engineering problems for problem solving

• 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

Recent Posts

How to Implement OSHA’s Requirement of Emergency Medical Services in Construction

Preventing Noise-Induced Issues in Construction

The Advantages of CAD for Modern Engineers

Get your free Engineering Toolkit for Engineering IRL listeners only

Get a copy of the Operational Technology Ultimate Guide for Engineers e-book for free.

Problem Solving in Mechanical Engineering With Real World Examples

• Mechanical Engineering

Mechanical engineering is all about solving problems by using science and math. Engineers have to come up with better designs and improve how things are made. They make sure everything works well and lasts long. It’s important because they need to know a lot about their field and think both creatively and logically to find solutions to real problems.

For instance, they might work on making heating and cooling systems use less energy, find ways to cut down on waste when making products, or create new materials for planes and spaceships. These examples show how crucial mechanical engineers are in making technology and industries better.

In simpler terms, mechanical engineers are like problem-solving wizards. They use their deep knowledge and smart thinking to tackle challenges, like making a car engine that uses less fuel or a machine that makes fewer errors. They’re always learning and inventing to make sure the things we use every day are the best they can be.

This is key because their work helps us save money, be safer, and even protect the environment. It’s how they play a big part in pushing technology forward and keeping industries running smoothly.

Understanding Fundamental Principles

In mechanical engineering, it’s crucial to really get thermodynamics, materials science, and how to analyze structures. Knowing these core ideas helps you figure out how forces and materials work together, how energy moves and changes, and how to make sure structures are strong enough to handle different kinds of pressure.

When dealing with complicated systems, you break them down to understand how they work under different situations. For example, when choosing materials, you look closely at their strength, how much they can bend, and how well they conduct heat to make sure they will work well and last a long time. Thermodynamics helps make energy systems work better and use less power. Every solution is carefully made using these ideas to make sure the engineering designs do what they’re supposed to and are safe.

As an example, when building a bridge, engineers will use materials science to pick the right steel that can support the weight of cars over time without bending too much. They’ll apply thermodynamics to design any moving parts, like a drawbridge, to work efficiently with minimal energy waste. By focusing on these principles, engineers make sure the bridge is not only functional, allowing people to cross safely, but also stands the test of time.

Analyzing Complex Systems

To really get how complex machinery works, engineers take it apart to look at each piece. This helps them see how all the parts fit together and make the machine do its job. They start by figuring out where the system begins and ends, then they take a closer look at the smaller parts, like the sensors and motors, and the computer brain that controls everything.

Engineers use special tools and tests, like checking what could go wrong and how likely it is (that’s called FMEA), running computer models, and seeing how changes affect the system. By doing all this, they make sure the machine is safe, reliable, and works well because they’ve checked everything carefully, not left it to luck.

It’s important that they do this because it helps prevent accidents and breakdowns. For example, think about a car: if engineers didn’t test all the parts, like brakes and airbags, we wouldn’t trust them to keep us safe on the road. So, they use these tools to make sure everything is in top shape. This kind of detailed work means that when you use something like a car or a dishwasher, it’s been checked to work properly and safely.

Innovating in Product Design

Creating new and better product designs starts with really understanding how current products work. Mechanical engineers look at these products in detail to figure out how they can make them work better, use less energy, and give people a better experience when using them.

The first step is to carefully study what the product is supposed to do, how people use it, and where it can be improved. Engineers have to take apart complicated parts and processes to spot opportunities for new ideas. They use practical engineering knowledge to make designs that are not just better, but also cost less and are better for the environment. They make sure every part of the new product has a reason to be there and helps make the product both new and useful.

Being committed to making these kinds of advances is a big part of what mechanical engineering is all about in product design.

For example, when engineers worked on a new blender, they saw that the old design was hard to clean. They redesigned the blades to be detachable, which made cleaning easier and the blender more efficient. This change also saved materials, making the blender more eco-friendly.

This kind of thoughtful redesign shows how engineers can make our everyday products better.

Optimizing Manufacturing Processes

In manufacturing, engineers focus on improving the process to achieve faster production, reduced waste, and cost savings. They analyze production methods, examining data and observing operations to identify bottlenecks and inefficiencies. Strategies such as lean manufacturing or Six Sigma are employed to optimize operations and enhance overall efficiency.

Improvements can be made by rearranging machine placement to minimize material movement, implementing proactive maintenance practices to prevent breakdowns, and introducing new technologies like robots. Additionally, engineers work on optimizing the timing of supply deliveries to minimize storage costs. These deliberate actions lead to smarter and more cost-effective manufacturing processes, giving companies a competitive edge.

Ensuring Quality and Reliability

After improving how things are made, it’s crucial to make sure the products are of high quality and can be relied upon. To do this, it’s essential to have a well-thought-out plan for checking the quality and making sure it’s consistent.

Engineers need to create detailed tests that really show what conditions and pressures the products will face in the real world. For example, they might use Failure Mode and Effects Analysis (FMEA) to find and fix possible weaknesses before they cause problems. They also keep an eye on the production process using Statistical Process Control (SPC) to ensure everything stays the same.

Moreover, they use reliability engineering to figure out how to make products last longer. This is all about cutting down on mistakes and making sure the product is as good as it can be, which makes customers happy and maintains the manufacturer’s good name.

To give a specific example, a car manufacturer might use crash tests to simulate real-life accidents. This helps them understand how the car would perform and what they need to improve to ensure passenger safety. By doing this, they not only meet safety standards but also build trust with their customers who know the vehicles are tested thoroughly.

To wrap things up, solving problems in mechanical engineering isn’t simple—it’s a detailed task that involves really understanding the basics, figuring out complicated machinery, being creative when making products, making sure manufacturing is as good as it can be, and always aiming for the highest quality and dependability. It’s vital that all these pieces work together to tackle the tough problems we see in the real world. Mechanical engineers must think things through step by step and apply what they know to keep coming up with new and better ways to move technology forward and make industries run more smoothly.

For example, when engineers work on a new car engine, they need to know exactly how each part works. They must come up with smart designs that make the engine more powerful without using more fuel. They also have to refine the way the engine is built so that the factory can make it without wasting time or materials. Plus, they have to test the engine over and over to make sure it will last a long time and won’t break down. This kind of detailed work is what pushes us ahead, making cars more efficient and reliable for everyone.

Related Posts

Exploring the Intersection of Marine and Mechanical Engineering

Job Openings in Fluid Mechanics Engineering

Harnessing Energy Through Mechanical Engineering Innovations

The Daily Responsibilities of a Mechanical Engineer

Advancing Your Skills With Short Courses in Mechanical Engineering

Choosing the Best Specialization in Mechanical Engineering

• 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 …

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 ® programming language to complete weekly software assignments.

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.

You are leaving MIT OpenCourseWare

Our systems are now restored following recent technical disruption, and we’re working hard to catch up on publishing. We apologise for the inconvenience caused. Find out more: https://www.cambridge.org/universitypress/about-us/news-and-blogs/cambridge-university-press-publishing-update-following-technical-disruption

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings .

Login Alert

• > Cambridge Handbook of Engineering Education Research
• > Engineers as Problem Solvers

Book contents

• Frontmatter
• Contributors
• Acknowledgments
• Introduction
• Chapter 1 Chronological and Ontological Development of Engineering Education as a Field of Scientific Inquiry
• Part 1 Engineering Thinking and Knowing
• Chapter 2 Learning Theories for Engineering Education Practice
• Chapter 3 Situative Frameworks for Engineering Learning Research
• Chapter 4 The Social Nature of Representational Engineering Knowledge
• Chapter 5 Conceptual Change and Misconceptions in Engineering Education
• Chapter 6 Engineers as Problem Solvers
• Chapter 7 Professional Engineering Work
• Part 2 Engineering Learning Mechanisms and Approaches
• Part 3 Pathways into Diversity and Inclusiveness
• Part 4 Engineering Education and Institutional Practices
• Part 5 Research Methods and Assessment
• Part 6 Cross-Cutting Issues and Perspectives

Chapter 6 - Engineers as Problem Solvers

Published online by Cambridge University Press:  05 February 2015

• Engineers as Problem Solvers

Evers, Rush, and Berdrow (1998) identi-fy numerous disconnects between skills acquired in college and those required of the workplace. Among the most important skills that ABET Inc., the primary engineering accreditation institution in the United States, has identified for the preparation of engineers are the abilities to identify, formulate, and solve workplace engineering problems and to function on multidisciplinary teams. Learning to solve workplace problems is an essential learning outcome for any engineering graduate. Every engineer is hired, retained, and rewarded for his or her ability to solve problems. However, engineering graduates are ill prepared to solve complex, workplace problems (Jonassen, Strobel, & Lee, 2006).

Problem solving from a cognitive perspective has been the primary focus of my research for the past decade and a half. My theory differs from traditional theories of problem solving in that I argue there are different kinds of problems that vary between contexts. The kinds of problems that practicing engineers solve are different from the problems that most undergraduate science, technology, engineering, and mathematics (STEM) students learn to solve. In most undergraduate classes, students learn to solve textbook problems that are constrained and well structured, with known solution paths and convergent answers (capstone courses are an exception). Workplace problems, on the other hand, tend to be ill structured and unpredictable because they possess conflicting goals, multiple solution methods, non-engineering success standards, non-engineering constraints, unanticipated problems, distributed knowledge, and collaborative activity systems (Jonassen et al., 2006). Learning to solve classroom problems does not effectively prepare engineering graduates to solve workplace problems. To prepare engineering graduates, it is necessary to articulate the differences between educational problems and workplace problems. To do that, I first describe how problems vary.

Access options

Save book to kindle.

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle .

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service .

• By David H. Jonassen , University of Missouri
• Edited by Aditya Johri , Virginia Polytechnic Institute and State University , Barbara M. Olds
• Book: Cambridge Handbook of Engineering Education Research
• Online publication: 05 February 2015
• Chapter DOI: https://doi.org/10.1017/CBO9781139013451.009

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox .

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive .

• EDUCATION & CAREER
• Engineering Books
• Science and Engineering Celebration Days

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.

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.

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

Disastrous engineering failures due to unethical practices of engineers, asme code of ethics for mechanical engineers, acm code of ethics for computing professionals.

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

• Harvard Business School →
• HBS Online →
• Business Insights →

Business Insights

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

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

7 Engineering Challenges Design Thinking Can Help Solve

• 19 Jan 2023

Several challenges face the engineering industry. Addressing them requires innovative solutions and structured processes, such as design thinking.

If you’re an engineer who wants to develop business skills , here's an overview of design thinking and seven engineering challenges it can help solve.

What Is Design Thinking?

Design thinking is one of the most effective approaches to problem-solving. It’s a solutions-based methodology focused on human-centered design and observing problems with empathy.

In the online course Design Thinking and Innovation , Harvard Business School Dean Srikant Datar structures the process using a four-stage framework. The stages are:

In the clarification stage, you observe a situation or challenge without bias and frame your findings in the form of a problem statement.

“Before you begin to generate innovative solutions for your own design problem, you must always think hard about how you’re going to frame that problem,” Datar says in the course.

Reframing the problem as a question is an excellent way to do this. For example, using "how might we" instead of "the problem is" can encourage empathy in the design process and shift your mindset toward potential solutions.

These questions are particularly important when considering empathetic design. According to the Harvard Business Review , engineers who put themselves in their audience's shoes while designing often develop innovative products . By understanding your audience’s unexpressed needs, you can effectively leverage your technical knowledge to create innovative solutions to previously unknown problems.

Once you've made your observations, you can explore potential solutions. The ideate stage is for divergent thinking—the process of exploring as many ideas as possible. It involves:

• Finding and categorizing similarities in users' pain points
• Considering the resources available to you and how you can use them to solve a problem
• Brainstorming potential solutions

Creativity and an open mind are vital at this stage. As you explore ideas, they can highlight other problems you were unaware of.

The development stage focuses on turning your ideas into workable prototypes. For ideas to be innovative, they must be both new and useful ; many, though creative, aren't feasible.

"As you prototype concepts in phase three, you may discover results that force you to return to phases one and two to reframe your question," Datar says in Design Thinking and Innovation .

