2}$ are two random uniform values distributed in the range $[\mathrm{0,1}]$ , which are used to improve the randomness of the particle search. $\omega$ inertia weight parameter, which is used to adjust the scale of the search range of the particle swarm 30 . The basic PSO sets the inertia weight parameter as a time-varying parameter to balance global exploration and local seeking. The updated equation of the inertia weight parameter is given as follows:

where ${\omega }_{max}$ and ${\omega }_{min}$ represent the upper and lower limits of the range of inertia weight parameter. $k$ and $Mk$ are the current iteration and maximum iteration.

Improved particle swarm optimization algorithm

According to the no free lunch theory 31 , it is known that no algorithm can solve every practical problem with high quality and efficiency for increasingly complex and diverse optimization problems. In this section, several improvement strategies are proposed to improve the search efficiency and overcome this shortcoming of the basic PSO algorithm.

Improvement strategies

The optimization strategies of the improved PSO algorithm are shown as follows:

The inertia weight parameter is updated by an improved chaotic variables method instead of a linear decreasing strategy. Chaotic mapping performs the whole search at a higher speed and is more resistant to falling into local optimal than the probability-dependent random search 32 . However, the population may result in that particles can easily fly out of the global optimum boundary. To ensure that the population can converge to the global optimum, an improved Iterative mapping is adopted and shown as follows:

Here ${\omega }_{k}$ is the inertia weight parameter in the iteration $k$ , $b$ is the control parameter in the range $[\mathrm{0,1}]$ .

The acceleration coefficients are updated by the linear transformation. ${c}_{1}$ and ${c}_{2}$ represent the influential coefficients of the particles by their own and population information, respectively. To improve the search performance of the population, ${c}_{1}$ and ${c}_{2}$ are changed from fixed values to time-varying parameter parameters, that are updated by linear transformation with the number of iterations:

where ${c}_{max}$ and ${c}_{min}$ are the maximum and minimum values of acceleration coefficients, respectively.

The initialization scheme is determined by elite opposition-based learning . The high-quality initial population will accelerate the solution speed of the algorithm and improve the accuracy of the optimal solution. Thus, the elite backward learning strategy 33 is introduced to generate the position matrix of the initial population. Suppose the elite individual of the population is ${X}=[{x}_{1},{x}_{2},{x}_{3},...,{x}_{j},...,{x}_{D}]$ , and the elite opposition-based solution of $X$ is ${X}_{o}=[{x}_{{\text{o}}1},{x}_{{\text{o}}2},{x}_{{\text{o}}3},...,{x}_{oj},...,{x}_{oD}]$ . The formula for the elite opposition-based solution is as follows:

where ${k}_{r}$ is the random value in the range $(\mathrm{0,1})$ . ${ux}_{oij}$ and ${lx}_{oij}$ are dynamic boundaries of the elite opposition-based solution in $j$ dimensional variables. The advantage of dynamic boundary is to reduce the exploration space of particles, which is beneficial to the convergence of the algorithm. When the elite opposition-based solution is out of bounds, the out-of-bounds processing is performed. The equation is given as follows:

After calculating the fitness function values of the elite solution and the elite opposition-based solution, respectively, $n$ high quality solutions were selected to form a new initial population position matrix.

The position updating Eq. ( 2 ) is modified based on the strategy of dynamic weight. To improve the speed of the global search of the population, the strategy of dynamic weight from the artificial bee colony algorithm 34 is introduced to enhance the computational performance. The new position updating equation is shown as follows:

Here $\rho$ is the random value in the range $(\mathrm{0,1})$ . $\psi$ represents the acceleration coefficient and ${\omega }{\prime}$ is the dynamic weight coefficient. The updated equations of the above parameters are as follows:

where $f(i)$ denotes the fitness function value of individual particle $i$ and u is the average of the population fitness function values in the current iteration. The Eqs. ( 11 , 12 ) are introduced into the position updating equation. And they can attract the particle towards positions of the best-so-far solution in the search space.

New local optimal jump-out strategy is added for escaping from the local optimal. When the value of the fitness function for the population optimal particles does not change in M iterations, the algorithm determines that the population falls into a local optimal. The scheme in which the population jumps out of the local optimum is to reset the position information of the 40% of individuals within the population, in other words, to randomly generate the position vector in the search space. M is set to 5% of the maximum number of iterations.

New spiral update search strategy is added after the local optimal jump-out strategy. Since the whale optimization algorithm (WOA) was good at exploring the local search space 35 , the spiral update search strategy in the WOA 36 is introduced to update the position of the particles after the swarm jumps out of local optimal. The equation for the spiral update is as follows:

Here $D=\left|{x}_{i}\left(k\right)-Gbest\right|$ denotes the distance between the particle itself and the global optimal solution so far. $B$ is the constant that defines the shape of the logarithmic spiral. $l$ is the random value in $[-\mathrm{1,1}]$ . $l$ represents the distance between the newly generated particle and the global optimal position, $l=-1$ means the closest distance, while $l=1$ means the farthest distance, and the meaning of this parameter can be directly observed by Fig. 1 .

