problem solving methods engineering

Oct 13, 2019

10 Steps to Problem Solving for Engineers

Updated: Dec 6, 2020

With the official launch of the engineering book 10+1 Steps to Problem Solving: An Engineer's Guide it may be interesting to know that formalization of the concept began in episode 2 of the Engineering IRL Podcast back in July 2018.

As noted in the book remnants of the steps had existed throughout my career and in this episode I actually recorded the episode off the top of my head.

My goal was to help engineers build a practical approach to problem solving.

Have a listen.

Who can advise on the best approach to problem solving other than the professional problem solvers - Yes. I'm talking about being an Engineer.

There are 2 main trains of thought with Engineering work for non-engineers and that's trying to change the world with leading edge tech and innovations, or plain old boring math nerd type things.

Whilst, somewhat the case what this means is most content I read around Tech and Engineering are either super technical and (excruciatingly) detailed. OR really riff raff at the high level reveling at the possibilities of changing the world as we know it. And so what we end up with is a base (engineer only details) and the topping (media innovation coverage) but what about the meat? The contents?

There's a lot of beauty and interesting things there too. And what's the centrepiece? The common ground between all engineers? Problem solving.

The number one thing an Engineer does is problem solving. Now you may say, "hey, that's the same as my profession" - well this would be true for virtually every single profession on earth. This is not saying there isn't problem solving required in other professions. Some problems require very basic problem solving techniques such is used in every day life, but sometimes problems get more complicated, maybe they involve other parties, maybe its a specific quirk of the system in a specific scenario. One thing you learn in engineering is that not all problems are equal. These are

The stages of problem solving like a pro:

Is the problem identified (no, really, are you actually asking the right question?)

Have you applied related troubleshooting step to above problem?

Have you applied basic troubleshooting steps (i.e. check if its plugged in, turned it on and off again, checked your basics)

Tried step 2 again? (Desperation seeps in, but check your bases)

Asked a colleague or someone else that may have dealt with your problem? (50/50 at this point)

Asked DR. Google (This is still ok)

Deployed RTFM protocol (Read the F***ing Manual - Engineers are notorious for not doing this)

Repeated tests, changing slight things, checking relation to time, or number of people, or location or environment (we are getting DEEP now)

Go to the bottom level, in networking this is packet sniffers to inspect packets, in systems this is taking systems apart and testing in isolation, in software this is checking if 1 equals 1, you are trying to prove basic human facts that everyone knows. If 1 is not equal to 1, you're in deep trouble.At this point you are at rebuild from scratch, re install, start again as your answer (extremely expensive, very rare)

And there you have it! Those are your levels of problem solving. As you go through each step, the more expensive the problem is. -- BUT WAIT. I picked something up along the way and this is where I typically thrive. Somewhere between problem solving step 8 and 10.

The secret step

My recommendation at this point is to try tests that are seemingly unrelated to anything to do with the problem at all.Pull a random cable, test with a random system off/on, try it at a specific time of the day, try it specifically after restarting or replugging something in. Now, not completely random but within some sort of scope. These test are the ones that when someone is having a problem when you suggest they say "that shouldn't fix the problem, that shouldn't be related" and they are absolutely correct.But here's the thing -- at this stage they have already tried everything that SHOULD fix the problem. Now it's time for the hail mary's, the long shots, the clutching at straws. This method works wonders for many reasons. 1. You really are trying to try "anything" at this point.

2. Most of the time we may think we have problem solving step number 1 covered, but we really don't.

3. Triggering correlations.

This is important.

Triggering correlations

In a later post I will cover correlation vs causation, but for now understand that sometimes all you want to do is throw in new inputs to the system or problem you are solving in order to get clues or re identify problems or give new ways to approach earlier problem solving steps. There you have it. Problem solve like a ninja. Approach that extremely experienced and smart person what their problem and as they describe all the things they've tried, throw in a random thing they haven't tried. And when they say, well that shouldn't fix it, you ask them, well if you've exhausted everything that should have worked, this is the time to try things that shouldn't. Either they will think of more tests they haven't considered so as to avoid doing your preposterous idea OR they try it and get a new clue to their problem. Heck, at worst they confirm that they do know SOMETHING about the system.

Go out and problem solve ! As always, thanks for reading and good luck with all of your side hustles.

If you prefer to listen to learn we got you covered with the Engineering IRL show!

For Youtube please go to:

https://youtu.be/EHaRNZhqmHA

For Spotify please go to:

https://open.spotify.com/show/3UZPfOvNwQkaCA1jLIOxp4

And don't forget to subscribe if you get any value from the Engineering IRL Content

Technical Tactics
10+1 Steps to Problem Solving

Lesson Problem Solving

Grade Level: 8 (6-8)

(two 40-minute class periods)

Lesson Dependency: The Energy Problem

Subject Areas: Physical Science, Science and Technology

Print lesson and its associated curriculum

Curriculum in this Unit Units serve as guides to a particular content or subject area. Nested under units are lessons (in purple) and hands-on activities (in blue). Note that not all lessons and activities will exist under a unit, and instead may exist as "standalone" curriculum.

Energy Forms and States Demonstrations
Energy Conversions
Watt Meters to Measure Energy Consumption
Household Energy Audit
Light vs. Heat Bulbs
Efficiency of an Electromechanical System
Efficiency of a Water Heating System
Solving Energy Problems
Energy Projects

TE Newsletter

Engineering connection, learning objectives, worksheets and attachments, more curriculum like this, introduction/motivation, associated activities, user comments & tips.

Engineering… because your dreams need doing

Scientists, engineers and ordinary people use problem solving each day to work out solutions to various problems. Using a systematic and iterative procedure to solve a problem is efficient and provides a logical flow of knowledge and progress.

Students demonstrate an understanding of the Technological Method of Problem Solving.
Students are able to apply the Technological Method of Problem Solving to a real-life problem.

Educational Standards Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards. All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN) , a project of D2L (www.achievementstandards.org). In the ASN, standards are hierarchically structured: first by source; e.g. , by state; within source by type; e.g. , science or mathematics; within type by subtype, then by grade, etc .

Ngss: next generation science standards - science.

View aligned curriculum

Do you agree with this alignment? Thanks for your feedback!

International Technology and Engineering Educators Association - Technology

State standards, national science education standards - science.

Scientists, engineers, and ordinary people use problem solving each day to work out solutions to various problems. Using a systematic and iterative procedure to solve a problem is efficient and provides a logical flow of knowledge and progress.

In this unit, we use what is called "The Technological Method of Problem Solving." This is a seven-step procedure that is highly iterative—you may go back and forth among the listed steps, and may not always follow them in order. Remember that in most engineering projects, more than one good answer exists. The goal is to get to the best solution for a given problem. Following the lesson conduct the associated activities Egg Drop and Solving Energy Problems for students to employ problem solving methods and techniques.

Lesson Background and Concepts for Teachers

The overall concept that is important in this lesson is: Using a standard method or procedure to solve problems makes the process easier and more effective.

1) Describe the problem, 2) describe the results you want, 3) gather information, 4) think of solutions, 5) choose the best solution, 6) implement the solution, 7) evaluate results and make necessary changes. Reenter the design spiral at any step to revise as necessary.

The specific process of problem solving used in this unit was adapted from an eighth-grade technology textbook written for New York State standard technology curriculum. The process is shown in Figure 1, with details included below. The spiral shape shows that this is an iterative, not linear, process. The process can skip ahead (for example, build a model early in the process to test a proof of concept) and go backwards (learn more about the problem or potential solutions if early ideas do not work well).

This process provides a reference that can be reiterated throughout the unit as students learn new material or ideas that are relevant to the completion of their unit projects.

Brainstorming about what we know about a problem or project and what we need to find out to move forward in a project is often a good starting point when faced with a new problem. This type of questioning provides a basis and relevance that is useful in other energy science and technology units. In this unit, the general problem that is addressed is the fact that Americans use a lot of energy, with the consequences that we have a dwindling supply of fossil fuels, and we are emitting a lot of carbon dioxide and other air pollutants. The specific project that students are assigned to address is an aspect of this problem that requires them to identify an action they can take in their own live to reduce their overall energy (or fossil fuel) consumption.

The Seven Steps of Problem Solving

1. Identify the problem

Clearly state the problem. (Short, sweet and to the point. This is the "big picture" problem, not the specific project you have been assigned.)

2. Establish what you want to achieve

Completion of a specific project that will help to solve the overall problem.
In one sentence answer the following question: How will I know I've completed this project?
List criteria and constraints: Criteria are things you want the solution to have. Constraints are limitations, sometimes called specifications, or restrictions that should be part of the solution. They could be the type of materials, the size or weight the solution must meet, the specific tools or machines you have available, time you have to complete the task and cost of construction or materials.

3. Gather information and research

Research is sometimes needed both to better understand the problem itself as well as possible solutions.
Don't reinvent the wheel – looking at other solutions can lead to better solutions.
Use past experiences.

4. Brainstorm possible solutions

List and/or sketch (as appropriate) as many solutions as you can think of.

5. Choose the best solution

Evaluate solution by: 1) Comparing possible solution against constraints and criteria 2) Making trade-offs to identify "best."

6. Implement the solution

Develop plans that include (as required): drawings with measurements, details of construction, construction procedure.
Define tasks and resources necessary for implementation.
Implement actual plan as appropriate for your particular project.

7. Test and evaluate the solution

Compare the solution against the criteria and constraints.
Define how you might modify the solution for different or better results.
Egg Drop - Use this demonstration or activity to introduce and use the problem solving method. Encourages creative design.
Solving Energy Problems - Unit project is assigned and students begin with problem solving techniques to begin to address project. Mostly they learn that they do not know enough yet to solve the problem.
Energy Projects - Students use what they learned about energy systems to create a project related to identifying and carrying out a personal change to reduce energy consumption.

The results of the problem solving activity provide a basis for the entire semester project. Collect and review the worksheets to make sure that students are started on the right track.