This iteration can occur in any of the four stages because each involves a different level of exploration that highlights new problems, questions, or solutions. This isn't cause for discouragement.

"Do not think of this as a setback,” Datar says in the course. “Iterating on solutions is a normal and expected result of design thinking.”

Design thinking’s ultimate objective is finding effective, workable solutions. The implementation phase involves finalizing developments and communicating their value to stakeholders.

This final stage can be challenging for many engineers. Since their work is so technical, it’s sometimes difficult for stakeholders to understand their impact on the organization. As a result, engineers should develop effective communication skills to ensure their ideas are implemented.

The Importance of Design Thinking in Engineering

Design thinking is a valuable skill for engineers to learn for several reasons. For one, engineering positions are among the most common occupations requiring design thinking skills .

Since engineers are often responsible for solving complex problems, it’s easy to get lost in the details and set creative problem-solving skills aside. Creativity in business is beneficial because it:

• Encourages innovation
• Boosts productivity
• Allows for adaptability
• Fosters growth

Leveraging design thinking skills to pursue innovation not only helps professionals find creative solutions but identify business opportunities , evaluate market needs , and design new products and services.

Engineers’ responsibilities can vary. Whether creating new products or maintaining existing ones, engineering revolves around design . For this reason, a systematic approach is highly valuable when encountering industry challenges.

7 Engineering Challenges Design Thinking Can Solve

Some of the challenges engineers often face include:

• Identifying obscure problems
• Overcoming cognitive fixedness
• Designing sustainable innovations
• Addressing the skilled labor shortage
• Encouraging diversity
• Keeping up with advancing technology
• Overcoming status-quo bias

Here’s an overview of how design thinking can help solve these problems.

1. Identifying Obscure Problems

Engineers often encounter problems that are difficult to identify. As a result, it can be easy for them to jump to conclusions based on preexisting knowledge of a design or situation. Datar discourages this in Design Thinking and Innovation .

"Whenever you have a difficult problem, you tend to solve the fringes of it,” Datar says. “But try and go for the most important part that you need to solve."

For example, if you're trying to remove a major obstacle preventing a project’s completion, you might be tempted to search for a cause equal in scope to its impact. However, some of the biggest design problems can be caused by something as simple as a misplaced hyphen or a loose screw. Often, the best approach is to consider the bigger picture. Is there anything in the design you don't understand?

The clarification stage in the design thinking framework encourages you to obtain insights through unbiased observation. An effective tool to accomplish this is journey mapping , which involves creating a chronological visual timeline of everything you know about a problem.

According to Design Thinking and Innovation , the three steps to developing a journey map are:

• Creating observations about the user's journey
• Writing those observations on a timeline
• Organizing the observations into different stages

Creating a timeline of events can help identify when a problem occurs, as well as what precedes and follows it. This can enable you to narrow down its cause.

2. Overcoming Cognitive Fixedness

Cognitive fixedness is a mindset that assumes there's just one way to accomplish tasks. It considers every situation through the lens of past decisions. Thinking "if it worked in the past, it'll work now" is easy to follow, especially in the engineering industry, where replicating past successes is often the best way to proceed.

For example, while new technology trends can succeed in the market because of their innovative features, incorporating those features into an existing design might not be feasible—and even prevent you from meeting critical deadlines. Furthermore, in areas with high risk to human life—such as submarine design—it may be advisable to incorporate technology that’s proven effective before creating something new.

While caution is important, cognitive fixedness can prevent innovation, resulting in obsolescence. You must strike a balance between the operational and the innovation worlds.

The difference between the two worlds is described in Design Thinking and Innovation :

• The operational world represents a business’s routine procedures.
• The innovation world facilitates open-endedly exploring ideas.

Although the operational world is important, it can result in cognitive fixedness and prevent ideas’ progression. If you're struggling to overcome cognitive fixedness—whether your own or someone else's—consider why there's an unwillingness to change to determine the next steps.

3. Designing Sustainable Innovations

Climate change is a pressing issue impacting businesses around the globe . An increasing number of organizational leaders are addressing it by focusing on the triple bottom line . According to the HBS Online course Sustainable Business Strategy , the triple bottom line considers:

• Profit: Satisfying shareholders and producing a profit
• People: Impacting society in a positive, measurable way
• The planet: Making a positive impact on the environment

By reframing problems and pursuing workable solutions that don't sacrifice profit, you can effectively incorporate sustainability into business strategies .

4. Addressing the Skilled Labor Shortage

The United States is experiencing a shortage of engineers , which has put a strain on employers hoping to hire qualified candidates in a shrinking market.

Consider how you'd approach this challenge from a design thinking perspective. Clarifying the problem might highlight opportunities you didn't previously think of. For instance, companies such as Google and Microsoft have invested in science, technology, engineering, and math (STEM) education , enabling more people to pursue careers in those industries.

Other companies have sought ways to attract engineering talent. It can be easy to draw candidates by raising salaries or increasing benefits, but many engineers aren't comfortable working for organizations that harm the environment. Your firm should consider adopting a sustainable business strategy that could benefit the planet and attract qualified applicants.

5. Encouraging Diversity

Engineering has historically been a male-dominated field. One of the primary causes of this imbalance is the workplace stereotype that STEM careers are masculine. This has resulted in implicit—and often direct—discouragement of women from pursuing STEM careers.

In the context of design thinking, clarifying and reframing the problem might result in questions like, "How can we empower more women to pursue STEM careers?"

Through exploring potential solutions, you may discover that encouraging and empowering a diverse population to pursue engineering can help address other challenges, such as the skilled labor shortage.

6. Keeping Up with Advancing Technology

Technology is continuously advancing; companies that fail to adapt might get left behind. For example, Blackberry was once one of the fastest-growing smartphone companies in the world. Yet, its products became obsolete when the company refused to adopt touch-screen technology. This resulted in Blackberry losing 90 percent of its market share between 2009 and 2013.

Design thinking encourages continual awareness to avoid these downward trends. Learning how to recognize opportunities and communicate them to others can prevent a business from falling behind.

7. Overcoming Status-Quo Bias

Resistance to change doesn't just occur within an organization—it happens among customers, too. This is known as status-quo bias , which is a challenge you must address during implementation.

The challenge is how to retain existing customers while appealing to the current market and acquiring new ones. Avoid assuming users will understand a design change you’ve implemented just because it makes sense to you.

According to Datar in Design Thinking and Innovation , you should consider three views during the implementation phase:

• The developer's view: The designer with knowledge and understanding of a design's utility and benefits
• The neutral view: Someone who doesn't have a preexisting opinion about the design
• Stakeholders' view: Existing customers and users who have existing opinions based on the status quo

Learning how to overcome status-quo bias is critical to successful innovation.

Improving Your Design Thinking Skills

Whether encountering one of the engineering challenges mentioned above or something more niche, design thinking can be a valuable tool for solving them.

Learning about the process and its business applications can enable you to climb the corporate ladder and make an impact on your organization.

Ready to learn the tools you need to innovate? Enroll in our online certificate course Design Thinking and Innovation —one of our entrepreneurship and innovation courses —and develop in-demand skills that can benefit your engineering career. If you aren’t sure which HBS Online course is right for you, download our free flowchart to explore your options.

About the Author

• Skip to primary navigation
• Skip to main content
• Skip to primary sidebar

Engineering Management Institute

TECC 244: Practical Problem-Solving Skills for Engineers

April 13, 2021 By EMI

document.createElement('audio'); https://media.blubrry.com/engineeringcareercoach/traffic.libsyn.com/secure/engineeringcareercoach/TECC244.mp3 Podcast: Play in new window | Download | Embed

In this episode, I talk to Andrew Sario, an intelligent transport systems engineer and OT cyber specialist, creator of Engineering IRL, and engineering book author, about problem-solving skills for engineers. Andrew provides some great tips that will help you to master these skills and become the best engineer you could be. Be sure to listen to the end of this episode for a special offer from guest Andrew Sario.

Engineering Quotes:

Here Are Some of the Key Points Discussed About Practical Problem-Solving Skills for Engineers:

• When working on many different projects, work on each one cyclically. It will make it easier to transition from one to the other and know what you need to do next. Breaking up each project into smaller chunks helps you not feel overwhelmed by the entire project.
• The book, “10+1 Steps to Problem Solving: An Engineer’s Guide,” is born from Andrew’s practical experiences. If you encounter similar problems repetitively, you begin to learn how to solve them quicker and easier. Many problems are solved by taking the same steps as used with other problems. Use this book in conjunction with the problem-solving techniques that you already have. It is a tool to help you think about the problem you have and solve it.
• Engineering problem-solving consists of breaking down big problems into smaller, solvable, individual parts and then putting them back together to solve the bigger problem. Many engineering problems are bigger than what one person can solve. Using a team to solve this problem is beneficial. Engineers capture the best practices over time to solve problems more safely and efficiently than before.
• If a problem has a known solution, then use it. Sometimes you need to use tools that give you a different perspective of the problem to solve the problem.
• Whatever tasks are given to you, no matter how small or trivial, do them well.
• Look for solutions to the problems that are standing in the way of your team moving forward. It will give people the mentality to see you as a problem-solver. When doing this, remember to keep step 1 in context.
• To get better at solving problems, you need to practice solving problems. Be happy if you fail in solving some of the problems you face. It adds to your practicing, and you learn what not to do next time.

The 10+1 Steps to Problem-Solving for Engineers Are:

• Are you asking the correct question? – Make sure you are asking the correct question from the beginning of your problem-solving techniques.
• The obvious. – Try the known solutions. If they do not work the first time, try them again, and they might work.
• Eyes. – Ensure you have all the correct tools in place to give you clues about the problem.
• Check yourself. – Check yourself before you wreck yourself. Make sure that all the basics are in place before getting too technical about solving the problem.
• Google it. – You do not have to know everything already, so Google for solutions to your problem. If you have a specific problem, there are online forums that you can consult about it.
• The R.T.F.M. protocol. – Read the manual. You could be surprised by the information you find in it.
• Strip . – Strip down the complexities of the problem and look for something basic to solve first. Prove you know something about the problem.
• What about the environment? – Look for things outside of your problem that could be influencing or impacting it.
• Phone a friend. – Ask someone who might know of a solution.
• Pray – Talk about your problem aloud to yourself. Find an inanimate object and tell it the problem you have and what is needed to solve it. It can get your subconscious working and help you get clarity on what is needed to solve it.
• You can find this step in the book – “ 10+1 Steps to Problem Solving: An Engineer’s Guide .”

More in This Episode…

In the Take Action Today segment of the show, Andrew talks about one tip for engineers to be better at problem-solving.

About Andrew Sario

“We cannot solve our problems with the same thinking we used when we created them.” ~ Albert Einstein

Books Mentioned in This Episode:

10+1 Steps to Problem Solving: An Engineer’s Guide

Resources and Links Mentioned in This Session Include:

Engineering in Real Life Cloudmate Networks Cisco Meraki Technology Connect with Andrew Sario on LinkedIn Send Andrew Sario an email

We would love to hear any questions you might have or stories you can share on practical problem-solving skills for engineers.

Please leave your comments, feedback, or questions in the section below.

• If you enjoyed this post, please consider downloading our free list of 33 Productivity Routines of Top Engineering Executives. Click the button below to download. Download the Productivity Routines

To your success,

Jeff Perry, MBA Host of The Engineering Career Coach Podcast

Related Posts

• TECC 224: People Skills for Engineers: Making a Good First Impression
• TECC 200: How to Develop Business Thinking Skills for Engineers and Techies
• TECC 169: Strategies Engineers can Take to Immediately Improve their Technical Writing Skills
• TECC 88: The Peak Performance Equation for Engineers
• TECC 192: Why Engineers Quit Managers Not Companies

ENGINEERING MANAGEMENT INSTITUTE

We can help you:.

• Build solutions to attract talented professionals.
• Develop your staff’s people skills.
• Create career roadmaps for your staff.
• Provide PM training for your professionals.
• Build custom development programs.
• Scale sustainably.