Spiral updating position.

The DE/best/2 mutation strategy is introduced to form the mutant particle. 4 individuals in the population are randomly selected that differ from the current particle, then the vector difference between them is rescaled, and the difference vector is combined with the global optimal position to form the mutant particle. The equation for mutation of particle position is shown as follows:

where ${x}^{*}$ is the mutated particle, $F$ is the scale factor of mutation, ${r}_{1}$ , ${r}_{2}$ , ${r}_{3}$ , ${r}_{4}$ are random integer values in $(0,n]$ and not equal to $i$ , respectively. Specific particles are selected for mutation with the screening conditions as follows:

where $Cr$ represents the probability of mutation, $rand\left(\mathrm{0,1}\right)$ is a random number in $\left(\mathrm{0,1}\right)$ , and ${i}_{rand}$ is a random integer value in $(0,n]$ .

The improved PSO incorporates the search ideas of other intelligent algorithms (DE, WOA), so the improved algorithm proposed in this paper is named NDWPSO. The pseudo-code for the NDWPSO algorithm is given as follows:

The main procedure of NDWPSO.

Comparing the distribution of inertia weight parameters

There are several improved PSO algorithms (such as CDWPSO 25 , and SDWPSO 26 ) that adopt the dynamic weighted particle position update strategy as their improvement strategy. The updated equations of the CDWPSO and the SDWPSO algorithm for the inertia weight parameters are given as follows:

where ${\text{A}}$ is a value in $(\mathrm{0,1}]$ . ${r}_{max}$ and ${r}_{min}$ are the upper and lower limits of the fluctuation range of the inertia weight parameters, $k$ is the current number of algorithm iterations, and $Mk$ denotes the maximum number of iterations.

Considering that the update method of inertia weight parameters by our proposed NDWPSO is comparable to the CDWPSO, and SDWPSO, a comparison experiment for the distribution of inertia weight parameters is set up in this section. The maximum number of iterations in the experiment is $Mk=500$ . The distributions of CDWPSO, SDWPSO, and NDWPSO inertia weights are shown sequentially in Fig. 2 .

The inertial weight distribution of CDWPSO, SDWPSO, and NDWPSO.

In Fig. 2 , the inertia weight value of CDWPSO is a random value in (0,1]. It may make individual particles fly out of the range in the late iteration of the algorithm. Similarly, the inertia weight value of SDWPSO is a value that tends to zero infinitely, so that the swarm no longer can fly in the search space, making the algorithm extremely easy to fall into the local optimal value. On the other hand, the distribution of the inertia weights of the NDWPSO forms a gentle slope by two curves. Thus, the swarm can faster lock the global optimum range in the early iterations and locate the global optimal more precisely in the late iterations. The reason is that the inertia weight values between two adjacent iterations are inversely proportional to each other. Besides, the time-varying part of the inertial weight within NDWPSO is designed to reduce the chaos characteristic of the parameters. The inertia weight value of NDWPSO avoids the disadvantages of the above two schemes, so its design is more reasonable.

Experiment and discussion

In this section, three experiments are set up to evaluate the performance of NDWPSO: (1) the experiment of 23 classical functions 37 between NDWPSO and three particle swarm algorithms (PSO 6 , CDWPSO 25 , SDWPSO 26 ); (2) the experiment of benchmark test functions between NDWPSO and other intelligent algorithms (Whale Optimization Algorithm (WOA) 36 , Harris Hawk Algorithm (HHO) 38 , Gray Wolf Optimization Algorithm (GWO) 39 , Archimedes Algorithm (AOA) 40 , Equilibrium Optimizer (EO) 41 and Differential Evolution (DE) 42 ); (3) the experiment for solving three real engineering problems (welded beam design 43 , pressure vessel design 44 , and three-bar truss design 38 ). All experiments are run on a computer with Intel i5-11400F GPU, 2.60 GHz, 16 GB RAM, and the code is written with MATLAB R2017b.

The benchmark test functions are 23 classical functions, which consist of indefinite unimodal (F1–F7), indefinite dimensional multimodal functions (F8–F13), and fixed-dimensional multimodal functions (F14–F23). The unimodal benchmark function is used to evaluate the global search performance of different algorithms, while the multimodal benchmark function reflects the ability of the algorithm to escape from the local optimal. The mathematical equations of the benchmark functions are shown and found as Supplementary Tables S1 – S3 online.