Learn the basics of the analysis of forces engineers perform at the truss joints to calculate the strength of a truss bridge known as the “method of joints.” Find the tensions and compressions to solve systems of linear equations where the size depends on the number of elements and nodes in the trus...

preview of 'Doing the Math: Analysis of Forces in a Truss Bridge' Lesson

Through role playing and problem solving, this lesson sets the stage for a friendly competition between groups to design and build a shielding device to protect humans traveling in space. The instructor asks students—how might we design radiation shielding for space travel?

preview of 'Shielding from Cosmic Radiation: Space Agency Scenario' Lesson

A process for technical problem solving is introduced and applied to a fun demonstration. Given the success with the demo, the iterative nature of the process can be illustrated.

The culminating energy project is introduced and the technical problem solving process is applied to get students started on the project. By the end of the class, students should have a good perspective on what they have already learned and what they still need to learn to complete the project.

preview of 'Solving Energy Problems' Activity

Hacker, M, Barden B., Living with Technology , 2nd edition. Albany NY: Delmar Publishers, 1993.

Other Related Information

This lesson was originally published by the Clarkson University K-12 Project Based Learning Partnership Program and may be accessed at http://internal.clarkson.edu/highschool/k12/project/energysystems.html.

Contributors

Supporting program, acknowledgements.

This lesson was developed under National Science Foundation grants no. DUE 0428127 and DGE 0338216. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.

Last modified: August 16, 2023

A Practical Guide to Problem-Solving Techniques in Systems Engineering

In the world of systems engineering, identifying and addressing issues is a significant part of the job. To ensure the smooth operation of complex systems, engineers employ various practical problem-solving techniques. Problem-solving techniques are not limited to solving issues specific to any one system, but can also be applied when generating new product ideas and solutions.

We'll start by exploring some common analytical and systematic problem-solving techniques, including thought experiments, the 5 Whys, and root cause analysis, before looking at some more creative techniques.

Analytical and Systematic Problem-Solving Techniques

Thought experiments.

A thought experiment is a disciplined imagination process that engineers use to ponder a problem or system without conducting physical experiments. By using hypothetical scenarios, engineers can predict potential challenges and find solutions without the cost and time of real-world testing.

For instance, consider the design of an urban traffic control system. Engineers can create a thought experiment about how the system would handle an emergency, such as a major traffic accident during rush hour. This mental exercise could help identify potential bottlenecks or gaps in the system, allowing engineers to design more effective controls or contingency plans.

The 5 Whys technique, originally developed by Toyota, is a simple yet effective method to drill down to the root of a problem. By repeatedly asking "why?" in response to the previous answer, engineers can uncover the underlying cause behind an issue.

Imagine a server crash in a data centre. The 5 Whys process might look like this:

Why did the server crash? Because it overheated.
Why did it overheat? Because the cooling system failed.
Why did the cooling system fail? Because the coolant was not circulating.
Why was the coolant not circulating? Because the pump was broken.
Why was the pump broken? Because it was not maintained as per the recommended schedule.

Through this process, we learn that the root cause of the server crash was inadequate maintenance, not merely a random hardware failure.

Root Cause Analysis (RCA)

Root cause analysis (RCA) is a systematic process for identifying the underlying causes of faults or problems. RCA aims to prevent the same problems from recurring by eliminating the root cause rather than treating the symptoms.

For example, suppose a manufacturing assembly line is regularly shutting down due to equipment failure. Rather than just fixing or replacing the equipment each time, an RCA might uncover that a specific part is consistently under high stress due to improper alignment, causing it to fail. By correcting this alignment, the systems engineer can prevent the problem from recurring.

Fault Tree Analysis (FTA)

Fault Tree Analysis (FTA) is a top-down, deductive analysis method used to explore the many different causes of a specific failure or undesirable outcome. It graphically represents the logical relationships between subsystem failures, potential human errors, and external events in the form of a tree.

Suppose a software system suffers from frequent downtime. The FTA would start with the undesired event at the top (downtime), and then branch out into various potential causes such as software bugs, hardware failure, network issues, and so on. Each of these branches can then be subdivided further into more specific faults, allowing the engineer to understand all potential causes of the problem and prioritise the most likely or serious ones for remediation.

Simulation Modelling

Simulation modelling is a powerful tool that allows systems engineers to predict the behaviour of a system under different conditions. By creating a digital twin of a real-world system, engineers can understand the system's response to changes in variables, identify potential issues, and test solutions.

For instance, in a complex logistics operation, a simulation model can be used to understand the impact of adding a new product line or increasing order volume. This could reveal potential bottlenecks or inefficiencies, allowing proactive adjustments to be made before they become real-world problems.

Creative Problem-Solving Techniques

Beyond the analytical and systematic problem-solving techniques traditionally used in engineering, there are numerous creative methods that can be applied. These techniques stimulate lateral thinking, enabling you to view problems from a fresh perspective and identify innovative solutions. Here are a few examples:

Brainstorming

Brainstorming is perhaps one of the most commonly used creative problem-solving techniques. It involves gathering a group of people and encouraging them to freely share their thoughts and ideas related to a specific problem. The key is to refrain from any judgment or criticism during the brainstorming process to encourage free thought and out-of-the-box ideas.

SCAMPER is a creative-thinking technique that uses seven types of transformations: Substitute, Combine, Adapt, Modify, Put to another use, Eliminate, and Reverse. By examining a problem through these different lenses, you can generate novel solutions. For example, if you're trying to enhance the efficiency of a manufacturing process, you might "Adapt" a method from a completely different industry or "Combine" two existing processes into one.

Mind Mapping

Mind Mapping is a visual tool that helps structure information, enabling you to better analyse, comprehend, and generate new ideas. Starting with a central concept, you add nodes branching out into related subtopics. This can reveal unexpected connections and encourage creative problem-solving.

Six Thinking Hats

This technique, devised by Edward de Bono, involves viewing a problem from six distinct perspectives, symbolised by hats of different colours. The white hat considers facts and information, the red hat looks at the issue emotionally, the black hat uses caution and considers risks, the yellow hat optimistically thinks about benefits, the green hat encourages creativity, and the blue hat manages the process and oversees the big picture.

Analogy Thinking

Analogy thinking, or analogous thinking, is a method of comparing the problem at hand to other similar situations or phenomena. By drawing parallels, you might find creative solutions that you would not have considered otherwise. For example, an engineer might draw inspiration from the natural world, such as how a bird flies or a tree distributes nutrients, to solve a complex mechanical or systems problem.

In conclusion, problem-solving in systems engineering represents a harmonious blend of art and science. It's not about completely discarding systematic, logical techniques, but instead complementing them with creative strategies. This combination of traditional and creative methods equips systems engineers with the tools to predict, identify, and address issues effectively and efficiently. By fostering a balance between analytical and innovative thinking, fresh insights can be gained and novel solutions developed. This fusion is often where the most impactful solutions are found. As these techniques are regularly practiced and mastered, they can lead to smoother operations, reduced downtime, and ultimately more successful projects. The artistry lies in the creativity, and the science in the application and understanding of these tools, culminating in an exciting, evolving, and rewarding field.

This content was generated using OpenAI's GPT Large Language Model (with some human curation!). Check out the post "Explain it like I'm 5: What is ChatGPT?" to learn more.

The Power of Active Inference in Systems Engineering

Applications of the pyramid principle in systems engineering, you might also like..., stock and flow modelling, the art of debugging, the importance of model testing and types.

Patching System Leaks

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

3 What is Problem Solving?

Chapter table of contents, what is problem solving.

What Does Problem Solving Look Like?

Developing Problem Solving Processes

Summary of strategies, problem solving: an important job skill.

The ability to solve problems is a basic life skill and is essential to our day-to-day lives, at home, at school, and at work. We solve problems every day without really thinking about how we solve them. For example: it’s raining and you need to go to the store. What do you do? There are lots of possible solutions. Take your umbrella and walk. If you don’t want to get wet, you can drive, or take the bus. You might decide to call a friend for a ride, or you might decide to go to the store another day. There is no right way to solve this problem and different people will solve it differently.

Problem solving is the process of identifying a problem, developing possible solution paths, and taking the appropriate course of action.

Why is problem solving important? Good problem solving skills empower you not only in your personal life but are critical in your professional life. In the current fast-changing global economy, employers often identify everyday problem solving as crucial to the success of their organizations. For employees, problem solving can be used to develop practical and creative solutions, and to show independence and initiative to employers.

what does problem solving look like?

The ability to solve problems is a skill at which you can improve. So how exactly do you practice problem solving? Learning about different problem solving strategies and when to use them will give you a good start. Problem solving is a process. Most strategies provide steps that help you identify the problem and choose the best solution. There are two basic types of strategies: algorithmic and heuristic.

Algorithmic strategies are traditional step-by-step guides to solving problems. They are great for solving math problems (in algebra: multiply and divide, then add or subtract) or for helping us remember the correct order of things (a mnemonic such as “Spring Forward, Fall Back” to remember which way the clock changes for daylight saving time, or “Righty Tighty, Lefty Loosey” to remember what direction to turn bolts and screws). Algorithms are best when there is a single path to the correct solution.

But what do you do when there is no single solution for your problem? Heuristic methods are general guides used to identify possible solutions. A popular one that is easy to remember is IDEAL [Bransford & Stein [1] ] :

IDEAL is just one problem solving strategy. Building a toolbox of problem solving strategies will improve your problem solving skills. With practice, you will be able to recognize and use multiple strategies to solve complex problems.

What is the best way to get a peanut out of a tube that cannot be moved? Watch a chimpanzee solve this problem in the video below [Geert Stienissen [2] ].

Problem solving is a process that uses steps to solve problems. But what does that really mean? Let's break it down and start building our toolbox of problem solving strategies.

What is the first step of solving any problem? The first step is to recognize that there is a problem and identify the right cause of the problem. This may sound obvious, but similar problems can arise from different events, and the real issue may not always be apparent. To really solve the problem, it's important to find out what started it all. This is called identifying the root cause .