50 E. Ridgewood Avenue #129

Ridgewood NJ, 07450

800-920-4007

SPECIAL DOWNLOAD

33 Productivity Routines of Top Engineering Executives

Student Approaches to Engineering Problem-Solving - School of Engineering Education - Purdue University

Student Approaches to Engineering Problem-Solving

Open-ended problem solving is a skill that is central to engineering practice. As a consequence, developing skills in solving such problems is imperative for engineering graduates. Open-ended problems are often ill-defined and can have more than one viable solution, which can create additional challenges for students and teachers. For example, solving open-ended problems can require consideration of a complex array of constraints, and the paths to a solution are many. This presentation presents results from a mixed methods project to understand open-ended problem solving of engineering undergraduate students. The overall goal of this project is to describe and understand the contributions of reflective judgment (i.e., students’ views of knowledge) and their cognitive ability (i.e., working memory capacity), when solving open-ended problems. We are particularly interested in specific problem-solving strategies undergraduate engineering students use when dealing with the ambiguity of open-ended problems.

Data were collected using a multi-stage process. Students were first given a set of quantitative instruments that measured their engineering content knowledge, epistemic views on knowledge, and working memory capacity. In the second stage students were asked to solve four problems that differed in their open-endedness and complexity; students were provided a text to use as a resource while solving the problems. Some of these students solved the problems using a think aloud protocol in which they were videotaped while speaking aloud about the strategies they were using. These students were subsequently interviewed to gain further information on their problem-solving processes. A number of insights regarding problem-solving by students have been obtained. For example, there was a significant negative correlation between time spent on the text and score on the problems. From the qualitative data three primary problem-solving strategies were identified: extreme fixation/distraction; fixated and uncertain; systematic and linear. Overall, the results indicate the importance of educating students in how to solve engineering problems that are complex and open-ended.

Dr. Elliot P. Douglas is Associate Chair, Associate Professor, and Distinguished Teaching Scholar in the Department of Materials Science and Engineering at the University of Florida. His research activities are in the areas of active learning, problem solving, critical thinking, and use of qualitative methodologies in engineering education. Specifically, he has published and presented work on the use of guided inquiry as an active learning technique for engineering; how critical thinking is used in practice by students; and how different epistemological stances are enacted in engineering education research. He has been involved in faculty development activities since 1998, through the ExCEEd Teaching Workshops of the American Society of Civil Engineers, the Essential Teaching Seminars of the American Society of Mechanical Engineers, and the US National Science Foundation-sponsored SUCCEED Coalition. He has received several awards for his work, including the Presidential Early Career Award for Scientists and Engineers, the Ralph Teetor Education Award from the Society of Automotive Engineers, and being named the University of Florida Teacher of the Year for 2003-04. He is a member of the American Society for Engineering Education and the American Educational Research Association and is currently Editor-in-Chief of Polymer Reviews .

• [email protected]
• Login / Register

Engineering Mathematics: The Backbone of Problem-Solving

Article 25 Sep 2024 67 0

Engineering mathematics is at the core of problem-solving in various engineering disciplines. It lays the foundation for developing solutions, driving innovation, and solving complex engineering challenges. By mastering mathematical concepts like calculus, algebra, and differential equations, engineers gain the essential tools needed to model, analyze, and optimize systems. This article explores the importance of engineering mathematics, its applications across different fields, and why it is indispensable for aspiring engineers.

The Importance of Engineering Mathematics in Problem-Solving

Engineering mathematics is not merely an abstract field; it’s a highly practical tool used to address real-world problems. From designing infrastructure to developing software algorithms, every engineering domain requires a robust understanding of mathematical principles.

Mathematics forms the backbone of many essential processes in engineering, such as:

• Structural Analysis : When designing buildings or bridges, engineers must calculate forces, loads, and stress points using principles from linear algebra and calculus.
• Electrical Circuit Design : Electrical engineers rely on differential equations and complex numbers to analyze circuit behavior and optimize system efficiency.
• Fluid Dynamics : The motion of fluids is modeled using partial differential equations, helping engineers develop efficient transportation systems, pipelines, and environmental engineering projects.

Each of these examples demonstrates how applied mathematical techniques are indispensable in converting theoretical knowledge into practical solutions.

Key Mathematical Concepts in Engineering

To appreciate how mathematics underpins problem-solving in engineering, it is essential to understand several fundamental mathematical concepts used in the field.

1. Linear Algebra

Linear algebra involves vectors, matrices, and linear transformations—key tools used in solving systems of equations that arise in engineering. Civil engineers, for example, use linear algebra to model forces on structures, ensuring stability and integrity.

2. Calculus

Calculus, including differential and integral calculus, is the language of change. Engineers use calculus to describe changes in quantities, such as velocity, force, or energy. In mechanical engineering, for instance, calculus helps in optimizing systems and improving the performance of machines.

3. Differential Equations

Differential equations describe how things evolve over time or space, making them vital in engineering simulations. Engineers use these equations to model everything from heat transfer to chemical reactions in processes such as automotive design or aerospace simulations.

4. Probability and Statistics

Uncertainty is a natural part of engineering processes, and probability and statistics help engineers model uncertainty, assess risks, and make data-driven decisions. For example, in the field of manufacturing, statistics are used for quality control to ensure that products meet specific standards.

Mathematical Modeling: Simulating the Real World

In engineering, mathematical modeling is used to represent physical systems through mathematical equations. These models allow engineers to simulate real-world scenarios, test variables, and predict outcomes.

For instance, a civil engineer might model the stress on a bridge under different traffic loads, or an aerospace engineer could simulate the aerodynamics of a new aircraft design. These models are built using the principles of engineering mathematics, and they offer a cost-effective, efficient way to test designs before physical prototypes are created.

Applications of Engineering Mathematics Across Disciplines

1. civil engineering.

Civil engineers use mathematical calculations to design infrastructure projects such as roads, bridges, and dams. They rely on geometry for site layout, calculus for material strength analysis, and statistics for risk assessment during construction.

2. Mechanical Engineering

In mechanical engineering, mathematical principles are employed in areas like thermodynamics, mechanics, and robotics. Engineers solve equations to understand how machines work, predict their behavior under stress, and optimize efficiency.

3. Electrical Engineering

Electrical engineers use mathematics to design circuits, control systems, and communication networks. Complex numbers and Fourier transforms are just two examples of mathematical tools that help electrical engineers develop efficient, high-performance systems.

4. Aerospace Engineering

In aerospace engineering, engineers use advanced mathematical techniques to model flight dynamics, analyze propulsion systems, and simulate the effects of external forces on aircraft. The mathematics of fluid dynamics and thermodynamics is crucial for designing safe and efficient aircraft.

Tools and Software Relying on Engineering Mathematics

To solve complex engineering problems, engineers often rely on software tools that are built on mathematical algorithms. Popular software used in the engineering world includes:

• MATLAB : A high-performance language for technical computing, used in a variety of applications from data analysis to system modeling.
• AutoCAD : A computer-aided design (CAD) software that incorporates mathematical tools to create detailed engineering drawings and models.
• ANSYS : A simulation software that uses mathematical models to predict how products will perform in real-world conditions.

These tools highlight the integral role that mathematics plays in the day-to-day work of engineers, providing a bridge between theoretical knowledge and practical application.

The Benefits of Engineering Mathematics for Students

For engineering students, mastering mathematical techniques is more than a requirement for passing exams—it is the key to future success in their careers. Here are a few reasons why engineering students should focus on mathematics:

• Improves Problem-Solving Skills : Mathematics teaches students to approach problems logically and methodically, a skill essential for engineers who must develop innovative solutions.
• Enhances Analytical Thinking : Engineering problems often require careful analysis, and mathematical skills help students break down complex systems into manageable parts.
• Prepares for Advanced Study : Many engineering fields require further study of specialized topics such as control theory, optimization, or machine learning—all of which are grounded in mathematics.

By building a strong foundation in engineering mathematics, students position themselves for success in both their academic and professional pursuits.

Why Engineering Mathematics is Critical in the Future of Engineering

As engineering continues to evolve, so too will the role of mathematics. With advances in fields like artificial intelligence, nanotechnology, and renewable energy, mathematical models will be critical for driving innovation and solving the engineering challenges of the future.

1. Artificial Intelligence (AI)

AI systems rely on complex algorithms that are grounded in mathematics. Machine learning, for instance, uses linear algebra and probability theory to develop predictive models. Engineers in AI must have a strong grasp of these mathematical concepts to create systems that can learn and improve over time.

2. Nanotechnology

In nanotechnology, engineers work on a microscopic scale, where the rules of physics change, and mathematical models are essential for understanding these new dynamics. Differential equations and computational mathematics play a central role in this emerging field.

3. Renewable Energy

Mathematics is crucial in optimizing renewable energy systems, whether it’s predicting solar panel efficiency or modeling wind turbine performance. Engineers in this field must rely on mathematical tools to maximize energy output and improve sustainability.

Conclusion: 

Engineering mathematics is more than just a subject—it is the foundation of problem-solving and innovation in the engineering world. Whether building infrastructure, designing cutting-edge technology, or developing sustainable solutions, engineers rely on mathematics to guide their decisions, improve efficiency, and solve problems.

For students and professionals alike, mastering engineering mathematics opens the door to a world of possibilities. It equips them with the tools needed to tackle the complex challenges of today and the unknown problems of tomorrow.

Mathematics, in its purest form, is the language of engineering. It is the bridge between theoretical concepts and practical solutions, making it the true backbone of problem-solving in engineering.

• Latest Articles

Bioprocess Engineering: Design of Biological Manufacturing Systems

How tech addiction is destroying our social lives, the impact of e-scooters on urban mobility, the future of filling machine technology: emerging trends and innovations, taming the project beast: a beginner's guide to project management, why the electron’s mass is essential for life in the universe, why digital literacy matters for students in the modern world, 10 benefits of taking a social media break | improve mental health, top 20 money-making skills every student must know, why critical thinking is important: skills and benefits explained, ai’s influence on job market trends | future of employment, shifts in pop culture & their societal implications, personalized learning: tailored education for every student, the impact of ai on employment: positive and negative effects on jobs, philosophy’s role in the 21st century: modern relevance, the role of technology in education: opportunities & challenges, negative impact of ai on employment: automation and job loss, apply online.

Find Detailed information on:

• Top Colleges & Universities
• Popular Courses
• Exam Preparation
• Admissions & Eligibility
• College Rankings

Sign Up or Login

Not a Member Yet! Join Us it's Free.

Already have account Please Login

Waqqas Ahmad

Process of Solving Engineering Problems

Filled Under

Engineering often involves applying a consistent, structured approach to the solving of problems. A general problem-solving approach and method can be defined, although variations will be required for specific problems.

Problems must be approached methodically, applying an algorithm , or step-by-step procedure by which one arrives at a solution.

The problem-solving process for a computational problem can be outlined as follows:

• Define the problem.
• Create a mathematical model.
• Develop a computational method for solving the problem.
• Implement the computational method.
• Test and assess the solution.

The boundaries between these steps can be blurred and for specific problems one or two of the steps may be more important than others. Nonetheless, having this approach and strategy in mind will help to focus our efforts as we solve problems

1. Problem Definition:

The first steps in problem solving include:

• Recognize and define the problem precisely by exploring it thoroughly (may be the most difficult step).
• Determine what question is to be answered and what output or results are to be produced.
• Determine what theoretical and experimental knowledge can be applied.
• Determine what input information or data is available

Many academic problems that you will be asked to solve have this step completed by the instructor.

For example, if your instructor ask you to solve a quadratic algebraic equation and provides you with all of the coefficients, the problem has been completely defined before it is given to you and little doubt remains about what the problem is.

If the problem is not well defined, considerable effort must be expended at the beginning in studying the problem, eliminating the things that are unimportant, and focusing on the root problem. Effort at this step pays great dividends by eliminating or reducing false trials, thereby shortening the time taken to complete later steps.

After defining the problem:

• Collect all data and information about the problem.
• Verify the accuracy of this data and information.
• Determine what information you must find: intermediate results or data may need to be

found before the required answer or results can be found.

2. Mathematical Model:

To create a mathematical model of the problem to be solved:

• Determine what fundamental principles are applicable.
• Draw sketches or block diagrams to better understand the problem.
• Define necessary variables and assign notation.
• Reduce the problem as originally stated into one expressed in purely mathematical terms.
• Apply mathematical expertise to extract the essentials from the underlying physical description of the problem.
• Simplify the problem only enough to allow the required information and results to be obtained.
• Identify and justify the assumptions and constraints inherent in this model.