Experiments on benchmark functions between NDWPSO, and other PSO variants

The purpose of the experiment is to show the performance advantages of the NDWPSO algorithm. Here, the dimensions and corresponding population sizes of 13 benchmark functions (7 unimodal and 6 multimodal) are set to (30, 40), (50, 70), and (100, 130). The population size of 10 fixed multimodal functions is set to 40. Each algorithm is repeated 30 times independently, and the maximum number of iterations is 200. The performance of the algorithm is measured by the mean and the standard deviation (SD) of the results for different benchmark functions. The parameters of the NDWPSO are set as: ${[{\omega }_{min},\omega }_{max}]=[\mathrm{0.4,0.9}]$ , $\left[{c}_{max},{c}_{min}\right]=\left[\mathrm{2.5,1.5}\right],{V}_{max}=0.1,b={e}^{-50}, M=0.05\times Mk, B=1,F=0.7, Cr=0.9.$ And, $A={\omega }_{max}$ for CDWPSO; ${[r}_{max},{r}_{min}]=[\mathrm{4,0}]$ for SDWPSO.

Besides, the experimental data are retained to two decimal places, but some experimental data will increase the number of retained data to pursue more accuracy in comparison. The best results in each group of experiments will be displayed in bold font. The experimental data is set to 0 if the value is below 10 –323 . The experimental parameter settings in this paper are different from the references (PSO 6 , CDWPSO 25 , SDWPSO 26 , so the final experimental data differ from the ones within the reference.

As shown in Tables 1 and 2 , the NDWPSO algorithm obtains better results for all 49 sets of data than other PSO variants, which include not only 13 indefinite-dimensional benchmark functions and 10 fixed-multimodal benchmark functions. Remarkably, the SDWPSO algorithm obtains the same accuracy of calculation as NDWPSO for both unimodal functions f 1 –f 4 and multimodal functions f 9 –f 11 . The solution accuracy of NDWPSO is higher than that of other PSO variants for fixed-multimodal benchmark functions f 14 -f 23 . The conclusion can be drawn that the NDWPSO has excellent global search capability, local search capability, and the capability for escaping the local optimal.

In addition, the convergence curves of the 23 benchmark functions are shown in Figs. 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 and 19 . The NDWPSO algorithm has a faster convergence speed in the early stage of the search for processing functions f1-f6, f8-f14, f16, f17, and finds the global optimal solution with a smaller number of iterations. In the remaining benchmark function experiments, the NDWPSO algorithm shows no outstanding performance for convergence speed in the early iterations. There are two reasons of no outstanding performance in the early iterations. On one hand, the fixed-multimodal benchmark function has many disturbances and local optimal solutions in the whole search space. on the other hand, the initialization scheme based on elite opposition-based learning is still stochastic, which leads to the initial position far from the global optimal solution. The inertia weight based on chaotic mapping and the strategy of spiral updating can significantly improve the convergence speed and computational accuracy of the algorithm in the late search stage. Finally, the NDWPSO algorithm can find better solutions than other algorithms in the middle and late stages of the search.

Evolution curve of NDWPSO and other PSO algorithms for f1 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f2 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f3 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f4 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f5 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f6 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f7 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f8 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f9 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f10 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f11(Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f12 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f13 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f14, f15, f16.

Evolution curve of NDWPSO and other PSO algorithms for f17, f18, f19.

Evolution curve of NDWPSO and other PSO algorithms for f20, f21, f22.

Evolution curve of NDWPSO and other PSO algorithms for f23.

To evaluate the performance of different PSO algorithms, a statistical test is conducted. Due to the stochastic nature of the meta-heuristics, it is not enough to compare algorithms based on only the mean and standard deviation values. The optimization results cannot be assumed to obey the normal distribution; thus, it is necessary to judge whether the results of the algorithms differ from each other in a statistically significant way. Here, the Wilcoxon non-parametric statistical test 45 is used to obtain a parameter called p -value to verify whether two sets of solutions are different to a statistically significant extent or not. Generally, it is considered that p ≤ 0.5 can be considered as a statistically significant superiority of the results. The p -values calculated in Wilcoxon’s rank-sum test comparing NDWPSO and other PSO algorithms are listed in Table 3 for all benchmark functions. The p -values in Table 3 additionally present the superiority of the NDWPSO because all of the p -values are much smaller than 0.5.

In general, the NDWPSO has the fastest convergence rate when finding the global optimum from Figs. 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 and 19 , and thus we can conclude that the NDWPSO is superior to the other PSO variants during the process of optimization.