Example: You and your classmates have been working long hours on a project in the school's workshop. The next afternoon, you try to use your student ID card to access the workshop, but discover that your magnetic strip has been demagnetized. Since the card was a couple of years old, you chalk it up to wear and tear and get a new ID card. Later that same week you learn that several of your classmates had the same problem! After a little investigation, you discover that a strong magnet was stored underneath a workbench in the workshop. The magnet was the root cause of the demagnetized student ID cards.

The best way to identify the root cause of the problem is to ask questions and gather information. If you have a vague problem, investigating facts is more productive than guessing a solution. Ask yourself questions about the problem. What do you know about the problem? What do you not know? When was the last time it worked correctly? What has changed since then? Can you diagram the process into separate steps? Where in the process is the problem occurring? Be curious, ask questions, gather facts, and make logical deductions rather than assumptions.

When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost, and save money. Although, each path in this exercise ended with a description of a problem solving tool for your toolbox, the first step is always to identify the problem and define the context in which it happened.

There are several strategies that can be used to identify the root cause of a problem. Root cause analysis (RCA) is a method of problem solving that helps people answer the question of why the problem occurred. RCA uses a specific set of steps, with associated tools like the “5 Why Analysis" or the “Cause and Effect Diagram,” to identify the origin of the problem, so that you can:

Once the underlying cause is identified and the scope of the issue defined, the next step is to explore possible strategies to fix the problem.

If you are not sure how to fix the problem, it is okay to ask for help. Problem solving is a process and a skill that is learned with practice. It is important to remember that everyone makes mistakes and that no one knows everything. Life is about learning. It is okay to ask for help when you don’t have the answer. When you collaborate to solve problems you improve workplace communication and accelerates finding solutions as similar problems arise.

One tool that can be useful for generating possible solutions is brainstorming . Brainstorming is a technique designed to generate a large number of ideas for the solution to a problem. The goal is to come up with as many ideas as you can, in a fixed amount of time. Although brainstorming is best done in a group, it can be done individually.

Depending on your path through the exercise, you may have discovered that a couple of your coworkers had experienced similar problems. This should have been an indicator that there was a larger problem that needed to be addressed.

In any workplace, communication of problems and issues (especially those that involve safety) is always important. This is especially crucial in manufacturing where people are constantly working with heavy, costly, and sometimes dangerous equipment. When issues and problems arise, it is important that they be addressed in an efficient and timely manner. Because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost and save money; effective communication is an important tool..

One strategy for improving communication is the huddle . Just like football players on the field, a huddle is a short meeting with everyone standing in a circle. It's always important that team members are aware of how their work impacts one another. A daily team huddle is a great way to ensure that as well as making team members aware of changes to the schedule or any problems or safety issues that have been identified. When done right, huddles create collaboration, communication, and accountability to results. Impromptu huddles can be used to gather information on a specific issue and get each team member's input.

"Never try to solve all the problems at once — make them line up for you one-by-one.” — Richard Sloma

Problem solving improves efficiency and communication on the shop floor. It increases a company's efficiency and profitability, so it's one of the top skills employers look for when hiring new employees. Employers consider professional skills, such as problem solving, as critical to their business’s success.

The 2011 survey, "Boiling Point? The skills gap in U.S. manufacturing [3] ," polled over a thousand manufacturing executives who reported that the number one skill deficiency among their current employees is problem solving, which makes it difficult for their companies to adapt to the changing needs of the industry.

Bransford, J. & Stein, B.S. (). The Ideal Problem Solver: A Guide For Improving Thinking, Learning, And Creativity . New York, NY: W.H. Freeman. ↵
National Geographic. [Geert Stienissen]. (2010, August 19). Insight learning: Chimpanzee Problem Solving [Video file]. Retrieved from http://www.youtube.com/watch?v=fPz6uvIbWZE ↵
Report: Boiling Point: The Skills Gap in U.S. Manufacturing Deloitte / The Manufacturing Institute, October 2011. Retrieved from http://www.themanufacturinginstitute.org/Hidden/2011-Skills-Gap-Report/2011-Skills-Gap-Report.aspx ↵

Share This Book

What is Chemical and Biological Engineering?
Engineering problem solving
Error and uncertainty
Process variables
Process Fundamentals
Material Balances
Reacting systems
Reaction kinetics
Reactor design
Bioreactors
Fluids and fluid flow
Mass transfer
Energy balances
Heat transfer
Heat exchangers
Mechanical energy balances
Process safety
Engineering ethics
Sustainability
Engineering in a global context
How ‘good’ a solution do you need
Steps in solving well-defined engineering process problems, including textbook problems
« What is Chemi...
Teamwork »

Engineering Problem Solving ¶

Some problems are so complex that you have to be highly intelligent and well-informed just to be undecided about them. —Laurence J. Peter

Steps in solving ‘real world’ engineering problems ¶

The following are the steps as enumerated in your textbook:

Collaboratively define the problem

List possible solutions

Evaluate and rank the possible solutions

Develop a detailed plan for the most attractive solution(s)

Re-evaluate the plan to check desirability

Implement the plan

Check the results

A critical part of the analysis process is the ‘last’ step: checking and verifying the results.

Depending on the circumstances, errors in an analysis, procedure, or implementation can have significant, adverse consequences (NASA Mars orbiter crash, Bhopal chemical leak tragedy, Hubble telescope vision issue, Y2K fiasco, BP oil rig blowout, …).

In a practical sense, these checks must be part of a comprehensive risk management strategy.

My experience with problem solving in industry was pretty close to this, though encumbered by numerous business practices (e.g., ‘go/no-go’ tollgates, complex approval processes and procedures).

In addition, solving problems in the ‘real world’ requires a multidisciplinary effort, involving people with various expertise: engineering, manufacturing, supply chain, legal, marketing, product service and warranty, …

Exercise: Problem solving

Step 3 above refers to ranking of alternatives.

Think of an existing product of interest.

What do you think was ranked highest when the product was developed?

Consider what would have happened if a different ranking was used. What would have changed about the product?

Brainstorm ideas with the students around you.

Defining problems collaboratively ¶

Especially in light of global engineering , we need to consider different perspectives as we define our problem. Let’s break the procedure down into steps:

Identify each perspective that is involved in the decision you face. Remember that problems often mean different things in different perspectives. Relevant differences might include national expectations, organizational positions, disciplines, career trajectories, etc. Consider using the mnemonic device “Location, Knowledge, and Desire.”

Location : Who is defining the problem? Where are they located or how are they positioned? How do they get in their positions? Do you know anything about the history of their positions, and what led to the particular configuration of positions you have today on the job? Where are the key boundaries among different types of groups, and where are the alliances?

Knowledge : What forms of knowledge do the representatives of each perspective have? How do they understand the problem at hand? What are their assumptions? From what sources did they gain their knowledge? How did their knowledge evolve?

Desire : What do the proponents of each perspective want? What are their objectives? How do these desires develop? Where are they trying to go? Learn what you can about the history of the issue at hand. Who might have gained or lost ground in previous encounters? How does each perspective view itself at present in relation to those it envisions as relevant to its future?

As formal problem definitions emerge, ask “Whose definition is this?” Remember that “defining the problem clearly” may very well assert one perspective at the expense of others. Once we think about problem solving in relation to people, we can begin to see that the very act of drawing a boundary around a problem has non-technical, or political dimensions, depending on who controls the definition, because someone gains a little power and someone loses a little power.

Map what alternative problem definitions mean to different participants. More than likely you will best understand problem definitions that fit your perspective. But ask “Does it fit other perspectives as well?” Look at those who hold Perspective A. Does your definition fit their location, their knowledge, and their desires? Now turn to those who hold Perspective B. Does your definition fit their location, knowledge, and desires? Completing this step is difficult because it requires stepping outside of one’s own perspective and attempting to understand the problem in terms of different perspectives.

To the extent you encounter disagreement or conclude that the achievement of it is insufficient, begin asking yourself the following: How might I adapt my problem definition to take account of other perspectives out there? Is there some way of accommodating myself to other perspectives rather than just demanding that the others simply recognize the inherent value and rationality of mine? Is there room for compromise among contrasting perspectives?

How ‘good’ a solution do you need ¶

There is also an important aspect of real-world problem solving that is rarely articulated and that is the idea that the ‘quality’ of the analysis and the resources expended should be dependent on the context.

This is difficult to assess without some experience in the particular environment.

How ‘Good’ a Solution Do You Need?

Some rough examples:

10 second answer (answering a question at a meeting in front of your manager or vice president)

10 minute answer (answering a quick question from a colleague)

10 hour answer (answering a request from an important customer)

10 day answer (assembling information as part of a trouble-shooting team)

10 month answer (putting together a comprehensive portfolio of information as part of the design for a new $200,000,000 chemical plant)

Steps in solving well-defined engineering process problems, including textbook problems ¶

Essential steps:

Carefully read the problem statement (perhaps repeatedly) until you understand exactly the scenario and what is being asked.

Translate elements of the word problem to symbols. Also, look for key words that may convey additional information, e.g., ‘steady state’, ‘constant density’, ‘isothermal’. Make note of this additional information on your work page.

Draw a diagram. This can generally be a simple block diagram showing all the input, output, and connecting streams.

Write all known quantities (flow rates, densities, etc.) from step 2 in the appropriate locations on, or near, the diagram. If symbols are used to designate known quantities, include those symbols.

Identify and assign symbols to all unknown quantities and write them in the appropriate locations on, or near, the diagram.

Construct the relevant equation(s). These could be material balances, energy balances, rate equations, etc.

Write down all equations in their general forms. Don’t simplify anything yet.

Discard terms that are equal to zero (or are assumed negligible) for your specific problem and write the simplified equations.

Replace remaining terms with more convenient forms (because of the given information or selected symbols).

Construct equations to express other known relationships between variables, e.g., relationships between stoichiometric coefficients, the sum of species mass fractions must be one.

Whenever possible, solve the equations for the unknown(s) algebraically .

Convert the units of your variables as needed to have a consistent set across your equations.

Substitute these values into the equation(s) from step 7 to get numerical results.

Check your answer.

Does it make sense?

Are the units of the answer correct?

Is the answer consistent with other information you have?