3. Computational Method:

A computational method for solving the problem is to be developed, based on the mathematical model.

• Derive a set of equations that allow the calculation of the desired parameters and variables.
• Develop an algorithm, or step-by-step method of evaluating the equations involved in the solution.
• Describe the algorithm in mathematical terms and then implement as a computer program.
• Carefully review the proposed solution, with thought given to alternative approaches

4. Implementation of Computational Method:

Once a computational method has been identified, the next step is to carry out the method with a computer, whether human or silicon.

Some things to consider in this implementation:

• Assess the computational power needed, as an acceptable implementation may be hand calculation with a pocket calculator.
• If a computer program is required, a variety of programming languages, each with different properties, are available.
• A variety of computers, ranging from the most basic home computers to the fastest parallel supercomputers, are available.
• The ability to choose the proper combination of programming language and computer, and use them to create and execute a correct and efficient implementation of the method, requires both knowledge and experience. In your engineering degree program, you will be exposed to several programming languages and computers, providing you with some exposure to this issue.

The mathematical algorithm developed in the previous step must be translated into a computational algorithm and then implemented as a computer program.

The steps in the algorithm should first be outlined and then decomposed into smaller steps that can be translated into programming commands.

One of the strengths of Matlab is that its commands match very closely to the steps that are used to solve engineering problems; thus the process of determining the steps to solve the problem also determines the Matlab commands. Furthermore, Matlab includes an extensive toolbox of numerical analysis algorithms, so the programming effort often involves implementing the mathematical model, characterizing the input data, and applying the available numerical algorithms.

5. Test and Assess the Solution:

The final step is to test and assess the solution. In many aspects, assessment is the most open-ended and difficult of the five steps involved in solving computational problems.

The numerical solution must be checked carefully:

• A simple version of the problem should be hand checked.
• The program should be executed on obtained or computed test data for which the answer or solution is either known or which can be obtained by independent means, such as hand or calculator computation.
• Intermediate values should be compared with expected results and estimated variations.
• When values deviate from expected results more than was estimated, the source of the deviation should be determined and the program modified as needed.
• A “reality check” should be performed on the solution to determine if it makes sense.
• The assumptions made in creating the mathematical model of the problem should be checked against the solution.

Subscribe to our newsletter!

• Computer Aided Analysis
• Engineering Projects
• Part Modeling
• Thermodynamics
• TurboMachine

Get Gears right in your inbox

2 responses to “process of solving engineering problems”.

why is your post 5 years ago

how to remove bearing after shrink fitting to reuse???

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed .

FREE K-12 standards-aligned STEM

curriculum for educators everywhere!

Find more at TeachEngineering.org .

• TeachEngineering
• Solving Everyday Problems Using the Engineering Design Cycle

Hands-on Activity Solving Everyday Problems Using the Engineering Design Cycle

Grade Level: 7 (6-8)

(two 60-minutes class periods)

Additional materials are required if the optional design/build activity extension is conducted.

Group Size: 4

Activity Dependency: None

Subject Areas: Science and Technology

NGSS Performance Expectations:

TE Newsletter

Engineering connection, learning objectives, materials list, worksheets and attachments, introduction/motivation, vocabulary/definitions, investigating questions, activity extensions, user comments & tips.

This activity introduces students to the steps of the engineering design process. Engineers use the engineering design process when brainstorming solutions to real-life problems; they develop these solutions by testing and redesigning prototypes that work within given constraints. For example, biomedical engineers who design new pacemakers are challenged to create devices that help to control the heart while being small enough to enable patients to move around in their daily lives.

After this activity, students should be able to:

• Explain the stages/steps of the engineering design process .
• Identify the engineering design process steps in a case study of a design/build example solution.
• Determine whether a design solution meets the project criteria and constraints.
• Think of daily life situations/problems that could be improved.
• Apply the engineering design process steps to develop their own innovations to real-life problems.
• Apply the engineering design cycle steps to future engineering assignments.

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.

International Technology and Engineering Educators Association - Technology

View aligned curriculum

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

State Standards

Massachusetts - science.

Each group needs:

• Marisol Case Study , one per student
• Group Leader Discussion Sheet , one per group

To share with the entire class:

• computer/projector setup to show the class the Introduction to the Engineering Design Cycle Presentation , a Microsoft® PowerPoint® file
• paper and pencils
• (optional) an assortment of scrap materials such as fabric, super glue, wood, paper, plastic, etc., provided by the teacher and/or contributed by students, to conduct the hands-on design/build extension activity

(Have the 19-slide Introduction to the Engineering Design Cycle Presentation , a PowerPoint® file, ready to show the class.)

Have you ever experienced a problem and wanted a solution to it? Maybe it was a broken backpack strap, a bookshelf that just kept falling over, or stuff spilling out of your closet? (Let students share some simple problems with the class). With a little bit of creativity and a good understanding of the engineering design process, you can find the solutions to many of these problems yourself!

But what is the engineering design process? (Listen to some student ideas shared with the class.) The engineering design process, or cycle, is a series of steps used by engineers to guide them as they solve problems.

(Show students the slide presentation. Refer to the notes under each slide for a suggested script and comments. The slides introduce the main steps of the engineering design process, and walk through a classroom problem—a teacher’s disorganized desk that is preventing timely return of graded papers—and how students devise a solution. It also describes the work of famous people—Katherine Johnson, Lee Anne Walters, Marc Edwards, James E. West and Jorge Odón—to illustrate successful examples of using the steps of the engineering design process.)

Now that we’ve explore the engineering design process, let’s see if we can solve a real-world problem. Marisol is a high-school student who is very excited to have their own locker. They have lots of books, assignments, papers and other items that they keep in their locker. However, Marisol is not very organized. Sometimes they are late to class because they need extra time to find things that were stuffed into their locker. What is Marisol’s problem? (Answer: Their locker is disorganized.) In your groups, you’ll read through Marisol’s situation and see how they use the engineering design process to solve it. Let’s get started!

This activity is intended as an introduction to the engineering design cycle. It is meant to be relatable to students and serve as a jumping off point for future engineering design work.

Engineers follow the steps of the engineering design process to guide them as they solve problems. The steps shown in Figure 1 are:

Ask: identify the need & constraints

• Identify and define the problem. Who does the problem affect? What needs to be accomplished? What is the overall goal of the project?
• Identify the criteria and constraints. The criteria are the requirements the solution must meet, such as designing a bag to hold at least 10 lbs. Constraints are the limitations and restrictions on a solution, such as a maximum budget or specific dimensions.

Research the problem

• Learn everything you can about the problem. Talk to experts and/or research what products or solutions already exist.
• If working for a client, such as designing new filters for a drinking water treatment plant, talk with the client to determine the needs and wants.

Imagine: develop possible solutions

• Brainstorm ideas and come up with as many solutions as possible. Wild and crazy ideas are welcome! Encourage teamwork and building on ideas.

Plan: select a promising solution

• Consider the pros and cons of all possible solutions, keeping in mind the criteria and constraints.
• Choose one solution and make a plan to move forward with it.

Create: build a prototype

• Create your chosen solution! Push for creativity, imagination and excellence in the design.

Test and evaluate prototype

• Test out the solution to see how well it works. Does it meet all the criteria and solve the need? Does it stay within the constraints? Talk about what worked during testing and what didn’t work. Communicate the results and get feedback. What could be improved?

Improve: redesign as needed

• Optimize the solution. Redesign parts that didn’t work, and test again.
• Iterate! Engineers improve their ideas and designs many times as they work towards a solution.

Some depictions of the engineering design process delineate a separate step—communication. In the Figure 1 graphic, communication is considered to be incorporated throughout the process. For this activity, we call out a final step— communicate the solution —as a concluding stage to explain to others how the solution was designed, why it is useful, and how they might benefit from it. See the diagram on slide 3.

For another introductory overview of engineering and design, see the What Is Engineering? What Is Design? lesson and/or show students the What Is Engineering? video. 

Before the Activity

• Make copies of the five-page Marisol Case Study , one per student, and the Group Leader Discussion Sheet , one per group.
• Be ready to show the class the Introduction to the Engineering Design Cycle Presentation , a PowerPoint® file.

With the Students

• As a pre-activity assessment, spend a few minutes asking students the questions provided in the Assessment section.
• Present the Introduction/Motivation content to the class, which includes using the slide presentation to introduce students to the engineering design cycle. Throughout, ask for their feedback, for example, any criteria or constraints that they would add, other design ideas or modifications, and so forth.
• Divide the class into groups of four. Ask each team to elect a group leader. Hand out the case study packets to each student. Provide each group leader with a discussion sheet.
• In their groups, have students work through the case study together.
• Alert students to the case study layout with its clearly labeled “stop” points, and direct them to just read section by section, not reading beyond those points.
• Suggest that students either taking turns reading each section aloud or read each section silently.
• Once all students in a group have read a section, the group leader refers to the discussion sheet and asks its questions of the group, facilitating a discussion that involves every student.
• Encourage students to annotate the case study as they like; for example, they might note in the margins Marisol’s stage in the design process at various points.
• As students work in their groups, walk around the classroom and encourage group discussion. Ensure that each group member contributes to the discussion and that group members are focused on the same section (no reading ahead).
• After all teams have finished the case study and its discussion questions, facilitate a class discussion about how Marisol used the engineering design cycle. This might include referring back to questions 4 and 5 in “Stop 5” to discuss remaining questions about the case study and relate the case study example back to the community problems students suggested in the pre-activity assessment.
• Administer the post-activity assessment.

brainstorming: A team creativity activity with the purpose to generate a large number of potential solutions to a design challenge.

constraint: A limitation or restriction. For engineers, design constraints are the requirements and limitations that the final design solutions must meet. Constraints are part of identifying and defining a problem, the first stage of the engineering design cycle.

criteria: For engineers, the specifications and requirements design solutions must meet. Criteria are part of identifying and defining a problem, the first stage of the engineering design cycle.

develop : In the engineering design cycle, to create different solutions to an engineering problem.

engineering: Creating new things for the benefit of humanity and our world. Designing and building products, structures, machines and systems that solve problems. The “E” in STEM.

engineering design process: A series of steps used by engineering teams to guide them as they develop new solutions, products or systems. The process is cyclical and iterative. Also called the engineering design cycle.

evaluate: To assess something (such as a design solution) and form an idea about its merit or value (such as whether it meets project criteria and constraints).

optimize: To make the solution better after testing. Part of the engineering design cycle.

Pre-Activity Assessment

Intro Discussion: To gauge how much students already know about the activity topic and start students thinking about potential design problems in their everyday lives, facilitate a brief class discussion by asking students the following questions:

• What do engineers do? (Example possible answers: Engineers design things that help people, they design/build/create new things, they work on computers, they solve problems, they create things that have never existed before, etc.)
• What are some problems in your home, school or community that could be solved through engineering? (Example possible answers: It is too dark in a community field/park at night, it is hard to carry shopping bags in grocery store carts, the dishwasher does not clean the dishes well, we spend too much time trying to find shoes—or other items—in the house/garage/classroom, etc.)
• How do engineers solve problems? (Example possible answers: They build new things, design new things, etc. If not mentioned, introduce students to the idea of the engineering design cycle. Liken this to how research scientists are guided by the steps of the scientific method.)

Activity Embedded Assessment

Small Group Discussions: As students work, observe their group discussions. Make sure the group leaders go through all the questions for each section, and that each group member contributes to the discussions.

Post-Activity Assessment

Marisol’s Design Process: Provide students with writing paper and have them write “Marisol’s Design Process” at the top. Direct them to clearly write out the steps that Marisol went through as they designed and completed their locker organizer design and label them according to where they fit in the engineering design cycle. For example, “Marisol had to jump back to avoid objects falling out of their locker” and they stated a desire to “wanted to find a way to organize their locker” both illustrate the “identifying the problem” step.