Comparison experiments between NDWPSO and other intelligent algorithms

Experiments are conducted to compare NDWPSO with several other intelligent algorithms (WOA, HHO, GWO, AOA, EO and DE). The experimental object is 23 benchmark functions, and the experimental parameters of the NDWPSO algorithm are set the same as in Experiment 4.1. The maximum number of iterations of the experiment is increased to 2000 to fully demonstrate the performance of each algorithm. Each algorithm is repeated 30 times individually. The parameters of the relevant intelligent algorithms in the experiments are set as shown in Table 4 . To ensure the fairness of the algorithm comparison, all parameters are concerning the original parameters in the relevant algorithm literature. The experimental results are shown in Tables 5 , 6 , 7 and 8 and Figs. 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 and 36 .

Evolution curve of NDWPSO and other algorithms for f1 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f2 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f3(Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f4 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f5 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f6 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f7 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f8 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f9(Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f10 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f11 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f12 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f13 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f14, f15, f16.

Evolution curve of NDWPSO and other algorithms for f17, f18, f19.

Evolution curve of NDWPSO and other algorithms for f20, f21, f22.

Evolution curve of NDWPSO and other algorithms for f23.

The experimental data of NDWPSO and other intelligent algorithms for handling 30, 50, and 100-dimensional benchmark functions ( ${f}_{1}-{f}_{13}$ ) are recorded in Tables 8 , 9 and 10 , respectively. The comparison data of fixed-multimodal benchmark tests ( ${f}_{14}-{f}_{23}$ ) are recorded in Table 11 . According to the data in Tables 5 , 6 and 7 , the NDWPSO algorithm obtains 69.2%, 84.6%, and 84.6% of the best results for the benchmark function ( ${f}_{1}-{f}_{13}$ ) in the search space of three dimensions (Dim = 30, 50, 100), respectively. In Table 8 , the NDWPSO algorithm obtains 80% of the optimal solutions in 10 fixed-multimodal benchmark functions.

The convergence curves of each algorithm are shown in Figs. 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 and 36 . The NDWPSO algorithm demonstrates two convergence behaviors when calculating the benchmark functions in 30, 50, and 100-dimensional search spaces. The first behavior is the fast convergence of NDWPSO with a small number of iterations at the beginning of the search. The reason is that the Iterative-mapping strategy and the position update scheme of dynamic weighting are used in the NDWPSO algorithm. This scheme can quickly target the region in the search space where the global optimum is located, and then precisely lock the optimal solution. When NDWPSO processes the functions ${f}_{1}-{f}_{4}$ , and ${f}_{9}-{f}_{11}$ , the behavior can be reflected in the convergence trend of their corresponding curves. The second behavior is that NDWPSO gradually improves the convergence accuracy and rapidly approaches the global optimal in the middle and late stages of the iteration. The NDWPSO algorithm fails to converge quickly in the early iterations, which is possible to prevent the swarm from falling into a local optimal. The behavior can be demonstrated by the convergence trend of the curves when NDWPSO handles the functions ${f}_{6}$ , ${f}_{12}$ , and ${f}_{13}$ , and it also shows that the NDWPSO algorithm has an excellent ability of local search.

Combining the experimental data with the convergence curves, it is concluded that the NDWPSO algorithm has a faster convergence speed, so the effectiveness and global convergence of the NDWPSO algorithm are more outstanding than other intelligent algorithms.

Experiments on classical engineering problems

Three constrained classical engineering design problems (welded beam design, pressure vessel design 43 , and three-bar truss design 38 ) are used to evaluate the NDWPSO algorithm. The experiments are the NDWPSO algorithm and 5 other intelligent algorithms (WOA 36 , HHO, GWO, AOA, EO 41 ). Each algorithm is provided with the maximum number of iterations and population size ( ${\text{Mk}}=500,\mathrm{ n}=40$ ), and then repeats 30 times, independently. The parameters of the algorithms are set the same as in Table 4 . The experimental results of three engineering design problems are recorded in Tables 9 , 10 and 11 in turn. The result data is the average value of the solved data.

Welded beam design

The target of the welded beam design problem is to find the optimal manufacturing cost for the welded beam with the constraints, as shown in Fig. 37 . The constraints are the thickness of the weld seam ( ${\text{h}}$ ), the length of the clamped bar ( ${\text{l}}$ ), the height of the bar ( ${\text{t}}$ ) and the thickness of the bar ( ${\text{b}}$ ). The mathematical formulation of the optimization problem is given as follows:

Welded beam design.

In Table 9 , the NDWPSO, GWO, and EO algorithms obtain the best optimal cost. Besides, the standard deviation (SD) of t NDWPSO is the lowest, which means it has very good results in solving the welded beam design problem.

Pressure vessel design

Kannan and Kramer 43 proposed the pressure vessel design problem as shown in Fig. 38 to minimize the total cost, including the cost of material, forming, and welding. There are four design optimized objects: the thickness of the shell ${T}_{s}$ ; the thickness of the head ${T}_{h}$ ; the inner radius ${\text{R}}$ ; the length of the cylindrical section without considering the head ${\text{L}}$ . The problem includes the objective function and constraints as follows:

Pressure vessel design.