Exercise: Checking results

How do you know your answer is right and that your analysis is correct?

This may be relatively easy for a homework problem, but what about your analysis for an ill-defined ‘real-world’ problem?

Browse Course Material

Course info, instructors.

Dr. George Kocur
Dr. Christopher Cassa
Prof. Marta C. Gonzalez

Departments

Civil and Environmental Engineering

As Taught In

Programming Languages
Software Design and Engineering
Computational Science and Engineering

Learning Resource Types

Introduction to computers and engineering problem solving, course description.

This course presents the fundamentals of object-oriented software design and development, computational methods and sensing for engineering, and scientific and managerial applications. It cover topics, including design of classes, inheritance, graphical user interfaces, numerical methods, streams, threads, sensors, and …

How is 1.00 different from other intro programming courses offered at MIT?

1.00 is a first course in programming. It assumes no prior experience, and it focuses on the use of computation to solve problems in engineering, science and management. The audience for 1.00 is non-computer science majors. 1.00 does not focus on writing compilers or parsers or computing tools where the computer is the system; it focuses on engineering problems where the computer is part of the system, or is used to model a physical or logical system.

1.00 teaches the Java programming language, and it focuses on the design and development of object-oriented software for technical problems. 1.00 is taught in an active learning style. Lecture segments alternating with laboratory exercises are used in every class to allow students to put concepts into practice immediately; this teaching style generates questions and feedback, and allows the teaching staff and students to interact when concepts are first introduced to ensure that core ideas are understood. Like many MIT classes, 1.00 has weekly assignments, which are programs based on actual engineering, science or management applications. The weekly assignments build on the class material from the previous week, and require students to put the concepts taught in the small in-class labs into a larger program that uses multiple elements of Java together.

One big and one small circuit board placed on a blue surface with attached wires

You are leaving MIT OpenCourseWare

Engineering Method

The engineering method (also known as engineering design) is a systematic approach used to reach the desired solution to a problem. There are six steps (or phases): idea, concept, planning, design, development, and launch from problem definition to desired result.

Engineering Method. Source: Ronald L. Lasser

The engineering method has six steps (or phases):

Development

The development step is often divided to include the iterative cycle of build, test, debug, and redesign. The engineering method by nature is an iterative process.

The idea phase usually begins with a problem. The problem statement is typically only vaguely defined and requires research into its viability and its feasibility. Viability suggests that there is significant value (or demand in the case of product development) in pursing the solution. Feasibility serves as a check on whether the idea can be realized. Feasibility may be high, medium, or low: where high feasibility means that people, technology, and time resources are readily available or known; medium is that resources may not be available directly, but can be found; and low means the resources may be rare or do not exist. The most critical part of the idea phase is to define the problem, validate its value, and identify the customer who desires its solution.

The concept phase is about generating numerous models (mathematical, physical, simulation, simple drawings or sketches), all of which should convey that the solution meets the customer’s expectations or requirements. The numerous concepts are generated using brainstorming techniques, which are review sessions in which elements of one concept are recombined with elements from other in an effort to find a single concept that fits best. Typical design judgment and compromise are required to merge concepts. The concept phase ends with a selection of a single concept.

3. Planning

The planning phase is about defining the implementation plan: identifying the people, tasks, task durations, task dependencies, task interconnections, and budget required to get the project done. Many tools are used to convey this information to team members and other stakeholders including Gantt and Pert charts, resource loading spreadsheets, sketches, drawings, proof-of-concept models to validate that the project can be successfully completed.

One critical tool of the planning phase is the system engineering diagram. This diagram shows the solution as an interconnection of smaller and less complicated sub-systems. A system engineering diagram establishes all the inputs and outputs for each module, as well as the way in which the module transforms the inputs into outputs.

The design phase is where “the rubber meets the road.” Details are specified; specifications are established. Some call this phase “design planning” and the development phase “detailed design.” But no matter what it is called, the purpose of this phase is to translate the customer requirements and systems engineering model into engineering specifications that an engineer (designer) can work with to design and build a working prototype. Specifications are detailed using a number with associated units, e.g., 4 volts, or 3.82 inches, or 58 Hz, or a completion time of 22 days.

5. Development

The purpose of development is to generate the engineering documentation: schematics, drawings, source code, and other design information into a working prototype that demonstrates the solution to the problem. The solution may be a tangible working prototype or an intangible working simulation. Of course, nothing works the first time, so this part of the process tends to be more iterative than the other phases. Specifically, it consists of the iterative cycle: design, test, debug, and redesign. If the project had earlier delays or is not on the planned schedule for other reasons, then this time may be the most frantic since the customer deadline may be closely looming.

While testing and debug are often consider a separate phase, most times they occur side-by-side with development as a design morphs from a concept to an artifact. The latter is recommended, reserving time at the end of development for a final test to confirm the desired result meets customer expectation and designer’s intent. Testing is the verification and validation phase where the concept meets both the anticipated design specifications and the customer’s requirements of the solution. Testing is achieved through experiments—an information-gathering method where dissimilarity and difference are assessed with respect to the design’s present and compared to desired state for the design. The purpose of an experiment is to determine whether test results agree or conflict with the a priori stated behavior. A sufficient numbers of successful testing verifications and validations are necessary to generate acceptable results and to reduce any risk that the desired behavior is present and functions as expected. If the test observations and results do not agree, then a debug process is necessary to identify the root causes and begin corrective action to resolve the discrepancies.

Launch includes the release of the engineering design and documentation package to manufacturing facilities for production. At this point, all qualification testing is complete, and the working prototype has demonstrated functionality.

Cited References

Ertas, A., & Jones, J. C. (1996). The Engineering design process (2nd ed.). New York: John Wiley & Sons. OCLC WorldCat Permalink: http://www.worldcat.org/oclc/807148675
Ullman, D. G. (2009). The Mechanical Design Process (4th ed.). New York, N.Y.: McGraw Hill. OCLC WorldCat Permalink: http://www.worldcat.org/oclc/244060468
Ulrich, K.T., & Eppinger, S. D. (2008). Product Design and Development (4th ed.) New York, N.Y.: McGraw Hill. OCLC WorldCat Permalink: http://www.worldcat.org/oclc/122424997
Articles > 1. Design Process > Engineering Method

Search the Handbook:

Handbook overview.

Introduction and Acknowledgements
Senior Capstone Projects Summary for the 2022-23 Academic Year
Senior Capstone Projects Summary for the 2021-22 Academic Year
Senior Capstone Projects Summary for the 2020-21 Academic Year
Senior Capstone Projects Summary for the 2019-20 Academic Year
Senior Capstone Projects Summary for the 2018-19 Academic Year
Senior Capstone Projects Summary for the 2017-18 Academic Year
Senior Capstone Projects Summary for the 2016-17 Academic Year
Senior Capstone Projects Summary for the 2015-16 Academic Year
Senior Capstone Projects Summary for the 2014-15 Academic Year
Senior Capstone Projects Summary for the 2013-14 Academic Year
Senior Capstone Projects Summary for the 2012-13 Academic Year
1. Design Process
2. Management
3. Technologies
4. Communications And Life Skills
5. Tech Notes
Electrical and Computer Engineering Design Handbook

Disclaimer | Non-Discrimination | Privacy | Terms for Creating and Maintaining Sites

What Is Problem Solving? How Software Engineers Approach Complex Challenges

From debugging an existing system to designing an entirely new software application, a day in the life of a software engineer is filled with various challenges and complexities. The one skill that glues these disparate tasks together and makes them manageable? Problem solving .

Throughout this blog post, we’ll explore why problem-solving skills are so critical for software engineers, delve into the techniques they use to address complex challenges, and discuss how hiring managers can identify these skills during the hiring process.

What Is Problem Solving?

But what exactly is problem solving in the context of software engineering? How does it work, and why is it so important?

Problem solving, in the simplest terms, is the process of identifying a problem, analyzing it, and finding the most effective solution to overcome it. For software engineers, this process is deeply embedded in their daily workflow. It could be something as simple as figuring out why a piece of code isn’t working as expected, or something as complex as designing the architecture for a new software system.

In a world where technology is evolving at a blistering pace, the complexity and volume of problems that software engineers face are also growing. As such, the ability to tackle these issues head-on and find innovative solutions is not only a handy skill — it’s a necessity.

The Importance of Problem-Solving Skills for Software Engineers

Problem-solving isn’t just another ability that software engineers pull out of their toolkits when they encounter a bug or a system failure. It’s a constant, ongoing process that’s intrinsic to every aspect of their work. Let’s break down why this skill is so critical.

Driving Development Forward

Without problem solving, software development would hit a standstill. Every new feature, every optimization, and every bug fix is a problem that needs solving. Whether it’s a performance issue that needs diagnosing or a user interface that needs improving, the capacity to tackle and solve these problems is what keeps the wheels of development turning.

It’s estimated that 60% of software development lifecycle costs are related to maintenance tasks, including debugging and problem solving. This highlights how pivotal this skill is to the everyday functioning and advancement of software systems.

Innovation and Optimization

The importance of problem solving isn’t confined to reactive scenarios; it also plays a major role in proactive, innovative initiatives . Software engineers often need to think outside the box to come up with creative solutions, whether it’s optimizing an algorithm to run faster or designing a new feature to meet customer needs. These are all forms of problem solving.

Consider the development of the modern smartphone. It wasn’t born out of a pre-existing issue but was a solution to a problem people didn’t realize they had — a device that combined communication, entertainment, and productivity into one handheld tool.

Increasing Efficiency and Productivity

Good problem-solving skills can save a lot of time and resources. Effective problem-solvers are adept at dissecting an issue to understand its root cause, thus reducing the time spent on trial and error. This efficiency means projects move faster, releases happen sooner, and businesses stay ahead of their competition.

Improving Software Quality

Problem solving also plays a significant role in enhancing the quality of the end product. By tackling the root causes of bugs and system failures, software engineers can deliver reliable, high-performing software. This is critical because, according to the Consortium for Information and Software Quality, poor quality software in the U.S. in 2022 cost at least $2.41 trillion in operational issues, wasted developer time, and other related problems.

Problem-Solving Techniques in Software Engineering

So how do software engineers go about tackling these complex challenges? Let’s explore some of the key problem-solving techniques, theories, and processes they commonly use.

Decomposition

Breaking down a problem into smaller, manageable parts is one of the first steps in the problem-solving process. It’s like dealing with a complicated puzzle. You don’t try to solve it all at once. Instead, you separate the pieces, group them based on similarities, and then start working on the smaller sets. This method allows software engineers to handle complex issues without being overwhelmed and makes it easier to identify where things might be going wrong.

Abstraction

In the realm of software engineering, abstraction means focusing on the necessary information only and ignoring irrelevant details. It is a way of simplifying complex systems to make them easier to understand and manage. For instance, a software engineer might ignore the details of how a database works to focus on the information it holds and how to retrieve or modify that information.

Algorithmic Thinking

At its core, software engineering is about creating algorithms — step-by-step procedures to solve a problem or accomplish a goal. Algorithmic thinking involves conceiving and expressing these procedures clearly and accurately and viewing every problem through an algorithmic lens. A well-designed algorithm not only solves the problem at hand but also does so efficiently, saving computational resources.

Parallel Thinking

Parallel thinking is a structured process where team members think in the same direction at the same time, allowing for more organized discussion and collaboration. It’s an approach popularized by Edward de Bono with the “ Six Thinking Hats ” technique, where each “hat” represents a different style of thinking.

In the context of software engineering, parallel thinking can be highly effective for problem solving. For instance, when dealing with a complex issue, the team can use the “White Hat” to focus solely on the data and facts about the problem, then the “Black Hat” to consider potential problems with a proposed solution, and so on. This structured approach can lead to more comprehensive analysis and more effective solutions, and it ensures that everyone’s perspectives are considered.

This is the process of identifying and fixing errors in code . Debugging involves carefully reviewing the code, reproducing and analyzing the error, and then making necessary modifications to rectify the problem. It’s a key part of maintaining and improving software quality.

Testing and Validation

Testing is an essential part of problem solving in software engineering. Engineers use a variety of tests to verify that their code works as expected and to uncover any potential issues. These range from unit tests that check individual components of the code to integration tests that ensure the pieces work well together. Validation, on the other hand, ensures that the solution not only works but also fulfills the intended requirements and objectives.

Explore verified tech roles & skills.

The definitive directory of tech roles, backed by machine learning and skills intelligence.

Explore all roles

Evaluating Problem-Solving Skills

We’ve examined the importance of problem-solving in the work of a software engineer and explored various techniques software engineers employ to approach complex challenges. Now, let’s delve into how hiring teams can identify and evaluate problem-solving skills during the hiring process.

Recognizing Problem-Solving Skills in Candidates

How can you tell if a candidate is a good problem solver? Look for these indicators:

Previous Experience: A history of dealing with complex, challenging projects is often a good sign. Ask the candidate to discuss a difficult problem they faced in a previous role and how they solved it.
Problem-Solving Questions: During interviews, pose hypothetical scenarios or present real problems your company has faced. Ask candidates to explain how they would tackle these issues. You’re not just looking for a correct solution but the thought process that led them there.
Technical Tests: Coding challenges and other technical tests can provide insight into a candidate’s problem-solving abilities. Consider leveraging a platform for assessing these skills in a realistic, job-related context.

Assessing Problem-Solving Skills

Once you’ve identified potential problem solvers, here are a few ways you can assess their skills:

Solution Effectiveness: Did the candidate solve the problem? How efficient and effective is their solution?
Approach and Process: Go beyond whether or not they solved the problem and examine how they arrived at their solution. Did they break the problem down into manageable parts? Did they consider different perspectives and possibilities?
Communication: A good problem solver can explain their thought process clearly. Can the candidate effectively communicate how they arrived at their solution and why they chose it?
Adaptability: Problem-solving often involves a degree of trial and error. How does the candidate handle roadblocks? Do they adapt their approach based on new information or feedback?

Hiring managers play a crucial role in identifying and fostering problem-solving skills within their teams. By focusing on these abilities during the hiring process, companies can build teams that are more capable, innovative, and resilient.

Key Takeaways

As you can see, problem solving plays a pivotal role in software engineering. Far from being an occasional requirement, it is the lifeblood that drives development forward, catalyzes innovation, and delivers of quality software.

By leveraging problem-solving techniques, software engineers employ a powerful suite of strategies to overcome complex challenges. But mastering these techniques isn’t simple feat. It requires a learning mindset, regular practice, collaboration, reflective thinking, resilience, and a commitment to staying updated with industry trends.

For hiring managers and team leads, recognizing these skills and fostering a culture that values and nurtures problem solving is key. It’s this emphasis on problem solving that can differentiate an average team from a high-performing one and an ordinary product from an industry-leading one.

At the end of the day, software engineering is fundamentally about solving problems — problems that matter to businesses, to users, and to the wider society. And it’s the proficient problem solvers who stand at the forefront of this dynamic field, turning challenges into opportunities, and ideas into reality.

This article was written with the help of AI. Can you tell which parts?

Get started with HackerRank

Over 2,500 companies and 40% of developers worldwide use HackerRank to hire tech talent and sharpen their skills.

Does a College Degree Still Matter for Developers in 2024?

Tips for Solving Engineering Problems Effectively

Problem solving is the process of determining the best feasible action to take in a given situation. Problem solving is an essential skill for engineers to have. Engineers are problem solvers, as the popular quote says:

“Engineers like to solve problems. If there are no problems handily available, they will create their own problems.” – Scott Adams

Engineers are faced with a range of problems in their everyday life. The nature of problems that engineers must solve differs between and among the various disciplines of engineering. Because of the diversity of problems there is no universal list of procedures that will fit every engineering problem. Engineers use various approaches while solving problems.

Engineering problems must be approached systematically, applying an algorithm, or step-by-step practice by which one arrives at a feasible solution. In this post, we’ve prepared a list of tips for solving engineering problems effectively.

#1 Identify the Problem

Evaluating the needs or identifying the problem is a key step in finding a solution for engineering problems. Recognize and describe the problem accurately by exploring it thoroughly. Define what question is to be answered and what outputs or results are to be produced. Also determine the available data and information about the problem in hand.

An improper definition of the problem will cause the engineer to waste time, lengthen the problem solving process and finally arrive at an incorrect solution. It is essential that the stated needs be real needs.

As an engineer, you should also be careful not to make the problem pointlessly bound. Placing too many limitations on the problem may make the solution extremely complex and tough or impossible to solve. To put it simply, eliminate the unnecessary details and only keep relevant details and the root problem.

#2 Collect Relevant Information and Data

After defining the problem, an engineer begins to collect all the relevant information and data needed to solve the problem. The collected data could be physical measurements, maps, outcomes of laboratory experiments, patents, results of conducted surveys, or any number of other types of information. Verify the accuracy of the collected data and information.

As an engineer, you should always try to build on what has already been done before. Don’t reinvent the wheel. Information on related problems that have been solved or unsolved earlier, may help engineers find the optimal solution for a given problem.

#3 Search for Creative Solutions

There are a number of methods to help a group or individual to produce original creative ideas. The development of these new ideas may come from creativity, a subconscious effort, or innovation, a conscious effort.

You can try to visualize the problem or make a conceptual model for the given problem. So think of visualizing the given problem and see if that can help you gain more knowledge about the problem.

#4 Develop a Mathematical Model

Mathematical modeling is the art of translating problems from an application area into tractable mathematical formulations whose theoretical and numerical analysis provides insight, answers, and guidance useful for the originating application.

To develop a mathematical model for the problem, determine what basic principles are applicable and then draw sketches or block diagrams to better understand the problem. Then define and introduce the necessary variables so that the problem is stated purely in mathematical terms.

Afterwards, simplify the problem so that you can obtain the required result. Also identify the and justify the assumptions and constraints in the mathematical model.

#5 Use Computational Method

You can use a computational method based on the mathematical method you’ve developed for the problem. Derive a set of equations that enable the calculation of the desired parameters and variables as described in your mathematical model. You can also develop an algorithm, or step-by-step procedure of evaluating the equations involved in the solution.

To do so, describe the algorithm in mathematical terms and then execute it as a computer program.

#6 Repeat the Problem Solving Process

Not every problem solving is immediately successful. Problems aren’t always solved appropriately the first time. You’ve to rethink and repeat the problem solving process or choose an alternative solution or approach to solving the problem.

Bottom-line:

Engineers often use the reverse-engineering method to solve problems. For example, by taking things apart to identify a problem, finding a solution and then putting the object back together again. Engineers are creative , they know how things work, and so they constantly analyze things and discover how they work.

Problem-solving skills help you to resolve obstacles in a situation. As stated earlier, problem solving is a skill that an engineer must have and fortunately it’s a skill that can be learned. This skill gives engineers a mechanism for identifying things, figuring out why they are broken and determining a course of action to fix them.

Subscribe Now!

Get our latest news, eBooks, tutorials, and free courses straight into your inbox.

What skills do nanotechnology engineers need?

Types of Engineers and What they Do [Explained]

Latest innovations in civil engineering and construction industry

Civil Engineering: The Hardest Engineering Degree?

Education & Career 34
Industry 24
Technology 18

GET OUR APP

Engineering Resources

Everything you need to know about National Space Day

Is Electrical Engineering Hard? Here’s What You Need to Know

35 problem-solving techniques and methods for solving complex problems

Design your next session with SessionLab

Join the 150,000+ facilitators  using SessionLab.

How do you identify problems?

How do you identify the right solution.

Tips for more effective problem-solving

Complete problem-solving methods

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

Problem-solving warm-up activities

Closing activities for a problem-solving process.

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

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

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

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

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

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

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

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

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

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

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

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

Tips for more effective problem solving

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

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

Clearly define the problem

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

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

Don’t jump to conclusions

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

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

Try different approaches

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

Don’t take it personally

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

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

Get the right people in the room

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

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

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

Document everything

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

Bring a facilitator

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

Develop your problem-solving skills

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

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

Design a great agenda

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

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

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

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

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

Design Sprint 2.0

Open Space Technology

1. Six Thinking Hats

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

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

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

2. Lightning Decision Jam

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

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

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

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

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

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

3. Problem Definition Process

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

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

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

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

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

4. The 5 Whys

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

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

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

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

5. World Cafe

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

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

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

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

6. Discovery & Action Dialogue (DAD)

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

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

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

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

7. Design Sprint 2.0

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

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

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

8. Open space technology

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

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

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

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

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

Techniques to identify and analyze problems

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

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

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

Let’s take a look!

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

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

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

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

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

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

10. The Creativity Dice

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

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

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

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

11. Fishbone Analysis

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

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

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

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

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

12. Problem Tree

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

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

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

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

13. SWOT Analysis

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

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

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

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

14. Agreement-Certainty Matrix

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

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

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

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

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

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

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

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

16. Speed Boat

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

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

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

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

17. The Journalistic Six

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

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

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

18. LEGO Challenge

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

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

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

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

19. What, So What, Now What?

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

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

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

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

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

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

20. Journalists

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

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

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

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

Problem-solving techniques for developing solutions

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

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

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

21. Mindspin

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

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

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

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

22. Improved Solutions

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

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

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

23. Four Step Sketch

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

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

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

24. 15% Solutions

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

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

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

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

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

25. How-Now-Wow Matrix

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

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

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

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

26. Impact and Effort Matrix

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

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

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

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

27. Dotmocracy

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

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

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

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

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

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

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

28. Check-in / Check-out

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

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

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

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

29. Doodling Together

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

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

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

30. Show and Tell

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

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

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

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

31. Constellations

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

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

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

32. Draw a Tree

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

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

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

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

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

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

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

One Breath Feedback
Who What When Matrix
Response Cards

How do I conclude a problem-solving process?

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

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

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

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

33. One Breath Feedback

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

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

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

34. Who What When Matrix

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

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

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

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

35. Response cards

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

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

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

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

Save time and effort discovering the right solutions

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

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

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

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

Over to you

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

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

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

Your list of techniques for problem solving can be helpfully extended by adding TRIZ to the list of techniques. TRIZ has 40 problem solving techniques derived from methods inventros and patent holders used to get new patents. About 10-12 are general approaches. many organization sponsor classes in TRIZ that are used to solve business problems or general organiztational problems. You can take a look at TRIZ and dwonload a free internet booklet to see if you feel it shound be included per your selection process.

Design your next workshop with SessionLab

Join the 150,000 facilitators using SessionLab

Learn Engineering & Technology

Methods to Solve Any Engineering Problem

In our day to day life we came across various engineering problems. Once we face these engineering problems few questions will come in our mind like How to resolve it? What are different methods? Which is the simplest or best method?

In this paragraphs, we will discuss various methods to solve any engineering problems & their comparison with each other. There are three basic methods to solve any engineering methods.

Analytical Methods
Numerical Methods
Experimental methods

1. Analytical Methods:

The analytical method is most widely used in curriculum study as well as used by industrial designers to solve the engineering problems. It is a classical approach which gives 100 % accurate results. This approach is also referred to as hand calculations; as in this method various mathematical equations & functions are used to find output variables & derive closed form solutions. This method is mainly applicable for simpler problems like cantilever and simply supported fixed beams, etc.

Though the analytical approach is 100 % accurate, it could also give approximate results if the solution is not closed form. An equation is said to be a closed-form solution if it solves a given problem in terms of mathematical operations & functions from a given generally accepted set. For example, an infinite sum would generally not be considered closed-form.

2. Numerical Method:

When we come across more complex problems, in which both analytical and experimental methods do not work, numerical methods are driving the solutions. CAE engineers or analysts most widely use numerical methods to solve their engineering problems. This numerical method uses computational techniques through simulation software’s & large infrastructures, etc. Numerical methods do not need physical models or prototypes, it builds mathematical models to replicate real life complex problems and while doing so, several assumptions were made to simulate the analysis. Therefore, the results from this method are approximate. So, you cannot believe the results blindly and hence, sometimes sanity checks are needed to validate the simulation either by hand calculations or by physical testing, etc.

The four common numerical methods used to solve engineering problems are:

The Finite Element Method (FEM) is a popular numerical technique used to determine the approximated solution for a partial differential equation (PDE).
Applications : Linear, nonlinear, buckling, thermal, dynamic, and fatigue analysis
Powerful and efficient technique to solve acoustics or NVH problems. Just like FEA, it also requires nodes and elements, but it only considers the outer boundary of the domain. So when the problem is of a volume, only the outer surfaces are considered. Similarly if the domain is of an area, then only the outer periphery is considered. By doing so it reduces the dimensionality of the problems by one degree resulting in faster problem solving. BEM is often more efficient than other methods in terms of computational resources for problems where there is a small surface or volume ratio.
Applications : Acoustics, NVH
The FVM method representing and evaluating partial differential equations as an algebraic equations method is used in many computational fluid dynamics packages. It is very similar to FDM, where the values are calculated at discrete volumes on a generic geometry. The advantage of this method is that it is easily formulated to allow for unstructured meshes.
Applications : CFD (Computational Fluid Dynamics) and Computational Electromagnetic
It uses Taylor’s series to convert a differential equation to an algebraic equation. In the conversion process, higher order terms are neglected.
It is used in combination with BEM or FVM to solve thermal and CFD coupled problems.

Can we solve the same problem with all Numerical methods? The answer is YES, but substantial differences exist between this method in terms of accuracy, ease of programming & computational time, etc.

3. Experimental Method:

Experimental method is also known as physical testing. It is one of the most reliable methods and widely used in industry for product prototype testing.

In this method, the product or component is tested in real time operating conditions & actual measurement were reported. So in order to use this method, you will need a physical prototype of the product or structure you want to be analyzed. Only one prototype testing is not sufficient, for final outcome of analysis 3 to 5 prototype testing is required. Due to this, the experimental method is time consuming, requires expensive physical setup which results in additional cost rather than actual products.

Physical testing is performed with the help of various measuring equipment like strain gauges, different sensors, measuring devices like accelerators, etc. to calculate various parameters of the experiment. Examples: Compressor manufacturers are doing prototype testing to mitigate the vibration levels on prototypes. Here, different accelerators are placed at various point on prototype and acceleration levels are measured for operational loads.

Below images shows the simple cantilever beam problems solution by three different methods approach.

Innovative Clustering-Driven Techniques for Enhancing Initial Solutions in Euclidean Traveling Salesman Problems with Machine Learning Integration

Research Article-Computer Engineering and Computer Science
Published: 18 May 2024

Cite this article

Aymen Takie Eddine Selmi ORCID: orcid.org/0000-0002-3776-7630 1 ,
Mohamed Faouzi Zerarka 2 &
Abdelhakim Cheriet 2 , 3

26 Accesses

Explore all metrics

Integrating machine learning techniques within metaheuristics has shown promise for effectively solving combinatorial problems like the Traveling Salesman Problem (TSP). However, key challenges remain in initializing metaheuristics to balance exploration and exploitation across vast search spaces. This paper introduces a novel clustering-driven technique for constructing high-quality initial solutions to Euclidean TSP instances. Our method uses hierarchical hybrid clustering with K-means, affinity propagation, and density peaks clustering to recursively partition cities into a compressed quadtree structure. A rigorous assessment using the Davies–Bouldin index and Gini coefficient optimizes intra- and inter-cluster quality and balance at each level. The multi-tiered decomposition strategically abstracts complex optimization landscapes into localized clusters that are solved efficiently in parallel within each using heuristics such as nearest neighbor and ant colony optimization. A genetic networking heuristic then interconnects independent intra-cluster solutions to construct unified inter-cluster routes. The clustering-guided initialization provides a diverse population of initialized tours that balance global exploration against localized exploitation. To validate our method, we conduct experiments using the generated solutions to seed a simulated annealing metaheuristic. This experimental evaluation will demonstrate this technique’s ability to initialize metaheuristics for TSP instances closer to optimality compared to traditional methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

An exhaustive review of the metaheuristic algorithms for search and optimization: taxonomy, applications, and open challenges

Spider wasp optimizer: a novel meta-heuristic optimization algorithm

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

Karimi-Mamaghan, M.; Mohammadi, M.; Meyer, P.; Karimi-Mamaghan, A.M.; Talbi, E.-G.: Machine learning at the service of meta-heuristics for solving combinatorial optimization problems: a state-of-the-art. Eur. J. Oper. Res. 296 , 393–422 (2022)

Article MathSciNet Google Scholar

Cook, W.J., Applegate, D.L., Bixby, R.E., & Chvatal, V.: The traveling salesman problem: a computational study (Princeton university press, 2011).

Ahsini, Y.; et al.: The electric vehicle traveling salesman problem on digital elevation models for traffic-aware urban logistics. Algorithms 16 , 402 (2023)

Article Google Scholar

Arkhipov, D.I.; Wu, D.; Wu, T.; Regan, A.C.: A parallel genetic algorithm framework for transportation planning and logistics management. Ieee Access 8 , 106506–106515 (2020)

Kyaw, P.T.; et al.: Coverage path planning for decomposition reconfigurable grid-maps using deep reinforcement learning based travelling salesman problem. IEEE Access 8 , 225945–225956 (2020)

Yang, X.; Ostermeier, M.; Hübner, A.: Winning the race to customers with micro-fulfillment centers: an approach for network planning in quick commerce. Central Eur. J. Oper. Res. 18 , 1–40 (2024)

Google Scholar

Nałkecz-Charkiewicz, K.; Nowak, R.M.: Algorithm for DNA sequence assembly by quantum annealing. BMC Bioinformatics 23 , 122 (2022)

Pyrkov, A.; et al.: Complexity of life sciences in quantum and AI era. Wiley Interdiscip. Rev. Comput. Mol. Sci. 14 , e1701 (2024)

Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem (1976)

Holland, J.H.: Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence (MIT press, 1992).

Kirkpatrick, S.; Gelatt, C.D., Jr.; Vecchi, M.P.: Optimization by simulated annealing. Science 220 , 671–680 (1983)

Tan, C.; Yang, K.: Privacy-preserving adaptive traffic signal control in a connected vehicle environment. Trans. Res. Part C Emerg. Technol. 158 , 104453 (2024)

Budak, G., Chen, X.: A hybrid mathematical model for flying sidekick travelling salesman problem with time windows, 4, 96 (2023)

Zhao, F.; Si, B.; Wei, Z.; Lu, T.: Time-dependent vehicle routing problem of perishable product delivery considering the differences among paths on the congested road. Oper. Res. Int. J. 23 , 5 (2023)

Kanda, J.; De Carvalho, A.; Hruschka, E.; Soares, C.; Brazdil, P.: Meta-learning to select the best meta-heuristic for the traveling salesman problem: a comparison of meta-features. Neurocomputing 205 , 393–406 (2016)

Fan, M., & Li, J.: Surrogate-assisted genetic algorithms for the travelling salesman problem and vehicle routing problem (2020)

Golabi, M., Essaid, M., Sulaman, M., & Idoumghar, L.: Extreme learning machine-based genetic algorithm for the facility location problem with distributed demands on network edges (2023)

Drori, I., et al.: Learning to solve combinatorial optimization problems on real-world graphs in linear time (2020)

Khalil, E., Dai, H., Zhang, Y., Dilkina, B., & Song, L.: Learning combinatorial optimization algorithms over graphs. Adv. Neural Inform. Process. Syst. 30 (2017)

Buzdalova, A., Kononov, V., & Buzdalov, M.: Initial explorations, Selecting evolutionary operators using reinforcement learning (2014)

Wang, Y.; Han, Z.: Ant colony optimization for traveling salesman problem based on parameters optimization. Appl. Soft Comput. 107 , 107439 (2021)

Hartono, N., et al: Parameter tuning for combinatorial bees algorithm in travelling salesman problems (2023)

Pukhkaiev, D., Semendiak, Y., Götz, S., & Aßmann, U.: Combined selection and parameter control of meta-heuristics (2020)

Alipour, M.M.; Razavi, S.N.; Feizi Derakhshi, M.R.; Balafar, M.A.: A hybrid algorithm using a genetic algorithm and multiagent reinforcement learning heuristic to solve the traveling salesman problem. Neural Comput. Appl. 30 , 2935–2951 (2018)

Miki, S., Yamamoto, D., & Ebara, H.: Applying deep learning and reinforcement learning to traveling salesman problem (2018)

Ali, I.M.; Essam, D.; Kasmarik, K.: A novel design of differential evolution for solving discrete traveling salesman problems. Swarm Evol. Comput. 52 , 100607 (2020)

Hartigan, J.A.; Wong, M.A.: Algorithm as 136: A k-means clustering algorithm. J. R. Stat. Soc. Series C Appl. Stat. 28 , 100–108 (1979)

Frey, B.J.; Dueck, D.: Clustering by passing messages between data points. Science 315 , 972–976 (2007)

Rodriguez, A.; Laio, A.: Clustering by fast search and find of density peaks. Science 344 , 1492–1496 (2014)

Davies, D.L.; Bouldin, D.W.: A cluster separation measure. IEEE Trans. Pattern Anal. Mach. Intell. 2 , 224–7 (1979)

Rendón, E.; Abundez, I.; Arizmendi, A.; Quiroz, E.M.: Internal versus external cluster validation indexes. Int. J. Comput. Commun. 5 , 27–34 (2011)

Liu, Y., Li, Z., Xiong, H., Gao, X., & Wu, J.: Understanding of internal clustering validation measures (2010)

Halkidi, M.; Batistakis, Y.; Vazirgiannis, M.: On clustering validation techniques. J. Intell. Inform. Syst. 17 , 107–145 (2001)

Dunn, J.C.: A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters (1973)

Ceriani, L.; Verme, P.: The origins of the gini index: extracts from variabilità e mutabilità (1912) by corrado gini. J. Econ. Inequal. 10 , 421–443 (2012)

Šulc, Z., & Řezanková, H.: Evaluation of recent similarity measures for categorical data (2014)

Dorigo, M.: Optimization, learning and natural algorithms. Ph. D. Thesis, Politecnico di Milano (1992)

Flood, M.M.: The traveling-salesman problem. Oper. Res. 4 , 61–75 (1956)

Liao, E.; Liu, C.: A hierarchical algorithm based on density peaks clustering and ant colony optimization for traveling salesman problem. IEEE Access 6 , 38921–38933 (2018)

Gülcü, Ş; Mahi, M.; Baykan, Ö.K.; Kodaz, H.: A parallel cooperative hybrid method based on ant colony optimization and 3-opt algorithm for solving traveling salesman problem. Soft. Comput. 22 , 1669–1685 (2018)

Mahi, M.; Baykan, Ö.K.; Kodaz, H.: A new hybrid method based on particle swarm optimization, ant colony optimization and 3-opt algorithms for traveling salesman problem. Appl. Soft Comput. 30 , 484–490 (2015)

Chen, S.-M.; Chien, C.-Y.: Solving the traveling salesman problem based on the genetic simulated annealing ant colony system with particle swarm optimization techniques. Expert Syst. Appl. 38 , 14439–14450 (2011)

Wang, Y.: The hybrid genetic algorithm with two local optimization strategies for traveling salesman problem. Comput. Ind. Eng. 70 , 124–133 (2014)

Sahin, M.: Solving tsp by using combinatorial bees algorithm with nearest neighbor method. Neural Comput. Appl. 35 , 1863–1879 (2023)

Wu, C.; Fu, X.; Pei, J.; Dong, Z.: A novel sparrow search algorithm for the traveling salesman problem. IEEE Access 9 , 153456–153471 (2021)

Toaza, B.; Esztergár-Kiss, D.: A review of metaheuristic algorithms for solving TSP-based scheduling optimization problems. Appl. Soft Comput. 11 , 110908 (2023)

Download references

Acknowledgements

This publication is the result of the work carried out in the project within the framework of the Doctoral Program of the Ministry of Higher Education and Scientific Research, Government of Algeria, which is implemented by LESIA and RLP Laboratories of the University of Biskra. Source code available on GitHub: https://github.com/aymentaki/Euclidean-TSP-Solver .

Author information

Authors and affiliations.

LESIA Laboratory, Mohamed Khider University of Biskra, 07000, Biskra, Algeria

Aymen Takie Eddine Selmi

RLP Laboratory, Mohamed Khider University of Biskra, 07000, Biskra, Algeria

Mohamed Faouzi Zerarka & Abdelhakim Cheriet

The National School of Artificial Intelligence, 16000, Algiers, Algeria

Abdelhakim Cheriet

You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aymen Takie Eddine Selmi .

Ethics declarations

Conflict of interest.

The authors declare that they have no conflict of interest.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Selmi, A.T.E., Zerarka, M.F. & Cheriet, A. Innovative Clustering-Driven Techniques for Enhancing Initial Solutions in Euclidean Traveling Salesman Problems with Machine Learning Integration. Arab J Sci Eng (2024). https://doi.org/10.1007/s13369-024-09094-3

Download citation

Received : 16 November 2023

Accepted : 17 April 2024

Published : 18 May 2024

DOI : https://doi.org/10.1007/s13369-024-09094-3

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Compressed quadtree
Davies–Bouldin Index
Gini coefficient
Metaheuristic
Clustering-driven
Euclidean Traveling Salesman Problem
Find a journal
Publish with us
Track your research

Facility for Rare Isotope Beams

At michigan state university, international research team uses wavefunction matching to solve quantum many-body problems, new approach makes calculations with realistic interactions possible.

FRIB researchers are part of an international research team solving challenging computational problems in quantum physics using a new method called wavefunction matching. The new approach has applications to fields such as nuclear physics, where it is enabling theoretical calculations of atomic nuclei that were previously not possible. The details are published in Nature (“Wavefunction matching for solving quantum many-body problems”) .

Ab initio methods and their computational challenges

An ab initio method describes a complex system by starting from a description of its elementary components and their interactions. For the case of nuclear physics, the elementary components are protons and neutrons. Some key questions that ab initio calculations can help address are the binding energies and properties of atomic nuclei not yet observed and linking nuclear structure to the underlying interactions among protons and neutrons.

Yet, some ab initio methods struggle to produce reliable calculations for systems with complex interactions. One such method is quantum Monte Carlo simulations. In quantum Monte Carlo simulations, quantities are computed using random or stochastic processes. While quantum Monte Carlo simulations can be efficient and powerful, they have a significant weakness: the sign problem. The sign problem develops when positive and negative weight contributions cancel each other out. This cancellation results in inaccurate final predictions. It is often the case that quantum Monte Carlo simulations can be performed for an approximate or simplified interaction, but the corresponding simulations for realistic interactions produce severe sign problems and are therefore not possible.

Using ‘plastic surgery’ to make calculations possible

The new wavefunction-matching approach is designed to solve such computational problems. The research team—from Gaziantep Islam Science and Technology University in Turkey; University of Bonn, Ruhr University Bochum, and Forschungszentrum Jülich in Germany; Institute for Basic Science in South Korea; South China Normal University, Sun Yat-Sen University, and Graduate School of China Academy of Engineering Physics in China; Tbilisi State University in Georgia; CEA Paris-Saclay and Université Paris-Saclay in France; and Mississippi State University and the Facility for Rare Isotope Beams (FRIB) at Michigan State University (MSU)—includes Dean Lee , professor of physics at FRIB and in MSU’s Department of Physics and Astronomy and head of the Theoretical Nuclear Science department at FRIB, and Yuan-Zhuo Ma , postdoctoral research associate at FRIB.

“We are often faced with the situation that we can perform calculations using a simple approximate interaction, but realistic high-fidelity interactions cause severe computational problems,” said Lee. “Wavefunction matching solves this problem by doing plastic surgery. It removes the short-distance part of the high-fidelity interaction, and replaces it with the short-distance part of an easily computable interaction.”

This transformation is done in a way that preserves all of the important properties of the original realistic interaction. Since the new wavefunctions look similar to that of the easily computable interaction, researchers can now perform calculations using the easily computable interaction and apply a standard procedure for handling small corrections called perturbation theory. A team effort

The research team applied this new method to lattice quantum Monte Carlo simulations for light nuclei, medium-mass nuclei, neutron matter, and nuclear matter. Using precise ab initio calculations, the results closely matched real-world data on nuclear properties such as size, structure, and binding energies. Calculations that were once impossible due to the sign problem can now be performed using wavefunction matching.

“It is a fantastic project and an excellent opportunity to work with the brightest nuclear scientist s in FRIB and around the globe,” said Ma. “As a theorist , I'm also very excited about programming and conducting research on the world's most powerful exascale supercomputers, such as Frontier , which allows us to implement wavefunction matching to explore the mysteries of nuclear physics.”

While the research team focused solely on quantum Monte Carlo simulations, wavefunction matching should be useful for many different ab initio approaches, including both classical and quantum computing calculations. The researchers at FRIB worked with collaborators at institutions in China, France, Germany, South Korea, Turkey, and United States.

“The work is the culmination of effort over many years to handle the computational problems associated with realistic high-fidelity nuclear interactions,” said Lee. “It is very satisfying to see that the computational problems are cleanly resolved with this new approach. We are grateful to all of the collaboration members who contributed to this project, in particular, the lead author, Serdar Elhatisari.”

This material is based upon work supported by the U.S. Department of Energy, the U.S. National Science Foundation, the German Research Foundation, the National Natural Science Foundation of China, the Chinese Academy of Sciences President’s International Fellowship Initiative, Volkswagen Stiftung, the European Research Council, the Scientific and Technological Research Council of Turkey, the National Natural Science Foundation of China, the National Security Academic Fund, the Rare Isotope Science Project of the Institute for Basic Science, the National Research Foundation of Korea, the Institute for Basic Science, and the Espace de Structure et de réactions Nucléaires Théorique.

Michigan State University operates the Facility for Rare Isotope Beams (FRIB) as a user facility for the U.S. Department of Energy Office of Science (DOE-SC), supporting the mission of the DOE-SC Office of Nuclear Physics. Hosting what is designed to be the most powerful heavy-ion accelerator, FRIB enables scientists to make discoveries about the properties of rare isotopes in order to better understand the physics of nuclei, nuclear astrophysics, fundamental interactions, and applications for society, including in medicine, homeland security, and industry.

The U.S. Department of Energy Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of today’s most pressing challenges. For more information, visit energy.gov/science.

IMAGES

5 step problem solving method
The problem-solving process chart
engineering problem solving process diagram
5 problem solving steps in engineering
The Engineering Problem Solving Process [12].
Engineering problem solving methods

VIDEO

Problem Solving Idea For Mechanical Engineering Project #engineering #shorts
3 problem solving methods that can be converted into business
Solve Projectile Motion Problems Using Mechanical Energy
Creative Thinking for Complex Problem Solving: Course Trailer
Mastering Exact Solutions: Simple Methods for Solving Problems (JJ TECH TUTORING)
Master Problem-Solving: Unveiling Kidlin's Law! 🔍✍️ #ProblemSolving #KidlinsLaw #Clarity

COMMENTS

1.3: What is Problem Solving?
If you are not sure how to fix the problem, it is okay to ask for help. Problem solving is a process and a skill that is learned with practice. It is important to remember that everyone makes mistakes and that no one knows everything. Life is about learning. It is okay to ask for help when you don't have the answer.
10 Steps to Problem Solving for Engineers
Now it's time for the hail mary's, the long shots, the clutching at straws. This method works wonders for many reasons. 1. You really are trying to try "anything" at this point. 2. Most of the time we may think we have problem solving step number 1 covered, but we really don't. 3. Triggering correlations. This is important.
Problem Solving
Remember that in most engineering projects, more than one good answer exists. The goal is to get to the best solution for a given problem. Following the lesson conduct the associated activities Egg Drop and Solving Energy Problems for students to employ problem solving methods and techniques. ...
PDF Introduction to Engineering Design and Problem Solving
Engineering design is the creative process of identifying needs and then devising a solution to fill those needs. This solution may be a product, a technique, a structure, a project, a method, or many other things depending on the problem. The general procedure for completing a good engineering design can be called the Engineering Method of ...
Methodologies for Problem Solving: An Engineering Approach
Methodologies for Problem Solving: An Engineering Approach by JAMES J. SHARP Professor and Chairman of Civil Engineering, Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John's, NF AIB 3X5 ... This has led directly to the realization that it is possible to teach strategies or method- ologies for handling ...
A Practical Guide to Problem-Solving Techniques in Systems Engineering
Creative Problem-Solving Techniques. Beyond the analytical and systematic problem-solving techniques traditionally used in engineering, there are numerous creative methods that can be applied. These techniques stimulate lateral thinking, enabling you to view problems from a fresh perspective and identify innovative solutions. Here are a few ...
What is Problem Solving?
Problem solving is a process. Most strategies provide steps that help you identify the problem and choose the best solution. There are two basic types of strategies: algorithmic and heuristic. Algorithmic strategies are traditional step-by-step guides to solving problems.
Engineering Problem Solving
Steps in solving 'real world' engineering problems ¶. The following are the steps as enumerated in your textbook: Collaboratively define the problem. List possible solutions. Evaluate and rank the possible solutions. Develop a detailed plan for the most attractive solution (s) Re-evaluate the plan to check desirability. Implement the plan.
Engineering Problem-Solving
Abstract. You are becoming an engineer to become a problem solver. That is why employers will hire you. Since problem-solving is an essential portion of the engineering profession, it is necessary to learn approaches that will lead to an acceptable resolution. In real-life, the problems engineers solve can vary from simple single solution ...
Introduction to Computers and Engineering Problem Solving
This course presents the fundamentals of object-oriented software design and development, computational methods and sensing for engineering, and scientific and managerial applications. It cover topics, including design of classes, inheritance, graphical user interfaces, numerical methods, streams, threads, sensors, and data structures. Students use Java{{< sup "®" >}} programming language to ...
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 ...
Methodologies for problem solving: An engineering approach
Therefore, using engineering problem-solving methods, control arms were designed, analyzed, and optimized. However, throughout this report, the process undertaken to achieve those results will be ...
Engineering Method
The engineering method (design) is a systematic approach used to support an engineer or project team in reaching the desired solution to a problem, which has been specified by customers, sponsors, or stakeholders who perceive value in resolving the problem. Figure 1. Engineering Method. Source: Ronald L. Lasser
What is Problem Solving? An Introduction
As you can see, problem solving plays a pivotal role in software engineering. Far from being an occasional requirement, it is the lifeblood that drives development forward, catalyzes innovation, and delivers of quality software. By leveraging problem-solving techniques, software engineers employ a powerful suite of strategies to overcome ...
Intro To Engineering Problem Solving: The SOLVEM Method
This video contains a brief introduction to the SOLVEM method for Engineering Problem Solving.00:00 Introduction00:35 Types of Problems01:35 SOLVEM Method03:...
Tips for Solving Engineering Problems Effectively
Repeat the Problem Solving Process. Not every problem solving is immediately successful. Problems aren't always solved appropriately the first time. You've to rethink and repeat the problem solving process or choose an alternative solution or approach to solving the problem. Bottom-line: Engineers often use the reverse-engineering method to ...
Problem‐Solving Methods
Each problem can be solved by performing experimental modeling, by doing theoretical modeling, or by using experience. One very important first step in solving a geotechnical engineering problem is to always start by making a drawing to scale of the problem. Two main types of laws are used to solve problems: fundamental laws and constitutive ...
35 problem-solving techniques and methods for solving complex problems
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.
The Engineering Method: A Step-by-Step Process for Solving Challenging
We created The Engineering Method, a simple set of steps that can help you break a problem down, find a path toward a solution, and avoid mistakes. Here at Formation, we apply the method to software engineering problems, but the same steps can be applied to many different fields. Step 1: Thoroughly understand the problem A. Ask clarifying questions
Methods to Solve Any Engineering Problem
There are three basic methods to solve any engineering methods. Analytical Methods. Numerical Methods. Experimental methods. 1. Analytical Methods: The analytical method is most widely used in curriculum study as well as used by industrial designers to solve the engineering problems. It is a classical approach which gives 100 % accurate results.
PDF THIRTEEN PROBLEM-SOLVING MODELS
The Six-Step method provides a focused procedure for the problem solving (PS) group. It ensures consistency, as everyone understands the approach to be used. By using data, it helps eliminate bias and preconceptions, leading to greater objectivity. It helps to remove divisions and encourages collaborative working.
Problem solving
There are many specialized problem-solving techniques and methods in fields such as engineering, business, medicine, mathematics, computer science, philosophy, and social organization. The mental techniques to identify, analyze, and solve problems are studied in psychology and cognitive sciences.
Boost Your Mech Engineering Team's Problem-Solving Skills
One effective method is to present real-world engineering challenges and observe how individuals tackle them. This process helps identify gaps in problem-solving skills and informs targeted ...
Exploring Behavioral and Strategic Factors Affecting Secondary Students
Despite the growing emphasis on integrating collaborative problem-solving (CPS) into science, technology, engineering, and mathematics (STEM) education, a comprehensive understanding of the critical factors that affect the effectiveness of this educational approach remains a challenge.
Innovative Clustering-Driven Techniques for Enhancing ...
Integrating machine learning techniques within metaheuristics has shown promise for effectively solving combinatorial problems like the Traveling Salesman Problem (TSP). However, key challenges remain in initializing metaheuristics to balance exploration and exploitation across vast search spaces. This paper introduces a novel clustering-driven technique for constructing high-quality initial ...
International research team uses wavefunction matching to solve quantum
New approach makes calculations with realistic interactions possibleFRIB researchers are part of an international research team solving challenging computational problems in quantum physics using a new method called wavefunction matching. The new approach has applications to fields such as nuclear physics, where it is enabling theoretical calculations of atomic nuclei that were previously not ...