• Which part of the engineering design cycle is Marisol working on as they design an organizer?
• Why is it important to identify the criteria and constraints of a project before building and testing a prototype? (Example possible answers: So that the prototype will be the right size, so that you do not go over budget, so that it will solve the problem, etc.)
• Why do engineers improve and optimize their designs? (Example possible answers: To make it work better, to fix unexpected problems that come up during testing, etc.)

To make this a more hands-on activity, have students design and build their own locker organizers (or other solutions to real-life problems they identified) in tandem with the above-described activity, incorporating the following changes/additions to the process:

• Before the activity: Inform students that they will be undertaking an engineering design challenge. Without handing out the case study packet, introduce students to Marisol’s problem: a disorganized locker. Ask students to bring materials from home that they think could help solve this problem. Then, gather assorted materials (wood and fabric scraps, craft materials, tape, glue, etc.) to provide for this challenge, giving each material a cost (for example, wood pieces cost 50¢, fabric costs 25¢, etc.) and write these on the board or on paper to hand out to the class. 
• Present the Introduction/Motivation content and slides to introduce students to the engineering design process (as described above). Then have students go through the steps of the engineering design process to create a locker organizer for Marisol. Inform them Marisol has only $3 to spend on an organizer, so they must work within this budget constraint. As a size constraint, tell students the locker is 32 inches tall, 12 inches wide and 9.5 inches deep. (Alternatively, have students measure their own lockers and determine the size themselves.) 
• As students work, ask them some reflection questions such as, “Which step of the engineering design process are you working on?” and “Why have you chosen that solution?”
• Let groups present their organizers to the class and explain the logic behind their designs.
• Next, distribute the case study packet and discussion sheets to the student groups. As the teams read through the packet, encourage them to discuss the differences between their design solutions and Marisol’s. Mention that in engineering design there is no one right answer; rather, many possible solutions may exist. Multiple designs may be successful in imagining and fabricating a solution that meets the project criteria and constraints.

Engineering Design Process . 2014. TeachEngineering, Web. Accessed June 20, 2017. https://www.teachengineering.org/k12engineering/designprocess

Contributors

Supporting program, acknowledgements.

This material is based upon work supported by the National Science Foundation CAREER award grant no. DRL 1552567 (Amy Wilson-Lopez) titled, Examining Factors that Foster Low-Income Latino Middle School Students' Engineering Design Thinking in Literacy-Infused Technology and Engineering Classrooms. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Last modified: October 26, 2023

Unfortunately we don't fully support your browser. If you have the option to, please upgrade to a newer version or use Mozilla Firefox , Microsoft Edge , Google Chrome , or Safari 14 or newer. If you are unable to, and need support, please send us your feedback .

We'd appreciate your feedback. Tell us what you think!   opens in new tab/window

10 major engineering challenges of the next decade

Challenges related to climate change continue to threaten the world's population. But solutions exist, and engineers will play a major role in solving them. Here are 10 major challenges and what engineers can do about them in 2023.

1. Upgrading the aging U.S. infrastructure

The American Society of Civil Engineers gives our  aging infrastructure   opens in new tab/window  a C- grade and  estimates  that the U.S. is spending just over half of what is needed. Significant action is needed to bring our roads   opens in new tab/window , bridges,   opens in new tab/window   water   opens in new tab/window ,  electrical   opens in new tab/window  and  sewage systems   opens in new tab/window  to proper safe working order.

2. Educating first world engineers to understand how to solve third world problems

The Renewable Resources Journal  reports  that the world’s population will grow by two billion over the next two decades, 95% of this in developing or underdeveloped countries. Engineers must learn new ways to  solve problems   opens in new tab/window in these countries.

3. Promoting  green engineering   opens in new tab/window  to improve sustainability and reduce the carbon footprint in manufacturing   opens in new tab/window

According to the U.S. Office of Energy Efficiency & Renewable Energy, manufacturing in the U.S. produced 19,237 trillion BTUs and 1,071 million metric tons of  carbon dioxide   opens in new tab/window .

4. Identifying viable  and renewable energy   opens in new tab/window  sources

The contributions to our energy production from renewables   opens in new tab/window and other  new fuel   opens in new tab/window  sources are growing at 6% per year according to BP  and will contribute 45% of the increment in  energy production   opens in new tab/window  by 2035.

5. Rethinking how the  city   opens in new tab/window  looks and works

54% of the world’s population lives in cities. Europe leads the way in sustainability   opens in new tab/window , with seven out of the world’s top 10 most sustainable cities, according to the  ARCADIS Sustainable Cities Index.

6. Making  STEM more appealing   opens in new tab/window  to young students

By 2018, the United States  will have  more than 1.2 million unfilled STEM jobs. Meanwhile, according to  a UCLA study, 40% of students enrolled as STEM majors switched subjects or failed to get a degree.

7. Safeguarding our personal data and wealth from cyberattacks   opens in new tab/window

34% of data breaches happen at financial institutions; 11% target retail companies; while 13% target government institutions   opens in new tab/window , according to the  2014 Data Breach Investigation Report.

8. Addressing  climate change   opens in new tab/window through engineering innovation

Six of the 10 cities with the largest annual flood   opens in new tab/window costs by 2050  are in India and China.  Three are in the U.S.: New York, Miami and New Orleans.

9. Feeding our growing population through cutting-edge bio-engineering and  agricultural innovations   opens in new tab/window

The  U.N. warns  that we must produce 60% more food by 2050 to keep up with demand, but how do we do this sustainably? Food   opens in new tab/window and  water   opens in new tab/window  access will be major issues in the future, and research must begin now.

10. Improving our health and well-being through life sciences, nanotechnology   opens in new tab/window  &  bio-engineering   opens in new tab/window

Administration on Aging,  by 2060 the population of Americans aged 65 and older will have more than doubled in size from 2011. This puts a lot of pressure on new drug creation and also on innovative engineering techniques to deliver drugs   opens in new tab/window .

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.

• Master of Engineering
• MS in Biomedical Engineering
• MS in Mechanical Engineering
• MS in Systems & Control Engineering
• State Authorization
• Technology Requirements
• Tuition and Financial Aid
• Class Profile
• Online Experience

7 Surprising Ways Engineering Has Solved Everyday Problems

In a culture where hacking and repurposing are commonplace, engineering-minded designers transform everyday items into innovative solutions. By following design-cycle steps, they turn science fiction into reality, addressing pervasive everyday problems. This post explores real-world challenges, showcasing the transformative power of engineering solutions—from the coffee cup sleeve to the selfie stick and beyond. Consider inventive creations that improve accessibility and tackle health issues. Discover the limitless potential of engineering expertise to address contemporary challenges and improve lives.

Expertise to Create the Unexpected

We live in a hacking culture where we break down and repurpose everything from IKEA furniture to power tools, redesigning them to fill a need or solve a problem for which they were not originally intended. By applying some of the basic design-cycle steps of Ask, Research, Imagine, Plan, Create, Test and Improve, engineering-minded product designers are turning what might have once been considered science fictional solutions into reality.

By sharpening your engineering skill set , you can put yourself in a unique position to address some pervasive everyday problems. Which would you like to take on? For a little inspiration, take a look at some real-world everyday challenges, big and small, that have been alleviated by some rather innovative engineering solutions.

Squeezing Out the Last Drop of Liquid

We’ve all experienced the frustration of attempting to squeeze the last drop of ketchup or toothpaste from their containers. That could end very soon, all thanks to a unique slippery coating that keeps thick, gooey substances from sticking to solid surfaces.

Called LiquiGlide, this material was initially was created to line oil and gas pipelines to protect against buildup. 1 It worked so well that the team developing this technology at MIT decided to explore other commercial applications for it. They researched and tested different combinations of materials to create new variations of LiquiGlide, including food-grade and medical-grade versions. These can help reduce product waste and enable viscous liquid medications to efficiently empty from tubes to improve proper dosing.

Holding Hot Coffee Without Spilling It

The coffee cup sleeve: With such deceptively simple design and such obvious value, it’s hard to believe it wasn’t invented sooner than it was, back in 1991. The idea was born two years prior, when piping hot coffee in a paper to-go cup burned the hands (and subsequently spilled on the lap) of future Java Jacket founder Jay Sorensen.

Sorensen did considerable research on the potential market demand for such a product, the kinds of materials that could be used to cost-effectively create it and the most successful physical design. He produced and tested several iterations of the sleeve before landing on the prototype that is still used today. 2 Now, the nearly ubiquitous coffee cup sleeves are helping save the fingers (and laps) of countless hot-java-drinking commuters—not to mention engineers.

A Far-Reaching Solution for Getting the Group Shot

By freeing us from having to rely on a willing passerby to take a group photo in front of a tourist attraction or a silhouette shot against a stunning sunset, the selfie stick has certainly made an impact in today’s social-media-savvy world.

Wayne Fromm didn’t invent camera-on-a-stick technology, but in 2005 he did patent a version that could hold almost any camera and, eventually, nearly any smartphone. 3 That’s the version that began to resonate with consumers worldwide.

Since then, the original selfie stick concept has evolved into several iterations by Fromm and other manufacturers to answer the demand for more uses—including ones that extend telescopically at the push of a button so you can fit more people or more background into your shot, that allow you to snap a shot via Bluetooth without needing to set the camera timer, or that take blur-free photographs and video while skydiving or partaking in other action sports.

Walking Your Way to Health at Work

Dr. James Levine, a medical doctor who researches obesity, found that sitting for several hours at a time negatively impacts our health much more than initially thought, even for those who regularly go to the gym. He argued that our increasingly sedentary lifestyle, fueled by demands at work requiring us to be at our desks, has contributed to a culture of people with poor posture, lack of energy, and increased risk of heart disease and diabetes.

Levine came up with a rather unusual solution: He rigged a used treadmill under a raised bedside tray. 4 Perhaps this prototype he created in 1999 wasn’t the most attractive setup, but its goal was clear: to give people a way to be active while working and help reduce sitting-related health risks.

Levine worked with a manufacturer to produce the first official treadmill desk, released in 2007. Today, many companies promoting a healthier workplace offer employees the option to have such a desk instead of a traditional one.

Overcoming Fear of Public Speaking

Sophia Velastegui, an influential engineer in the technology sector, applied several engineering design steps early in her career to conquer a common phobia: speaking in front of a crowd. 5

Velastegui did this by:

• Identifying specific problems to address: her shyness and fear of public speaking
• Looking into ways to work on them (such as volunteering to speak at company meetings)
• Setting up a plan of action to overcome her shyness with strangers: research people to meet at conferences, contact them, choose discussion topics and maintain regular contact
• Continuing to improve her speaking and networking skills through constant practice

Velastegui’s process improved her public speaking—and her confidence and management skills—so thoroughly that it has been invaluable to her rise through desirable positions at top companies. Not only that, she was named to Business Insider's list of most powerful female engineers in 2017.

Eating With Confidence, Without Spilling

Many of us take the simple act of feeding ourselves for granted. But for anyone with trembling hands, it can be a frustrating struggle to keep food on a fork or spoon long enough to reach their mouth without it winding up on the table or their clothing. Liftware Level™ utensils were created by inventors with loved ones experiencing such limitations.

Liftware uses sensor technology that makes real-time adjustments to accommodate any mild-to-severe shaking and trembling movements. 6 This improves accessibility and independence for those suffering from conditions such as Parkinson’s disease.

Liftware developers are taking their testing to a new level: They created an app that records motion data using an accelerometer sensor found in smartphones. They use this data when creating prototypes for versions of other common products that can be used by people with disabilities.

Diagnosing Deep Gastrointestinal Diseases

In 1981, inspired by a friend experiencing small intestine pain with no apparent source, rocket engineer Gavriel Iddan wondered if there was a way to create a “missile”—complete with a camera—that could be launched into the intestine to snap photographs in order to help physicians make accurate diagnoses.

Applying his knowledge of rocket engineering to a completely unrelated problem led to his invention of the ingestible camera. “PillCam” actually took 17 years to become reality, thanks to Iddan’s diligence and the development of micro cameras, transmitters and LED lights that could fit into a large pill-sized capsule. 7

Now the diagnostic standard, doctors can properly identify conditions that are deep in the digestive tract, areas previously unreachable by other nonsurgical methods.