The results in Table 10 show that the NDWPSO algorithm obtains the lowest optimal cost with the same constraints and has the lowest standard deviation compared with other algorithms, which again proves the good performance of NDWPSO in terms of solution accuracy.

Three-bar truss design

This structural design problem 44 is one of the most widely-used case studies as shown in Fig. 39 . There are two main design parameters: the area of the bar1 and 3 ( ${A}_{1}={A}_{3}$ ) and area of bar 2 ( ${A}_{2}$ ). The objective is to minimize the weight of the truss. This problem is subject to several constraints as well: stress, deflection, and buckling constraints. The problem is formulated as follows:

Three-bar truss design.

From Table 11 , NDWPSO obtains the best design solution in this engineering problem and has the smallest standard deviation of the result data. In summary, the NDWPSO can reveal very competitive results compared to other intelligent algorithms.

Conclusions and future works

An improved algorithm named NDWPSO is proposed to enhance the solving speed and improve the computational accuracy at the same time. The improved NDWPSO algorithm incorporates the search ideas of other intelligent algorithms (DE, WOA). Besides, we also proposed some new hybrid strategies to adjust the distribution of algorithm parameters (such as the inertia weight parameter, the acceleration coefficients, the initialization scheme, the position updating equation, and so on).

23 classical benchmark functions: indefinite unimodal (f1-f7), indefinite multimodal (f8-f13), and fixed-dimensional multimodal(f14-f23) are applied to evaluate the effective line and feasibility of the NDWPSO algorithm. Firstly, NDWPSO is compared with PSO, CDWPSO, and SDWPSO. The simulation results can prove the exploitative, exploratory, and local optima avoidance of NDWPSO. Secondly, the NDWPSO algorithm is compared with 5 other intelligent algorithms (WOA, HHO, GWO, AOA, EO). The NDWPSO algorithm also has better performance than other intelligent algorithms. Finally, 3 classical engineering problems are applied to prove that the NDWPSO algorithm shows superior results compared to other algorithms for the constrained engineering optimization problems.

Although the proposed NDWPSO is superior in many computation aspects, there are still some limitations and further improvements are needed. The NDWPSO performs a limit initialize on each particle by the strategy of “elite opposition-based learning”, it takes more computation time before speed update. Besides, the” local optimal jump-out” strategy also brings some random process. How to reduce the random process and how to improve the limit initialize efficiency are the issues that need to be further discussed. In addition, in future work, researchers will try to apply the NDWPSO algorithm to wider fields to solve more complex and diverse optimization problems.

Data availability

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

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This work was supported by Key R&D plan of Shandong Province, China (2021CXGC010207, 2023CXGC01020); First batch of talent research projects of Qilu University of Technology in 2023 (2023RCKY116); Introduction of urgently needed talent projects in Key Supported Regions of Shandong Province; Key Projects of Natural Science Foundation of Shandong Province (ZR2020ME116); the Innovation Ability Improvement Project for Technology-based Small- and Medium-sized Enterprises of Shandong Province (2022TSGC2051, 2023TSGC0024, 2023TSGC0931); National Key R&D Program of China (2019YFB1705002), LiaoNing Revitalization Talents Program (XLYC2002041) and Young Innovative Talents Introduction & Cultivation Program for Colleges and Universities of Shandong Province (Granted by Department of Education of Shandong Province, Sub-Title: Innovative Research Team of High Performance Integrated Device).

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Debt Free Family

Teach Kids Financial Responsibility: Learn How to Make Money as a Child with These 12 Exciting Ideas.

Posted: April 23, 2024 | Last updated: April 23, 2024

Lets face it, as kids a lot of us wished we had the resources available to kids today, and while we all love back "back in my days" stories, we should take pleasure in giving our kids the tools we never had, or took for granted while growing up.Children have the opportunity to develop their entrepreneurial spirit and learn the fundamentals of money management at a young age in a world where invention and creativity recognize no age boundaries. There are many methods for youngsters to make money while simultaneously learning important life skills, whether they are motivated by a desire for financial independence or the excitement of seeing their ideas come to life.

10 Ways to Make Money As a Kid

Sure you can donate your kids' old clothes and toys to benefit from a small tax break. But often time you could make more cash as well as instill everlasting life-long lessons by teaching your children how much value is still left in their old clothes, toys, and even videogames. Once they see the results, kids may even being to take better care of their possessions knowing that they could recoup some of the value in the form of cash which can be used towards the next "it" toy or game. Sites like Ebay, Facebook Marketplace, Offerup, and even Craigslist and great for letting go of unwanted items and bringing in some extra cash.

1. Selling Used Clothes and Toys

Hard work and perseverance are frequently used to pave the way to financial freedom. Kids have the chance to make money while developing a solid work ethic by performing chores and yard labor. It takes strength and endurance to work in the yard, such as mowing lawns, raking leaves, and gardening. Kids rapidly discover the thrill of turning an unkempt yard into a neatly maintained area via their diligence. This event teaches the importance of perseverance, discipline, and the benefits of making a sincere attempt.

2. Yard Work and Chores

The well-known lemonade stand is a representation of young entrepreneurship that embodies the qualities of imagination, initiative, and involvement in the community. Selling pleasant drinks at a lemonade stand in your community is more than just a way to get kids interested in business, marketing, and money management. The takeaways from this ostensibly straightforward undertaking go far beyond the tinkling of coins at the cash register.

3. Lemonade Stand

Kids with a creative streak can turn the world into a canvas on which to turn their interests into money. Whether their specialty is making personalized T-shirts, painting, or making jewelry by hand, creative endeavors give them a way to express their artistic energy while making money. These activities not only release creativity but also develop a variety of useful skills that establish the groundwork for future entrepreneurial efforts. For instance, making jewelry by hand helps children develop their fine motor skills and artistic expression. Young businesspeople participate in a hands-on process that cultivates patience and attention to detail, from choosing materials to constructing complicated components.

4. Creative Ventures

Older children who are strong in a particular area can help younger students by tutoring or providing academic support. Struggling pupils gain from this by getting better marks, and the tutor also develops personally as a result. Tutoring improves communication, patience, and teaching skills since the tutor can modify their strategy to fit the student's preferred learning method. Due to the fact that students see the benefits of their knowledge in others' lives, tutoring cultivates a sense of responsibility and accomplishment in students. The encounter fosters empathy and a deeper comprehension of various learning requirements. Additionally, tutoring sharpens problem-solving abilities as tutors come up with creative ways to break down challenging material and explain complex ideas.

5. Tutoring and Academic Support

Kids now have a ton of options to make money online, thanks to the digital era. The online environment provides young businesspeople with opportunities to explore, including content production on websites like YouTube, compensated online survey participation, and freelance writing for websites geared toward children. Children can express their hobbies, demonstrate their talents, and interact with a large audience by creating material for websites like YouTube. Crafting, gaming, and making instructional videos are all activities that foster presenting abilities, creativity, and a flare for narrative.

6. Online Ventures

Collecting recyclable items like cans, bottles, and paper goods is a necessary step in participating in recycling activities. Kids may get money by selling these goods to recycling facilities while also actively decreasing trash and conserving resources. They learn the value of responsible consumption and waste minimization as a result of this experience, which helps them make the connection between their activities and their effects on the environment. By repurposing waste into fresh, usable products, upcycling goes beyond recycling. Children with artistic flare can recycle materials to make jewelry, home décor, and useful objects. Upcycling emphasizes the idea of giving outdated products new life while showcasing their creativity and resourcefulness. As children learn to repurpose items in creative ways, this practice fosters critical thinking and problem-solving abilities.

7. Recycling and Upcycling

Making money off of a child's natural affinity for plants and gardening is a fulfilling endeavor. They can discover the world of horticulture while learning about responsibility, patience, and the cycles of nature via gardening and plant sales.Growing plants, herbs, or vegetables fosters a profound respect for the natural world and the cultivation process. Through their care and attention, kids see the magic of a little seed growing into a healthy plant. Because gardening involves consistent work, it teaches children the value of dedication and the benefits of caring for living things.

8. Gardening and Plant Sales

As children become older, opportunities to make money rise, and additional tasks that resemble adult responsibilities are added. In addition to providing cash remuneration, babysitting, and pet sitting are two jobs that emphasize responsibility, reliability, and empathy while teaching important life skills. Babysitting entails providing a secure and nurturing environment for young children. Children who are given this duty learn how to successfully manage their time, making sure that their needs are satisfied and that their activities are enjoyable. As they deal with unforeseen circumstances and make decisions on behalf of their charges, they also develop problem-solving skills.

9. Babysitting and Pet Sitting

Regulations pertaining to employing kids vary by state. Check with city agencies about teen jobs in your area for availably and requirements. Search the web for ""teen job openings near me" or 'teen job hiring near me." Another option is to pay attention to concerts, events coming to your city, and holiday celebrations. Often times agencies are hiring for these events and will gladly support motivated teens looking to make some extra bucks. Another benefit of taking on local temporary jobs is the chance to network and make connections. Get your name and work ethic out there. Like financial literacy, its never too early to start fostering traits that are essential to success as an adult.

10. Apply for Temporary Teen Jobs Locally

If you're creatively inclined, selling crafts or artwork can be a lucrative way to make money as a kid. Consider making handmade jewelry, paintings, pottery, or other unique items that showcase your artistic talents. You can sell your creations at local craft fairs, farmers' markets, or community events. Additionally, you can set up an online store on platforms like Etsy to reach a broader audience. Don't forget to invest time in marketing your products through social media, word of mouth, or collaborations with local businesses. By offering high-quality and visually appealing crafts or artwork, you can attract customers and establish yourself as a talented artisan.

11. Sell Crafts or Artwork.

If you have a knack for baking, consider turning your passion into profit by making homemade treats such as cookies, cupcakes, or brownies to sell. You can experiment with different recipes and flavors to create a unique product that appeals to your target market. Once your treats are ready, you can set up a small bake sale in your neighborhood, at local events, or even online through social media platforms. Make sure to package your treats attractively and consider offering samples to entice potential customers.

12. Baking and Selling Treats.

The experience of working for money as a young person goes much beyond monetary gain. Every entrepreneurial endeavor offers a special chance for kids to acquire important life skills that mold their character and determine their future success. Children who participate in different business activities not only learn about their hobbies and passions but also develop a sense of empowerment and independence. Their personal development is aided by the lessons they acquire from handling money, engaging with clients, and conquering obstacles. Pexels

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The McKinsey guide to problem solving. Become a better problem solver with insights and advice from leaders around the world on topics including developing a problem-solving mindset, solving problems in uncertain times, problem solving with AI, and much more.
The Ultimate Problem-Solving Process Guide: 31 Steps & Resources
It starts with an "affirmative topic," followed by the "positive core (strengths).". Then this method delves into the following stages: Discovery (fact-finding) Dream (visioning the future) Design (strategic purpose) Destiny (continuous improvement) 3. "FIVE WHYS" METHOD. The 5 Whys of Problem-Solving Method.
14 Effective Problem-Solving Strategies
14 types of problem-solving strategies. Here are some examples of problem-solving strategies you can practice using to see which works best for you in different situations: 1. Define the problem. Taking the time to define a potential challenge can help you identify certain elements to create a plan to resolve them.
Problem solving
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue ...
The Basics of Structured Problem-Solving Methodologies: DMAIC ...
DMAIC is best suited for a complex problem, or if the risk is high. 8D is known as the Eight Disciplines of problem-solving. It consists of eight steps to solve difficult, recurring, or critical problems. The methodology consists of problem-solving tools to help you identify, correct, and eliminate the source of problems within your organization.
12 Approaches To Problem-Solving for Every Situation
Here are the seven steps of the rational approach: Define the problem. Identify possible causes. Brainstorm options to solve the problem. Select an option. Create an implementation plan. Execute the plan and monitor the results. Evaluate the solution. Read more: Effective Problem Solving Steps in the Workplace.
A Step-by-Step Guide to A3 Problem Solving Methodology
The goal of the A3 report is to provide a visual representation of the problem-solving process that all members of the organisation can easily understand and share. A3 Problem Solving has been adopted by organisations in a variety of industries over the years, and it has become a widely used and recognised method for problem-solving.
Adopting the right problem-solving approach
In our 2013 classic from the Quarterly, senior partner Olivier Leclerc highlights the value of taking a number of different approaches simultaneously to solve difficult problems. Read on to discover the five flexons, or problem-solving languages, that can be applied to the same problem to generate richer insights and more innovative solutions.
PDF Creative Problem Solving
Creative Problem Solving is a proven method for approaching a problem or a challenge in an imaginative and innovative way. It's a process that helps people re-define the problems they think they face, come up with breakthrough ideas and then take action on these new ideas all with the same innovative spirit. ...
The six thinking hats method: how to use it for effective brainstorming
There are many benefits of the six thinking hats brainstorming technique that may be of interest when problem-solving and decision-making. Some of these include: 1. Enhanced creativity . The six thinking hats method stimulates creative thinking by encouraging participants to explore various perspectives, generate new ideas, and think outside ...
The scientific method (article)
The scientific method. At the core of biology and other sciences lies a problem-solving approach called the scientific method. The scientific method has five basic steps, plus one feedback step: Make an observation. Ask a question. Form a hypothesis, or testable explanation. Make a prediction based on the hypothesis.
What Is Creative Problem-Solving & Why Is It Important?
Creative problem-solving primarily operates in the ideate phase of design thinking but can be applied to others. This is because design thinking is an iterative process that moves between the stages as ideas are generated and pursued. This is normal and encouraged, as innovation requires exploring multiple ideas.
Using the Scientific Method to Solve Problems
The scientific method is a process used to explore observations and answer questions. Originally used by scientists looking to prove new theories, its use has spread into many other areas, including that of problem-solving and decision-making. The scientific method is designed to eliminate the influences of bias, prejudice and personal beliefs ...
What is 8D? Eight Disciplines Problem Solving Process
The eight disciplines (8D) model is a problem solving approach typically employed by quality engineers or other professionals, and is most commonly used by the automotive industry but has also been successfully applied in healthcare, retail, finance, government, and manufacturing. The purpose of the 8D methodology is to identify, correct, and ...
11 Methods to Forecast, Analyze, and Solve Problems
Kaizen is a problem-solving method that can be used to help your teams brainstorm ways to be more productive and efficient and to reduce losses. This methodology aims to question staff at all levels, from CEO to assembly line workers, in terms of waste that leads them to a problem: Movement - useless actions.
A hybrid particle swarm optimization algorithm for solving ...
The particle swarm optimization algorithm is a population intelligence algorithm for solving continuous and discrete optimization problems. It originated from the social behavior of individuals in ...
An effective deep actor-critic reinforcement learning method for
DOI: 10.1007/s00521-024-09654-6 Corpus ID: 269257244; An effective deep actor-critic reinforcement learning method for solving the flexible job shop scheduling problem @article{Wan2024AnED, title={An effective deep actor-critic reinforcement learning method for solving the flexible job shop scheduling problem}, author={Lanjun Wan and Xueyan Cui and Haoxin Zhao and Changyun Li and Zhibing Wang ...
Okhotsimsky-Egorov Method for Solving the Euler-Lambert Problem
Abstract. A method for solving the Euler-Lambert problem by V.A. Egorov is presented, based on the work of D.E. Okhotsimsky and on the analysis of a set of orbits for а flight between two given positions in the central Newtonian field. The method allows to find the orbit of the flight for a given time. The unknown parameter of the orbit is set ...
Golden ratio method for solving monotone variational inequality
In this article, a generalized variational inequality problem in the setting of Hadamard spaces is introduced and analyzed. For approximating a solution of the problem when the underlined mapping is monotone, an adaptive algorithm that requires the computation of only one proximal operator at each iteration is proposed.
Teach Kids Financial Responsibility: Learn How to Make Money as a ...
As they deal with unforeseen circumstances and make decisions on behalf of their charges, they also develop problem-solving skills. In a similar vein, caring for pets necessitates a strong sense ...
A Relaxed Inertial Method for Solving Monotone Inclusion ...
We study a relaxed inertial forward-backward-half-forward splitting approach with variable step size to solve a monotone inclusion problem involving a maximal monotone operator, a cocoercive operator, and a monotone Lipschitz operator. The convergence of the sequence of iterations generated by the discretisations of a continuous-time dynamical system is established under suitable conditions.