Put Your Engineering Skills to Use

The world is full of countless challenges waiting for that one solution to be created or tweaked that can make life just a little easier, healthier or better. What problems are you planning on tackling with an engineering approach? What inefficiencies are you improving? And better yet, how many more opportunities might present themselves as you continue to hone your engineering expertise?

Using your engineering knowledge, there’s no limit to what you can do. Explore our online graduate engineering degree programs at Case Western Reserve University to get started improving the world around you today.

• Retrieved on September 8, 2018, from liquiglide.com/
• Retrieved on September 8, 2018, from smithsonianmag.com/arts-culture/how-the-coffee-cup-sleeve-was-invented-119479/
• Retrieved on September 8, 2018, from businessinsider.com/wayne-fromm-is-the-inventor-of-the-modern-selfie-stick-2015-8
• Retrieved on September 8, 2018, from newyorker.com/magazine/2013/05/20/the-walking-alive
• Retrieved on September 8, 2018, from businessinsider.com/how-this-engineer-hacked-her-career-and-became-a-gm-at-microsoft-2018-2
• Retrieved on September 8, 2018, from launchforth.io/blog/post/invention-spotlight-liftware-level/2335/
• Retrieved on September 8, 2018, from epo.org/learning-events/european-inventor/finalists/2011/iddan/impact.html

Return to Online Engineering Blog

Complete the form below before proceeding to the application portal.

Case Western Reserve University has engaged Everspring , a leading provider of education and technology services, to support select aspects of program delivery.

A new accurate and fast convergence cuckoo search algorithm for solving constrained engineering optimization problems

New citation alert added.

This alert has been successfully added and will be sent to:

You will be notified whenever a record that you have chosen has been cited.

To manage your alert preferences, click on the button below.

New Citation Alert!

Please log in to your account

Information & Contributors

Bibliometrics & citations, view options, index terms.

Computing methodologies

Artificial intelligence

Search methodologies

Continuous space search

Randomized search

Symbolic and algebraic manipulation

Symbolic and algebraic algorithms

Optimization algorithms

Mathematics of computing

Mathematical analysis

Mathematical optimization

Continuous optimization

Bio-inspired optimization

Discrete optimization

Optimization with randomized search heuristics

Theory of computation

Design and analysis of algorithms

Evolutionary algorithms

Recommendations

A bacterial gene recombination algorithm for solving constrained optimization problems.

Creature evolution manifests itself in the improved ability of species to adapt to their surroundings. Swarm intelligence and gene optimization are found in the population of interacting agents that are able to self-organize and self-strengthen. In this ...

Optimization of constrained mathematical and engineering design problems using chaos game optimization

• A novel metaheuristic algorithm is proposed for constrained optimization.

In the past few decades, many different metaheuristic algorithms have been developed for optimization purposes each of which have specific advantages and disadvantages due to multiple applications in different optimization fields. The ...

Constrained Problem Optimization using Altered Artificial Bee Colony Algorithm

Constraint optimization is one of the major fields of decision science where variables and solutions are often constrained or restricted to a certain feasible space only. Moreover, it is always not possible to replace constraints by penalization ...

Information

Published in.

Netherlands

Publication History

Author tags.

• Nonlinear optimization problem
• constrained problems
• engineering designing problems
• penalty function
• cuckoo optimization algorithm
• Research-article

Contributors

Other metrics, bibliometrics, article metrics.

• 0 Total Citations
• 0 Total Downloads
• Downloads (Last 12 months) 0
• Downloads (Last 6 weeks) 0

View options

Login options.

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Share this publication link.

Copying failed.

Share on social media

Affiliations, export citations.

• Please download or close your previous search result export first before starting a new bulk export. Preview is not available. By clicking download, a status dialog will open to start the export process. The process may take a few minutes but once it finishes a file will be downloadable from your browser. You may continue to browse the DL while the export process is in progress. Download
• Download citation
• Copy citation

We are preparing your search results for download ...

We will inform you here when the file is ready.

Your file of search results citations is now ready.

Your search export query has expired. Please try again.

Workshop on “Code Your Career: Kickstart to Problem-Solving”

The “Code Your Career: Kickstart to Problem-Solving” workshop took place on September 17th, where participants mastered the basics of coding and problem-solving. Ideal for beginners, this interactive session offered hands-on exercises, expert guidance, and a participation e-certificate.

Share this:

• Pinterest 1

About BAUET

Bangladesh Army University of Engineering & Technology (BAUET) the pioneer Technical Institutes of Armed Forces, started its journey from 2015. It was the visionary leadership of the Honorable Prime Minister of People’s Republic of Bangladesh Sheikh Hasina to establish a Technical Institute of Armed Forces.

Featured Links

Copyright ©2024, BAUET All Rights Reserved.

• September 2024
• February 2024
• November 2023
• September 2023
• August 2023
• February 2023
• January 2023
• December 2022
• November 2022
• October 2022
• August 2022
• January 2022
• December 2021
• October 2021
• September 2021
• August 2021
• January 2021
• December 2020
• November 2020
• September 2020
• December 2019
• November 2019
• August 2018
• Achievement
• Campus Life/Gallery
• Exam Notice
• MoU/Collaboration
• News & Events
• Photo Gallery
• Success Story
• Entries feed
• Comments feed
• WordPress.org

Solving numerical and engineering optimization problems using a dynamic dual-population differential evolution algorithm

• Original Article
• Published: 14 September 2024

Cite this article

• Wenlu Zuo 1 , 2 &
• Yuelin Gao   ORCID: orcid.org/0000-0003-2021-2097 1 , 2  

14 Accesses

Explore all metrics

Differential evolution (DE) is a cutting-edge meta-heuristic algorithm known for its simplicity and low computational overhead. But the traditional DE cannot effectively balance between exploration and exploitation. To solve this problem, in this paper, a dynamic dual-population DE variant (ADPDE) is proposed. Firstly, the dynamic population division mechanism based on individual potential value is presented to divide the population into two subgroups, effectively improving the population diversity. Secondly, a nonlinear reduction mechanism is designed to dynamically adjust the size of potential subgroup to allocate computing resources reasonably. Thirdly, two unique mutation strategies are adopted for two subgroups respectively to better utilise the effective information of potential individuals and ensure fast convergence speed. Finally, adaptive parameter setting methods of two subgroups further achieve the balance between exploration and exploitation. The effectiveness of improved strategies is verified on 21 classical benchmark functions. Then, to verify the overall performance of ADPDE, it is compared with three standard DE algorithms, eight excellent DE variants and seven advanced evolutionary algorithms on CEC2013, CEC2017 and CEC2020 test suites, respectively, and the results show that ADPDE has higher accuracy and faster convergence speed. Furthermore, ADPDE is compared with eight well-known optimizers and CEC2020 winner algorithms on nine real-world engineering optimization problems, and the results indicate ADPDE has the development potential for constrained optimization problems as well.

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

Access this article

Subscribe and save.

• Get 10 units per month
• Download Article/Chapter or eBook
• 1 Unit = 1 Article or 1 Chapter
• Cancel anytime

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Similar content being viewed by others

Developments and Design of Differential Evolution Algorithm for Non-linear/Non-convex Engineering Optimization

Solving Constrained Non-linear Integer and Mixed-Integer Global Optimization Problems Using Enhanced Directed Differential Evolution Algorithm

An efficient modified differential evolution algorithm for solving constrained non-linear integer and mixed-integer global optimization problems, explore related subjects.

• Artificial Intelligence

Data availability

All the data in Sect.  6 are obtained under the same experimental setting. Then, the source code of CEC2013 test suite can be downloaded from https://github.com/P-N-Suganthan/CEC2013 . The source code of CEC2017 test suite can be downloaded from https://github.com/P-N-Suganthan/CEC2017-BoundContrained . The source code of CEC2020 test suite can be downloaded from https://github.com/P-N-Suganthan/2020-Bound-Constrained-Opt-Benchmark . The source code of the nine engineering problems can be downloaded in https://github.com/P-N-Suganthan/2020-RW-Constrained-Optimisation . We solemnly declare that all data in this paper is true and valid.

Hajipour V, Kheirkhah AS, Tavana M et al (2015) Novel Pareto-based meta-heuristics for solving multi-objective multi-item capacitated lot-sizing problems. Int J Adv Manuf Technol 80:31–45. https://doi.org/10.1007/s00170-015-6993-6

Article   Google Scholar  

Abdel-Basset M, Abdel-Fatah L, Sangaiah AK (2018) Chapter 10-metaheuristic algorithms: a comprehensive review in computational intelligence for multimedia big data on the cloud with engineering applications. https://doi.org/10.1016/B978-0-12-813314-9.00010-4

Ribagin S, Lyubenova V (2021) Metaheuristic algorithms: theory and applications. In: research in computer science in the Bulgarian academy of sciences, pp 385–419. https://doi.org/10.1007/978-3-030-72284-5_18

Sloss AN, Gustafson S (2019) evolutionary algorithms review. In: Genetic programming theory and practice XVII, 2020, pp 307–344. https://doi.org/10.1007/978-3-030-39958-0_16

Ahmad MF, Isa NAM, Lim WH et al (2022) Differential evolution: a recent review based on state-of-the-art works. Alex Eng J 61(5):3831–3872. https://doi.org/10.1016/j.aej.2021.09.013

Lambora A, Gupta K, Chopra K (2019) Genetic algorithm—a literature review. In 2019 international conference on machine learning, big data, cloud and parallel computing (COMITCon). IEEE, pp 380–384. https://doi.org/10.1109/COMITCon.2019.8862255

Mehr AD, Nourani V, Kahya E et al (2018) Genetic programming in water resources engineering: a state-of-the-art review. J Hydrol 566:643–667. https://doi.org/10.1016/j.jhydrol.2018.09.043

Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341. https://doi.org/10.1023/A:1008202821328

Article   MathSciNet   Google Scholar  

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

Montiel O, Castillo O, Melin P et al (2007) Human evolutionary model: a new approach to optimization. Inf Sci 177(10):2075–2098. https://doi.org/10.1016/j.ins.2006.09.012

Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95-international conference on neural networks, vol 4. IEEE, pp 1942–1948. https://doi.org/10.1109/ICNN.1995.488968

Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008

Heidari AA, Mirjalili S, Faris H et al (2019) Harris hawks optimization: algorithm and applications. Future Gener Comput Syst 97:849–872. https://doi.org/10.1016/j.future.2019.02.028

HaDehghani M, Montazeri Z, Trojovská E et al (2023) Coati optimization algorithm: a new bio-inspired metaheuristic algorithm for solving optimization problems. Knowl-Based Syst 259:110011. https://doi.org/10.1016/j.knosys.2022.110011

Xue J, Shen B (2023) Dung beetle optimizer: a new meta-heuristic algorithm for global optimization. J Supercomput 79(7):7305–7336. https://doi.org/10.1007/s11227-022-04959-6

Maheri A, Jalili S, Hosseinzadeh Y et al (2021) A comprehensive survey on cultural algorithms. Swarm Evol Comput 62:100846. https://doi.org/10.1016/j.swevo.2021.100846

Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68. https://doi.org/10.1177/003754970107600201

Rao RV, Savsani VJ, Vakharia DP (2011) Teaching-learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des 43(3):303–315. https://doi.org/10.1016/j.cad.2010.12.015

Das B, Mukherjee V, Das D (2020) Student psychology based optimization algorithm: a new population based optimization algorithm for solving optimization problems. Adv Eng Softw 146:102804. https://doi.org/10.1016/j.advengsoft.2020.102804

Wagan AI, Shaikh MM (2020) A new metaheuristic optimization algorithm inspired by human dynasties with an application to the wind turbine micrositing problem. Appl Soft Comput 90:106176. https://doi.org/10.1016/j.asoc.2020.106176

Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248. https://doi.org/10.1016/j.ins.2009.03.004

Patel VK, Savsani VJ (2015) Heat transfer search (HTS): a novel optimization algorithm. Inf Sci 324:217–246. https://doi.org/10.1016/j.ins.2015.06.044

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

Yadav A (2019) AEFA: artificial electric field algorithm for global optimization. Swarm Evol Comput 48:93–108. https://doi.org/10.1016/j.swevo.2019.03.013