35 problem-solving techniques and methods for solving complex problems

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Recommended Articles

How do you identify problems?

Complete problem-solving methods

Problem-solving warm-up activities

Tips for more effective problem solving

Clearly define the problem

Don’t jump to conclusions

Try different approaches

Don’t take it personally

Get the right people in the room

Document everything

Bring a facilitator

Develop your problem-solving skills

Design a great agenda

1. Six Thinking Hats

2. Lightning Decision Jam

3. Problem Definition Process

4. The 5 Whys

5. World Cafe

6. Discovery & Action Dialogue (DAD)

7. Design Sprint 2.0

8. Open space technology

Techniques to identify and analyze problems

10. The Creativity Dice

11. Fishbone Analysis

12. Problem Tree

13. SWOT Analysis

14. Agreement-Certainty Matrix

16. Speed Boat

17. The Journalistic Six

18. LEGO Challenge

19. What, So What, Now What?

20. Journalists

Problem-solving techniques for developing solutions

21. Mindspin

22. Improved Solutions

23. Four Step Sketch

24. 15% Solutions

25. How-Now-Wow Matrix

26. Impact and Effort Matrix

27. Dotmocracy

28. Check-in / Check-out

29. Doodling Together

30. Show and Tell

31. Constellations

32. Draw a Tree

How do I conclude a problem-solving process?

33. One Breath Feedback

34. Who What When Matrix

35. Response cards

Save time and effort discovering the right solutions

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Problem-Solving Strategies and Obstacles

What Is Problem-Solving?

Problem-Solving Mental Processes

Problem-Solving Strategies

Trial and Error

How to Apply Problem-Solving Strategies in Real Life

Obstacles to Problem-Solving

How to Improve Your Problem-Solving Skills

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

What Is Problem Solving?

Problem-Solving Steps

Defining the Problem

Generating Solutions

Evaluating and Selecting Solutions

Implementing and Monitoring the Solution

Problem-Solving Techniques

Brainstorming

Root Cause Analysis

SWOT Analysis

Mind Mapping

Examples of Problem Solving in Various Contexts

The Ultimate Problem-Solving Process Guide: 31 Steps and Resources

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9 PROFITABLE PROBLEM-SOLVING TECHNIQUES AND METHODS