Su H, Zhao D, Heidari AA et al (2023) RIME: a physics-based optimization. Neurocomputing 532:183–214. https://doi.org/10.1016/j.neucom.2023.02.010

Pekár J, Čičková Z, Brezina I (2016) Portfolio performance measurement using differential evolution. CEJOR 24:421–433. https://doi.org/10.1007/s10100-015-0393-8

Kaur M, Kumar V, Li L (2019) Color image encryption approach based on memetic differential evolution. Neural Comput Appl 31:7975–7987. https://doi.org/10.1007/s00521-018-3642-7

Abderazek H, Yildiz AR, Sait SM (2019) Mechanical engineering design optimisation using novel adaptive differential evolution algorithm. Int J Veh Des 80(2–4):285–329. https://doi.org/10.1504/IJVD.2019.109873

Mahmoodjanloo M, Tavakkoli-Moghaddam R, Baboli A et al (2020) Flexible job shop scheduling problem with reconfigurable machine tools: an improved differential evolution algorithm. Appl Soft Comput 94:106416. https://doi.org/10.1016/j.asoc.2020.106416

Zhang Y, Gong D, Gao X et al (2020) Binary differential evolution with self-learning for multi-objective feature selection. Inf Sci 507:67–85. https://doi.org/10.1016/j.ins.2019.08.040

Reddy SS (2019) Optimal power flow using hybrid differential evolution and harmony search algorithm. Int J Mach Learn Cybern 10(5):1077–1091. https://doi.org/10.1007/s13042-018-0786-9

Chai X, Zheng Z, Xiao J et al (2022) Multi-strategy fusion differential evolution algorithm for UAV path planning in complex environment. Aerosp Sci Technol 121:107287. https://doi.org/10.1016/j.ast.2021.107287

Awad NH, Ali MZ, Suganthan PN (2017) Ensemble sinusoidal differential covariance matrix adaptation with Euclidean neighborhood for solving CEC2017 benchmark problems. In: 2017 IEEE congress on evolutionary computation (CEC). IEEE, pp 372–379. https://doi.org/10.1109/CEC.2017.7969336

Sallam KM, Elsayed SM, Chakrabortty RK et al (2020) Improved multi-operator differential evolution algorithm for solving unconstrained problems. In: IEEE congress on evolutionary computation (CEC). IEEE, pp 1–8. https://doi.org/10.1109/CEC48606.2020.9185577

Biswas S, Saha D, De S et al (2021) Improving differential evolution through Bayesian hyperparameter optimization. In: 2021 IEEE Congress on evolutionary computation (CEC). IEEE, pp 832–840. https://doi.org/10.1109/CEC45853.2021.9504792

Qin AK, Huang VL, Suganthan PN (2008) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417. https://doi.org/10.1109/TEVC.2008.927706

Draa A, Bouzoubia S, Boukhalfa I (2015) A sinusoidal differential evolution algorithm for numerical optimisation. Appl Soft Comput 27:99–126. https://doi.org/10.1016/j.asoc.2014.11.003

Hassan S, Hemeida AM, Alkhalaf S et al (2020) Multi-variant differential evolution algorithm for feature selection. Sci Rep 10(1):1–16. https://doi.org/10.1038/s41598-020-74228-0

Layeb A (2024) Differential evolution algorithms with novel mutations, adaptive parameters, and Weibull flight operator. Soft Comput. https://doi.org/10.1007/s00500-023-09561-3

Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958. https://doi.org/10.1109/TEVC.2009.2014613

Tanabe R, Fukunaga A (2013) Success-history based parameter adaptation for differential evolution. In: IEEE congress on evolutionary computation. IEEE, pp 71–78. https://doi.org/10.1109/CEC.2013.6557555

Tanabe R, Fukunaga AS (2014) Improving the search performance of SHADE using linear population size reduction. In: 2014 IEEE congress on evolutionary computation (CEC). IEEE, pp 1658–1665. https://doi.org/10.1109/CEC.2014.6900380

Tian M, Gao X, Dai C (2017) Differential evolution with improved individual-based parameter setting and selection strategy. Appl Soft Comput 56:286–297. https://doi.org/10.1016/j.asoc.2017.03.010

Meng Z, Pan JS, Tseng KK (2019) PaDE: an enhanced differential evolution algorithm with novel control parameter adaptation schemes for numerical optimization. Knowl-Based Syst 168:80–99. https://doi.org/10.1016/j.knosys.2019.01.006

Sun G, Yang B, Yang Z et al (2020) An adaptive differential evolution with combined strategy for global numerical optimization. Soft Comput 24:6277–6296. https://doi.org/10.1007/s00500-019-03934-3

Gupta S, Su R (2022) An efficient differential evolution with fitness-based dynamic mutation strategy and control parameters. Knowl-Based Syst 251:109280. https://doi.org/10.1016/j.knosys.2022.109280

Meng Z, Song Z, Shao X et al (2023) FD-DE: differential evolution with fitness deviation based adaptation in parameter control. ISA Trans. https://doi.org/10.1016/j.isatra.2023.05.005

Song Y, Zhao G, Zhang B et al (2023) An enhanced distributed differential evolution algorithm for portfolio optimization problems. Eng Appl Artif Intell 121:106004. https://doi.org/10.1016/j.engappai.2023.106004

Das S, Abraham A, Chakraborty UK et al (2009) Differential evolution using a neighborhood-based mutation operator. IEEE Trans Evol Comput 13(3):526–553. https://doi.org/10.1109/TEVC.2008.2009457

Wang Y, Cai Z, Zhang Q (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15(1):55–66. https://doi.org/10.1109/TEVC.2010.2087271

Gong W, Cai Z (2013) Differential evolution with ranking-based mutation operators. IEEE Trans Cybern 43(6):2066–2081. https://doi.org/10.1109/TCYB.2013.2239988

Wang H, Rahnamayan S, Sun H et al (2013) Gaussian bare-bones differential evolution. IEEE Trans Cybern 43(2):634–647. https://doi.org/10.1109/TSMCB.2012.2213808

Peng H, Wu Z, Zhou X et al (2015) Bare-bones differential evolution algorithm based on trigonometry. J Comput Res Dev 52:2776. https://doi.org/10.7544/issn1000-1239.2015.20140230

Mohamed AW, Mohamed AK (2019) Adaptive guided differential evolution algorithm with novel mutation for numerical optimization. Int J Mach Learn Cybern 10:253–277. https://doi.org/10.1007/s13042-017-0711-7

Sun G, Lan Y, Zhao R (2019) Differential evolution with Gaussian mutation and dynamic parameter adjustment. Soft Comput 23:1615–1642. https://doi.org/10.1007/s00500-017-2885-z

Sun G, Xu G, Jiang N (2020) A simple differential evolution with time-varying strategy for continuous optimization. Soft Comput 24:2727–2747. https://doi.org/10.1007/s00500-019-04159-0

Xia X, Tong L, Zhang Y et al (2021) NFDDE: a novelty-hybrid-fitness driving differential evolution algorithm. Inf Sci 579:33–54. https://doi.org/10.1016/j.ins.2021.07.082

Yi W, Chen Y, Pei Z et al (2022) Adaptive differential evolution with ensembling operators for continuous optimization problems. Swarm Evol Comput 69:100994. https://doi.org/10.1016/j.swevo.2021.100994

Meng Z, Yang C (2022) Two-stage differential evolution with novel parameter control. Inf Sci 596:321–342. https://doi.org/10.1016/j.ins.2022.03.043

Chen B, Ouyang H, Li S et al (2024) Differential evolution algorithm with a complementary mutation strategy and data fusion-based parameter adaptation. Inf Sci 668:120522. https://doi.org/10.1016/j.ins.2024.120522

Awad NH, Ali MZ, Suganthan PN et al (2017) CADE: a hybridization of cultural algorithm and differential evolution for numerical optimization. Inf Sci 378:215–241. https://doi.org/10.1016/j.ins.2016.10.039

Chaudhary D, Tailor AK, Sharma VP et al (2019) HyGADE: hybrid of genetic algorithm and differential evolution algorithm. In: 2019 10th international conference on computing, communication and networking technologies (ICCCNT). IEEE, pp 1–4. https://doi.org/10.1109/ICCCNT45670.2019.8944822

Rosić MB, Simić MI, Pejović PV (2021) An improved adaptive hybrid firefly differential evolution algorithm for passive target localization. Soft Comput 25:5559–5585. https://doi.org/10.1007/s00500-020-05554-8

Pan Q, Tang J, Wang H et al (2022) SFSADE: an improved self-adaptive differential evolution algorithm with a shuffled frog-leaping strategy. Artif Intell Rev. https://doi.org/10.1007/s10462-021-10099-9

Li J, Gao Y, Zhang H et al (2022) Self-adaptive opposition-based differential evolution with subpopulation strategy for numerical and engineering optimization problems. Complex Intell Syst 8(3):2051–2089. https://doi.org/10.1007/s40747-022-00734-5

Lin M, Wang Z, Zheng W (2023) Hybrid particle swarm-differential evolution algorithm and its engineering applications. Soft Comput 27(22):16983–17010. https://doi.org/10.1007/s00500-023-09025-8

Zhong JH, Shen M, Zhang J et al (2012) A differential evolution algorithm with dual populations for solving periodic railway timetable scheduling problem. IEEE Trans Evol Comput 17(4):512–527. https://doi.org/10.1109/TEVC.2012.2206394

Zhan ZH, Liu XF, Zhang H et al (2016) Cloudde: a heterogeneous differential evolution algorithm and its distributed cloud version. IEEE Trans Parallel Distrib Syst 28(3):704–716. https://doi.org/10.1109/TPDS.2016.2597826

Wu G, Mallipeddi R, Suganthan PN et al (2016) Differential evolution with multi-population based ensemble of mutation strategies. Inf Sci 329:329–345. https://doi.org/10.1016/j.ins.2015.09.009

Civicioglu P, Besdok E, Gunen MA et al (2020) Weighted differential evolution algorithm for numerical function optimization: a comparative study with cuckoo search, artificial bee colony, adaptive differential evolution, and backtracking search optimization algorithms. Neural Comput Appl 32:3923–3937. https://doi.org/10.1007/s00521-018-3822-5

Zhu L, Ma Y, Bai Y (2020) A self-adaptive multi-population differential evolution algorithm. Nat Comput 19:211–235. https://doi.org/10.1007/s11047-019-09757-3

Zhong X, Cheng P (2021) An elite-guided hierarchical differential evolution algorithm. Appl Intell 51:4962–4983. https://doi.org/10.1007/s10489-020-02091-7

Deng L, Li C, Han R et al (2021) TPDE: a tri-population differential evolution based on zonal-constraint stepped division mechanism and multiple adaptive guided mutation strategies. Inf Sci 575:22–40. https://doi.org/10.1016/j.ins.2021.06.035

Deng Y, Chen D, Zou F et al (2022) Heterogeneous ensemble algorithms for function optimization. Appl Intell 52(11):13310–13338. https://doi.org/10.1007/s10489-022-03197-w

Huang Y, Qian X, Song W (2023) Improving dual-population differential evolution based on hierarchical mutation and selection strategy. Electronics 13(1):62. https://doi.org/10.3390/electronics13010062

Hussain K, Salleh MNM, Cheng S et al (2019) On the exploration and exploitation in popular swarm-based metaheuristic algorithms. Neural Comput Appl 31:7665–7683. https://doi.org/10.1007/s00521-018-3592-0

Morales-Castañeda B, Zaldivar D, Cuevas E et al (2020) A better balance in metaheuristic algorithms: does it exist? Swarm Evol Comput 54:100671. https://doi.org/10.1016/j.swevo.2020.100671

Das S, Mullick SS, Suganthan PN (2016) Recent advances in differential evolution-an updated survey. Swarm Evol Comput 27:1–30. https://doi.org/10.1016/j.swevo.2016.01.004

Pant M, Zaheer H, Garcia-Hernandez L et al (2020) Differential Evolution: a review of more than two decades of research. Eng Appl Artif Intell 90:103479. https://doi.org/10.1016/j.engappai.2020.103479

Kumar V, Kumar D (2021) A systematic review on firefly algorithm: past, present, and future. Arch Comput Methods Eng 28:3269–3291. https://doi.org/10.1007/s11831-020-09498-y

Eusuff MM, Lansey KE (2003) Optimization of water distribution network design using the shuffled frog leaping algorithm. J Water Resour Plan Manag 129(3):210–225. https://doi.org/10.1061/(ASCE)0733-9496(2003)129:3(210)

Ma H, Shen S, Yu M et al (2019) Multi-population techniques in nature inspired optimization algorithms: a comprehensive survey. Swarm Evol Comput 44:365–387. https://doi.org/10.1016/j.swevo.2018.04.011

Novoa-Hernández P, Corona CC, Pelta DA (2013) Self-adaptive, multipopulation differential evolution in dynamic environments. Soft Comput 17:1861–1881. https://doi.org/10.1007/s00500-013-1022-x

Bai X, Yan W, Ge SS et al (2018) An integrated multi-population genetic algorithm for multi-vehicle task assignment in a drift field. Inf Sci 453:227–238. https://doi.org/10.1016/j.ins.2018.04.044

Heidari AA, Chen H, Chen H et al (2020) Multi-population differential evolution-assisted Harris hawks optimization: framework and case studies. Future Gener Comput Syst 111:175–198. https://doi.org/10.1016/j.future.2020.04.008

Navarro MA, Oliva D, Ramos-Michel A et al (2022) An improved multi-population whale optimization algorithm. Int J Mach Learn Cybern 13(9):2447–2478. https://doi.org/10.1007/s13042-022-01537-3

Cao Y, Shi H, Chang DL (2022) Differential evolution algorithm with dynamic multi-population applied to flexible job shop schedule. Eng Optim 54(3):387–408. https://doi.org/10.1080/0305215X.2021.1872067

Tian L, Li Z, Yan X (2020) High-performance differential evolution algorithm guided by information from individuals with potential. Appl Soft Comput 95:106531. https://doi.org/10.1016/j.asoc.2020.106531

Zhang X, Wen S, Wang D (2022) Multi-population biogeography-based optimization algorithm and its application to image segmentation. Appl Soft Comput 124:109005. https://doi.org/10.1016/j.asoc.2022.109005

Liu Q, Pang T, Chen K et al (2022) Multi-subpopulation adaptive, based differential evolution for global optimization. In: 2022 IEEE congress on evolutionary computation (CEC). IEEE, pp 1–7. https://doi.org/10.1109/CEC55065.2022.9870398

Li C, Sun G, Deng L et al (2023) A population state evaluation-based improvement framework for differential evolution. Inf Sci 629:15–38. https://doi.org/10.1016/j.ins.2023.01.120

Das R, Das KN, Mallik S et al (2024) A novel self-adaptive multi-population quadratic approximation guided jaya for solving real-parameter constrained optimization problems. Expert Syst Appl 238:121898. https://doi.org/10.1016/j.eswa.2023.121898

Brest J, Zamuda A, Fister I et al (2010) Large scale global optimization using self-adaptive differential evolution algorithm. In: IEEE congress on evolutionary computation. IEEE, pp 1–8. https://doi.org/10.1016/j.eswa.2023.121898

Guan Y, Yang L, Sheng W (2017) Population control in evolutionary algorithms: review and comparison. In: Bio-inspired computing: theories and applications: 12th international conference, BIC-TA 2017, Harbin, December 1–3, Proceedings 12. Springer Singapore, pp 161–174. https://doi.org/10.1007/978-981-10-7179-9_13

Yan H, Zhu Y (2015) Bang-bang control model for uncertain switched systems. Appl Math Model 39(10–11):2994–3002. https://doi.org/10.1016/j.apm.2014.10.042

Tang L, Dong Y, Liu J (2014) Differential evolution with an individual-dependent mechanism. IEEE Trans Evol Comput 19(4):560–574. https://doi.org/10.1109/TEVC.2014.2360890

Wang J, Ouyang H, Zhang C et al (2023) A novel intelligent global harmony search algorithm based on improved search stability strategy. Sci Rep 13(1):7705. https://doi.org/10.1038/s41598-023-34736-1

Tian L, Li Z, Yan X (2020) Potential-based differential evolution algorithm with joint adaptation of parameters and strategies. IEEE Access 8:100562–100577. https://doi.org/10.1109/ACCESS.2020.2997355

Liang JJ, Qu BY, Suganthan PN et al (2013) Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization. Zhengzhou University, Zhengzhou, China and Nanyang Technological University, Singapore, Technical Report, Computational Intelligence Laboratory

Awad N, Ali M, Liang J et al (2017) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on singe objective bound constrained real-parameter numerical optimization. Technical report, Nanyang Technological University, Singapore

Yue CT, Price KV, Suganthan PN, Liang JJ, Ali MZ, Qu BY, Awad NH, Biswas PP (2019) Problem definitions and evaluation criteria for the CEC 2020 special session and competition on single objective bound constrained numerical optimization. Technical Report, Zhengzhou University and Nanyang Technological University

Derrac J, García S, Molina D et al (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18. https://doi.org/10.1016/j.swevo.2011.02.002

Seyyedabbasi A, Kiani F (2022) Sand cat swarm optimization: a nature-inspired algorithm to solve global optimization problems. Eng Comput. https://doi.org/10.1007/s00366-022-01604-x

Hashim FA, Houssein EH, Hussain K et al (2022) Honey badger algorithm: new metaheuristic algorithm for solving optimization problems. Math Comput Simul 192:84–110. https://doi.org/10.1016/j.matcom.2021.08.013

Chopra NH, Ansari MM (2022) Golden jackal optimization: a novel nature-inspired optimizer for engineering applications. Expert Syst Appl 198:116924. https://doi.org/10.1016/j.eswa.2022.116924

Liu W, Wang Z, Yuan Y et al (2019) A novel sigmoid-function-based adaptive weighted particle swarm optimizer. IEEE Trans Cybern 51(2):1085–1093. https://doi.org/10.1109/TCYB.2019.2925015

Zhang Z, Gao Y, Liu Y et al (2023) A hybrid biogeography-based optimization algorithm to solve high-dimensional optimization problems and real-world engineering problems. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2023.110514

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

Chou JS, Truong DN (2021) A novel metaheuristic optimizer inspired by behavior of jellyfish in ocean. Appl Math Comput 389:125535. https://doi.org/10.1016/j.amc.2020.125535

Abdollahzadeh B, Gharehchopogh FS, Mirjalili S (2021) African vultures optimization algorithm: a new nature-inspired metaheuristic algorithm for global optimization problems. Comput Ind Eng 158:107408. https://doi.org/10.1016/j.cie.2021.107408

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

Hashim FA, Hussien AG (2022) Snake optimizer: a novel meta-heuristic optimization algorithm. Knowl-Based Syst 242:108320. https://doi.org/10.1016/j.knosys.2022.108320

Zhong C, Li G, Meng Z (2022) Beluga whale optimization: a novel nature-inspired metaheuristic algorithm. Knowl-Based Syst. https://doi.org/10.1016/j.knosys.2022.109215

Azizi M, Talatahari S, Gandomi AH (2023) Fire hawk optimizer: a novel metaheuristic algorithm. Artif Intell Rev 56(1):287–363. https://doi.org/10.1007/s10462-022-10173-w

Wang L, Cao Q, Zhang Z et al (2022) Artificial rabbits optimization: a new bio-inspired meta-heuristic algorithm for solving engineering optimization problems. Eng Appl Artif Intell 114:105082. https://doi.org/10.1016/j.engappai.2022.105082

Coello CAC (2002) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput Methods Appl Mech Eng 191(11–12):1245–1287. https://doi.org/10.1016/S0045-7825(01)00323-1

Download references

Acknowledgements

This work was supported by the Key Project of Ningxia Natural Science Foundation (2022AAC02043), the First-class Discipline Construction Fund Project of Ningxia Higher Education (NXYLXK2017B09), the Major Scientific Research Special of North Minzu University (ZDZX201901), the 2023 Graduate Innovation Project of North Minzu University (YCX23075) and the Basic Discipline Research Projects Supported by Nanjing Securities (NJZQJCXK202201).

Author information

Authors and affiliations.

School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, China

Wenlu Zuo & Yuelin Gao

Ningxia Province Key Laboratory of Intelligent Information and Data Processing, Yinchuan, 750021, China

You can also search for this author in PubMed   Google Scholar

Contributions

Wenlu Zuo: investigation, methodology, experiment, writing: original draft, review and editing. Yuelin Gao: supervision, funding acquisition.

Corresponding author

Correspondence to Yuelin Gao .

Ethics declarations

Conflict of interest.

We declare that we have no financial interest or personal competition that could affect the work described herein. All of us authors guarantee that the paper is legitimate and entirely our own scientific research. No copying, plagiarism, infringement, data forgery and other bad behavior, no state secrets involved. The sources of other works cited in the manuscript are noted. We will be responsible for the financial losses and negative effects caused by our bad behavior.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A: Mathematical models of nine engineering problems

1.1 a.1 pressure vessel design, 1.2 a.2 rolling element bearing design, 1.3 a.3 tension/compression spring design, 1.4 a.4 welded beam design, 1.5 a.5 multiple disk clutch brake design, 1.6 a.6 step-cone pulley problem, 1.7 a.7 speed reducer design, 1.8 a.8 planetary gear train design, 1.9 a.9 robot gripper problem, 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

Zuo, W., Gao, Y. Solving numerical and engineering optimization problems using a dynamic dual-population differential evolution algorithm. Int. J. Mach. Learn. & Cyber. (2024). https://doi.org/10.1007/s13042-024-02361-7

Download citation

Received : 01 September 2023

Accepted : 20 August 2024

Published : 14 September 2024

DOI : https://doi.org/10.1007/s13042-024-02361-7

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

• Differential evolution
• Dual-population
• Individual potential value
• Engineering optimization
• Find a journal
• Publish with us
• Track your research

Use knowledge of division to solve problems

I can use knowledge of division to solve problems.

Lesson details

Key learning points.

• When solving division problems, sometimes a remainder is recorded as the number left over.
• When solving division problems, sometimes a remainder can be ignored.
• When solving division problems, sometimes an extra group is made to include the remainder.
• The question asked in the problem shows whether we should ignore or include the remainder.

Common misconception

Children may struggle to visualise how the remainder relates to the question asked in the problem, or may solve the equation without relating back to the question asked.

Encourage them to write the division equation for the problem and say what each part represents, focusing particularly on the role of the remainder and how it relates to the question asked.

Remainder - A remainder is the amount left over after division when the dividend does not divide exactly by the divisor.

This content is © Oak National Academy Limited ( 2024 ), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Starter quiz

6 questions.

• International
• Education Jobs
• Schools directory
• Resources Education Jobs Schools directory News Search

Social Story: Solving Problems Together | Social Skills | Conflict Resolution

Subject: Special educational needs

Age range: 5 - 11

Resource type: Lesson (complete)

Last updated

23 September 2024

• Share through email
• Share through twitter
• Share through linkedin
• Share through facebook
• Share through pinterest

Social Story: Solving Problems Together

Problem-solving amongst peers is an important life skill, but is often challenging for our students. Like any other skill, problem solving requires practice in order to get better at it. This social story helps students to develop healthy boundaries and relationships with their peers, and to navigate how to problem-solve and engage in conversation without creating conflict or negative feelings.

This 12-page social story conveys these themes using practical examples, engaging visuals, and developmentally appropriate language. It is best suited to K-6, and special education settings. We hope this social story helps you, help the children you work with!

What You Will Receive: 1 high-quality PDF file 8.5"x11" in size 12 Pages

How to Use:

• After uploading product, save file to your device
• Print either at home, or via local print provider or online print service
• Bind, laminate, or place in duotang to use with your students

Personal Note: Should you require a different file format or size, let us know and we can do this for you.

We love what we do and so would appreciate your feedback and review so we can continue to provide practical resources to our fellow educators. THANK YOU.

Tes paid licence How can I reuse this?

Your rating is required to reflect your happiness.

It's good to leave some feedback.

Something went wrong, please try again later.

This resource hasn't been reviewed yet

To ensure quality for our reviews, only customers who have purchased this resource can review it

Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch.

Not quite what you were looking for? Search by keyword to find the right resource: