what is strategic problem solving and empathy

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Crafting Better Strategy: Why Empathy Matters

March 21, 2019 • 10 min read.

Empathy is increasingly a valuable skill for chief strategy officers, notes the author of this opinion piece.

Empathy is increasingly a valuable skill for chief strategy officers, notes this opinion piece by Mark Leiter, chairman of Leiter & Company, a consulting and investment firm aiming to raise the performance of business-to-business organizations. He is the author of the book, Crafting Strategy in an Accelerating World . In this opinion piece, he notes that “the effective strategist has a natural platform for encouraging the team to pause, reflect, and step back — even for just a few moments — to consider the broader implications of upcoming decisions.”

Do you ever have days when you are just utterly exhausted by the escalating pace and unpredictability of business? If this sounds familiar, then you have my empathy.

As a member of Strategy 50 — a global community of chief strategy officers — I’ve spent years comparing notes with fellow members on how strategy development is evolving in an accelerating world that is moving forward with far greater velocity and volatility.

Last year, I took these conversations a step further and conducted a research project with the community to examine this topic in more detail. Participating corporations ranged from $2 billion to over $200 billion in revenues. The chief strategy officers addressed issues spanning a wide range of sectors, including industrial glass, power grids and railroads through to automobiles, electronic payments, stock exchanges and open-source software solutions.

One surprising theme emerging from these discussions was the increasing value and importance of empathy to the strategist.

Why is this surprising? Strategists are traditionally hired for their IQ over their EQ. Back in my McKinsey & Company days, when we interviewed prospective consultants we assessed “intellectual horsepower,” “problem-solving skills,” “conceptual thinking,” and “quantitative reasoning skills.” Demonstrated capacity for empathy — the ability to understand what another person is thinking and feeling through their unique frame of reference — wasn’t tested in any interview. I can’t recall a time when it was even discussed.

Life as a chief strategy officer today requires a broader skill set. Executives are pushed and pulled in more directions while facing constantly rising expectations for improving every performance metric that matters.

“Strategists are traditionally hired for their IQ over their EQ.”

“This environment puts enormous pressure on our senior leadership team, such that everyone is always stressed out regardless of our performance,” said one chief strategy officer operating in an iconic company that generated $35 billion in revenues last year. “We are not in huge distress; our business is solid, and our stock is up. But none of that changes the team’s intrinsic stress level.”

As the stress on the team ratchets up, the ability to quickly internalize your colleagues’ mindsets and pressure points has become an essential skill that can play a big role in elevating the strategist’s craft from good to great.

How Challenging Is It on the Front Lines?

Consider Nielsen, where I served as the company’s chief strategy officer. When our current U.S. President proclaims that he is “great for the ratings,” he means the Nielsen TV ratings. While it is the most famous part of the company, Nielsen is much more than TV ratings.

Founded in 1923, Nielsen operates at the epicenter of the global marketing, media and retailing ecosystem. It influences trillions of dollars in consumer consumption and billions in advertising expenditures. During my tenure working with the firm, Nielsen’s enterprise value tripled — from $9 billion to $27 billion. Generating this outcome required navigating massive innovation coming from multiple directions.

A “big data” company long before that term was popular, Nielsen primarily measures market performance for two sectors: media and fast-moving consumer goods (FMCG). The team has been arming domain experts with the latest advances in analytics, algorithms, AI, machine learning and data-as-a-service systems to deliver value to clients. This has required shifts in capital allocation, talent development and go-to-market methods.

Measuring these sectors grows more challenging by the minute. Notably, the media industry landscape — both audio and video — has grown more complex. It now includes such wildly diverse companies as Amazon (via prime video), Apple, CBS, Comcast, Disney, Facebook, Hulu, Netflix, Spotify, Tencent, YouTube and Verizon. The media value chain is in constant flux, spanning content creation through to distribution and consumption. It isn’t any easier analyzing where consumers shop and what they buy in physical and online retailers. We’ve watched disruption on the retail front lines thanks to players that include Alibaba, Amazon, Costco, CVS, eBay, JD.com, Target and Walmart.

The rapid and unstoppable technology and business model innovation across these three domains — information services, media and retailing — is enormously challenging to absorb. I’ve always had empathy for the Nielsen teams as they traversed this terrain. To that end, I would underscore a point made by Eric “Astro” Teller, the “Captain of Moonshots” (CEO) at X, an Alphabet R&D lab, when he said, “although humans and societies have steadily adapted to change, on average the rate of technological change is now accelerating so fast that it has risen above the rate at which most people can absorb all of these changes. Many of us can’t keep pace anymore.” [1]

However, technology isn’t the only major driver of change and innovation. Strategists are concurrently adapting their methods to evolving organizational models that are inherently designed to move business forward with greater speed, precision and agility. At Nielsen, every facet of the company’s operating model was reimagined over the last dozen years in parallel to tackling external and internal technology innovation.

When Strategy Meets Operations

Every company, in its own way, is mixing all of this rapid change — technology, operations, organization — into the corporate blender alongside continuous competitive and customer evolution. To be effective in this context, the strategist must be able to build empathy with colleagues who are trying to juggle their fast-paced, frenzied day job with participation in more reflective and deliberative strategy conversations.

“The ability to quickly internalize your colleagues’ mindsets and pressure points has become an essential skill that can play a big role in elevating the strategist’s craft from good to great.”

This is particularly apparent when strategy meets operations. “To manage complexity on a faster timeline, operators must work in a fully agile, continuous mode,” says Vince McCarthy, group president at Verisk Analytics and previously the company’s head of corporate development and strategy. “They are constantly building momentum by driving multiple commercial initiatives and product innovations while putting out any fires. While they will help co-create new strategic themes and ideas for the company, they aren’t waiting around for a new strategy to shape immediate priorities and decisions.”

Even the military — the historical progenitor for top-down cultures — has shifted to a more agile, adaptive model. This comes in response to a new kind of enemy that is tech-savvy, networked and dispersed, and which has disrupted historical combat norms. “The familiar pursuit of efficiency must change course,” wrote General Stanley McChrystal, former commander of the U.S. Joint Special Operations Command, in the introduction to his book Team of Teams. “Efficiency remains important, but the ability to adapt to complexity and continual change has become an imperative.” [2]

Not surprisingly, operators often get their adrenaline rush from being on the front lines, not being stuck in a room debating strategy. Most companies reward action and outcomes. In a world where every day counts, there is unbelievable pressure to spend every hour accomplishing something that moves the needle in a measurable way.

“The more we re-engineer the enterprise to fluidly adapt to changing conditions, the more the lines blur between strategy and operations,” says Tom Manning, Harvard University fellow and former CEO of Dun & Bradstreet. “In many ways, this is what we desire: an adaptive organization that is continuously changing to seize the day. On the other hand, it dramatically raises the bar for the value the chief strategy officer must deliver to the CEO and the operators to enable their success.”

To be successful in this world, chief strategy officers must be able to quickly understand the needs driving each of the leaders they interact with and to help them access relevant strategies that have been used successfully elsewhere in the organization. This requires a broad skill set.

According to Janine Ames, a leader of Spencer Stuart’s chief strategy officer practice who counsels CEOs and board members, “CEOs increasingly want chief strategy officers who are the full package. Their short hand specification is a mix of strategy consulting and operating experience. The former provides the core training in strategy development over a range of complex problems, while the latter instills an appreciation for what operators face on the front lines. The CEO simply can’t afford to lose momentum with a brilliant, visionary chief strategy officer who lacks sufficient empathy for his or her colleagues.”

Moreover, while the CEO ultimately owns the corporate strategy with the board, he or she is always seeking more leverage. “As the world moves faster and faster, the line outside the CEO’s door gets longer and longer — and their time to deeply reflect and think about strategy gets shorter and shorter,” as one chief strategy officer put it.

In contrast, the chief strategy officer’s mandate includes spending enough time scanning and thinking about what’s possible as well as how to solve some of the toughest problems facing the company. This frees up more time for the CEO and key executives as they work overtime to build confidence with investors, customers and employees.

“While it’s tempting to imagine the answer is to simply think faster, even the smartest minds have their limits.”

A Call for More Empathy

Speed and stress are the natural enemies of thoughtful strategy development. Yet, we can’t make the world simpler, nor slow it down. Each year typically brings only higher performance expectations, changing and conflicting priorities, tighter budgets and a perceived decrease in the available “time to decision.”

While it’s tempting to imagine the answer is to simply think faster, even the smartest minds have their limits. The effective strategist has a natural platform for encouraging the team to pause, reflect, and step back — even for just a few moments — to consider the broader implications of upcoming decisions. Having a shared sense of vision, values, purpose and principles is the starting point for taming the complexity. These are “north stars” that help us guide strategic decisions.

What else can we do? We can dial up our collective empathy. While this skill comes more naturally to some individuals than others, everyone can try harder to see the world through their colleagues’ eyes. From empathy comes deeper understanding, and a clearer path to achieving alignment and momentum.

We might believe we now have less time to be empathetic — but that’s not an excuse. We can all find enough time to understand what our colleagues are thinking and feeling. As the poet Maya Angelou said, “I think we all have empathy. We may not have enough courage to display it.” My advice: Be courageous.

[1] Thomas L. Friedman, Thank You for Being Late (Farrar, Straus and Giroux, 2016); pages 28-35.

[2] McChrystal, Stanley. Team of Teams: New Rules of Engagement for a Complex World (Penguin, 2015).

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Why empathy is a must-have business strategy

Empathy helps create a sense of belonging, reinforcing the belief that employees’ perspectives matter. Image:  Wallpaper Mania

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Stay up to date:, future of work.

• The COVID-19 pandemic has exacerbated issues of work-life balance, financial pressures and fears about job security.
• Greater empathy within organizations as part of everyday culture can help address these problems.
• Empathy can increase employee engagement and deepen loyalty, while driving greater innovation and diversity in the workforce.

“Empathy is important, but not enough to put significant investment behind it”. That sentiment, expressed to me by a senior banker, was the dominant position before the COVID-19 pandemic. Empathy was seen as a “nice to have”, something that was warm and fuzzy and made you feel good as a leader, rather than as a tool to expedite growth. For many, it was a tick-box exercise. Management would run empathy training and then everyone would go back to their day job.

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Why employees' needs should shape the workplaces of the future, work can be better post-covid-19. here's what employers need to know, the rise of the ‘belief-driven’ employee.

Fast-forward 18 months to a global pandemic that resulted in workforce burnout, and empathy is taking on a critical role in company culture. Driven by respected CEOs, such as Jane Fraser at Citi and Satya Nadella at Microsoft, empathy has risen to the top of the board’s agenda.

What’s changed? COVID-19 has pushed us all to our limits. Talent is leaving businesses in droves. Many of us are exhausted emotionally and physically, giving rise to workplace burnout, a WHO-recognized condition described as “chronic workplace stress that has not been successfully managed”. It is now accepted that burnout resides in workplaces and cultures, not in individuals. Harvard Business Review states that “the responsibility for managing it [burnout] has shifted away from the individual and towards the organization”. It’s the company's responsibility.

One of the main issues has involved the blurring of home and work life, leading to increased loneliness and social isolation. As Microsoft’s Nadella says: “ Work from home feels like sleeping at work .” This lack of boundaries, greater financial pressure and fears about job security have resulted in a decline in mental health coupled with increased anxiety. In a global study by Qualtrics , two in five (41.6%) respondents said their mental health had declined since the outbreak of COVID-19, while 57.2% reported higher levels of anxiety.

Empathy can play a vital role in addressing these issues. It helps create a sense of belonging, reinforcing the belief that employees’ perspectives matter and their voices are heard.

Empathy drives innovation and engagement

Addressing the empathy deficit is good business. New research from Catalyst highlights the negative impact unempathetic leadership can have: 61% of people surveyed with highly empathic senior leaders report often or always being innovative at work compared to only 13% of those with less empathic senior leaders. Meanwhile, 76% of people surveyed with highly empathic senior leaders report often or always feeling engaged, compared to only 32% of those with less empathic senior leaders.

As study author Tara Van Bommel explains: “Our findings demonstrate that not only is empathy an effective business strategy, it is a strategic imperative to respond to crisis, transformation, and a critical ingredient for building inclusive workplaces where everyone can belong, contribute and thrive.”

Lack of empathy disproportionately affects women of colour

The survey’s findings also suggest women are disproportionately affected by unempathetic leaders. Those with highly empathic managers experienced less COVID-19-related burnout at work (54%) than women with less empathic managers (63%). Women of colour are even more adversely affected, reporting lower levels of general workplace burnout (54%) than those with less empathic senior leaders (67%). This can cause employee productivity, engagement and organizational commitment to plummet.

The feeling of being valued and respected in the workplace was also significantly less for women of colour (40%) and white women (42%) compared to white men (64%). Empathy has a significant role to play in creating inclusive and diverse cultures and leaders often fail to realize the proximity between diversity and empathy.

How you can implement empathy

Show your commitment

Start by debunking some of the myths around empathy. Show that you are serious about empathy and realize it’s not just a gimmick. It’s not about bringing your dog to a Zoom call but about being committed to making empathy part of everyday culture. Include empathy as one of your metrics, appoint a chief empathy officer, add empathy to your investment decision criteria – show your people that empathy is here to stay and not just a tick-box exercise.

Use data to measure progress

It’s crucial to introduce a series of data-driven metrics to help measure your progress. Use polls to measure empathy levels in online meetings. Make sure there’s a direct question about empathy in your employee and customer surveys and run them monthly not yearly. Break down empathy into its essential components: empowerment, meaning, belonging, reassurance, authenticity, collaboration and ethics. Data is critical to empathy, enabling you to pinpoint your empathy deficits and strengths.

Start with small-scale nudges

Empathy is not about grandiose gestures; it’s about multiple, small-scale “empathy nudges”, which are low-cost, high-impact measures. In one company, we developed more than 40 nudges as part of an empathy programme. Individually they may seem trivial but together they combine to generate an empathy revolution. An empathy nudge could be measuring the amount of time people get interrupted in meetings or sending out a monthly email from the CEO recognizing those who have gone above and beyond. It could be changing a job title to reflect the impact the person has rather than the status of the role. Disney receptionists are called “directors of first impressions” in recognition of the importance of their role. These small changes have a huge impact on empathy levels.

Empathy is a must-have in today’s organizations

The world has changed and leaders need to adapt. Mental health, stress and burnout are now perceived as responsibilities of the organization. The failure to deploy empathy means less innovation, lower engagement and reduced loyalty, as well as diluting your diversity agenda. The good news is that leaders can fix this. You need to show your commitment to empathy; measure progress and implement a series of nudges that will stimulate an empathy revolution. The time is now.

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How to master the seven-step problem-solving process

In this episode of the McKinsey Podcast , Simon London speaks with Charles Conn, CEO of venture-capital firm Oxford Sciences Innovation, and McKinsey senior partner Hugo Sarrazin about the complexities of different problem-solving strategies.

Podcast transcript

Simon London: Hello, and welcome to this episode of the McKinsey Podcast , with me, Simon London. What’s the number-one skill you need to succeed professionally? Salesmanship, perhaps? Or a facility with statistics? Or maybe the ability to communicate crisply and clearly? Many would argue that at the very top of the list comes problem solving: that is, the ability to think through and come up with an optimal course of action to address any complex challenge—in business, in public policy, or indeed in life.

Looked at this way, it’s no surprise that McKinsey takes problem solving very seriously, testing for it during the recruiting process and then honing it, in McKinsey consultants, through immersion in a structured seven-step method. To discuss the art of problem solving, I sat down in California with McKinsey senior partner Hugo Sarrazin and also with Charles Conn. Charles is a former McKinsey partner, entrepreneur, executive, and coauthor of the book Bulletproof Problem Solving: The One Skill That Changes Everything [John Wiley & Sons, 2018].

Charles and Hugo, welcome to the podcast. Thank you for being here.

Hugo Sarrazin: Our pleasure.

Charles Conn: It’s terrific to be here.

Simon London: Problem solving is a really interesting piece of terminology. It could mean so many different things. I have a son who’s a teenage climber. They talk about solving problems. Climbing is problem solving. Charles, when you talk about problem solving, what are you talking about?

Charles Conn: For me, problem solving is the answer to the question “What should I do?” It’s interesting when there’s uncertainty and complexity, and when it’s meaningful because there are consequences. Your son’s climbing is a perfect example. There are consequences, and it’s complicated, and there’s uncertainty—can he make that grab? I think we can apply that same frame almost at any level. You can think about questions like “What town would I like to live in?” or “Should I put solar panels on my roof?”

You might think that’s a funny thing to apply problem solving to, but in my mind it’s not fundamentally different from business problem solving, which answers the question “What should my strategy be?” Or problem solving at the policy level: “How do we combat climate change?” “Should I support the local school bond?” I think these are all part and parcel of the same type of question, “What should I do?”

I’m a big fan of structured problem solving. By following steps, we can more clearly understand what problem it is we’re solving, what are the components of the problem that we’re solving, which components are the most important ones for us to pay attention to, which analytic techniques we should apply to those, and how we can synthesize what we’ve learned back into a compelling story. That’s all it is, at its heart.

I think sometimes when people think about seven steps, they assume that there’s a rigidity to this. That’s not it at all. It’s actually to give you the scope for creativity, which often doesn’t exist when your problem solving is muddled.

Simon London: You were just talking about the seven-step process. That’s what’s written down in the book, but it’s a very McKinsey process as well. Without getting too deep into the weeds, let’s go through the steps, one by one. You were just talking about problem definition as being a particularly important thing to get right first. That’s the first step. Hugo, tell us about that.

Hugo Sarrazin: It is surprising how often people jump past this step and make a bunch of assumptions. The most powerful thing is to step back and ask the basic questions—“What are we trying to solve? What are the constraints that exist? What are the dependencies?” Let’s make those explicit and really push the thinking and defining. At McKinsey, we spend an enormous amount of time in writing that little statement, and the statement, if you’re a logic purist, is great. You debate. “Is it an ‘or’? Is it an ‘and’? What’s the action verb?” Because all these specific words help you get to the heart of what matters.

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Simon London: So this is a concise problem statement.

Hugo Sarrazin: Yeah. It’s not like “Can we grow in Japan?” That’s interesting, but it is “What, specifically, are we trying to uncover in the growth of a product in Japan? Or a segment in Japan? Or a channel in Japan?” When you spend an enormous amount of time, in the first meeting of the different stakeholders, debating this and having different people put forward what they think the problem definition is, you realize that people have completely different views of why they’re here. That, to me, is the most important step.

Charles Conn: I would agree with that. For me, the problem context is critical. When we understand “What are the forces acting upon your decision maker? How quickly is the answer needed? With what precision is the answer needed? Are there areas that are off limits or areas where we would particularly like to find our solution? Is the decision maker open to exploring other areas?” then you not only become more efficient, and move toward what we call the critical path in problem solving, but you also make it so much more likely that you’re not going to waste your time or your decision maker’s time.

How often do especially bright young people run off with half of the idea about what the problem is and start collecting data and start building models—only to discover that they’ve really gone off half-cocked.

Hugo Sarrazin: Yeah.

Charles Conn: And in the wrong direction.

Simon London: OK. So step one—and there is a real art and a structure to it—is define the problem. Step two, Charles?

Charles Conn: My favorite step is step two, which is to use logic trees to disaggregate the problem. Every problem we’re solving has some complexity and some uncertainty in it. The only way that we can really get our team working on the problem is to take the problem apart into logical pieces.

What we find, of course, is that the way to disaggregate the problem often gives you an insight into the answer to the problem quite quickly. I love to do two or three different cuts at it, each one giving a bit of a different insight into what might be going wrong. By doing sensible disaggregations, using logic trees, we can figure out which parts of the problem we should be looking at, and we can assign those different parts to team members.

Simon London: What’s a good example of a logic tree on a sort of ratable problem?

Charles Conn: Maybe the easiest one is the classic profit tree. Almost in every business that I would take a look at, I would start with a profit or return-on-assets tree. In its simplest form, you have the components of revenue, which are price and quantity, and the components of cost, which are cost and quantity. Each of those can be broken out. Cost can be broken into variable cost and fixed cost. The components of price can be broken into what your pricing scheme is. That simple tree often provides insight into what’s going on in a business or what the difference is between that business and the competitors.

If we add the leg, which is “What’s the asset base or investment element?”—so profit divided by assets—then we can ask the question “Is the business using its investments sensibly?” whether that’s in stores or in manufacturing or in transportation assets. I hope we can see just how simple this is, even though we’re describing it in words.

When I went to work with Gordon Moore at the Moore Foundation, the problem that he asked us to look at was “How can we save Pacific salmon?” Now, that sounds like an impossible question, but it was amenable to precisely the same type of disaggregation and allowed us to organize what became a 15-year effort to improve the likelihood of good outcomes for Pacific salmon.

Simon London: Now, is there a danger that your logic tree can be impossibly large? This, I think, brings us onto the third step in the process, which is that you have to prioritize.

Charles Conn: Absolutely. The third step, which we also emphasize, along with good problem definition, is rigorous prioritization—we ask the questions “How important is this lever or this branch of the tree in the overall outcome that we seek to achieve? How much can I move that lever?” Obviously, we try and focus our efforts on ones that have a big impact on the problem and the ones that we have the ability to change. With salmon, ocean conditions turned out to be a big lever, but not one that we could adjust. We focused our attention on fish habitats and fish-harvesting practices, which were big levers that we could affect.

People spend a lot of time arguing about branches that are either not important or that none of us can change. We see it in the public square. When we deal with questions at the policy level—“Should you support the death penalty?” “How do we affect climate change?” “How can we uncover the causes and address homelessness?”—it’s even more important that we’re focusing on levers that are big and movable.

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Simon London: Let’s move swiftly on to step four. You’ve defined your problem, you disaggregate it, you prioritize where you want to analyze—what you want to really look at hard. Then you got to the work plan. Now, what does that mean in practice?

Hugo Sarrazin: Depending on what you’ve prioritized, there are many things you could do. It could be breaking the work among the team members so that people have a clear piece of the work to do. It could be defining the specific analyses that need to get done and executed, and being clear on time lines. There’s always a level-one answer, there’s a level-two answer, there’s a level-three answer. Without being too flippant, I can solve any problem during a good dinner with wine. It won’t have a whole lot of backing.

Simon London: Not going to have a lot of depth to it.

Hugo Sarrazin: No, but it may be useful as a starting point. If the stakes are not that high, that could be OK. If it’s really high stakes, you may need level three and have the whole model validated in three different ways. You need to find a work plan that reflects the level of precision, the time frame you have, and the stakeholders you need to bring along in the exercise.

Charles Conn: I love the way you’ve described that, because, again, some people think of problem solving as a linear thing, but of course what’s critical is that it’s iterative. As you say, you can solve the problem in one day or even one hour.

Charles Conn: We encourage our teams everywhere to do that. We call it the one-day answer or the one-hour answer. In work planning, we’re always iterating. Every time you see a 50-page work plan that stretches out to three months, you know it’s wrong. It will be outmoded very quickly by that learning process that you described. Iterative problem solving is a critical part of this. Sometimes, people think work planning sounds dull, but it isn’t. It’s how we know what’s expected of us and when we need to deliver it and how we’re progressing toward the answer. It’s also the place where we can deal with biases. Bias is a feature of every human decision-making process. If we design our team interactions intelligently, we can avoid the worst sort of biases.

Simon London: Here we’re talking about cognitive biases primarily, right? It’s not that I’m biased against you because of your accent or something. These are the cognitive biases that behavioral sciences have shown we all carry around, things like anchoring, overoptimism—these kinds of things.

Both: Yeah.

Charles Conn: Availability bias is the one that I’m always alert to. You think you’ve seen the problem before, and therefore what’s available is your previous conception of it—and we have to be most careful about that. In any human setting, we also have to be careful about biases that are based on hierarchies, sometimes called sunflower bias. I’m sure, Hugo, with your teams, you make sure that the youngest team members speak first. Not the oldest team members, because it’s easy for people to look at who’s senior and alter their own creative approaches.

Hugo Sarrazin: It’s helpful, at that moment—if someone is asserting a point of view—to ask the question “This was true in what context?” You’re trying to apply something that worked in one context to a different one. That can be deadly if the context has changed, and that’s why organizations struggle to change. You promote all these people because they did something that worked well in the past, and then there’s a disruption in the industry, and they keep doing what got them promoted even though the context has changed.

Simon London: Right. Right.

Hugo Sarrazin: So it’s the same thing in problem solving.

Charles Conn: And it’s why diversity in our teams is so important. It’s one of the best things about the world that we’re in now. We’re likely to have people from different socioeconomic, ethnic, and national backgrounds, each of whom sees problems from a slightly different perspective. It is therefore much more likely that the team will uncover a truly creative and clever approach to problem solving.

Simon London: Let’s move on to step five. You’ve done your work plan. Now you’ve actually got to do the analysis. The thing that strikes me here is that the range of tools that we have at our disposal now, of course, is just huge, particularly with advances in computation, advanced analytics. There’s so many things that you can apply here. Just talk about the analysis stage. How do you pick the right tools?

Charles Conn: For me, the most important thing is that we start with simple heuristics and explanatory statistics before we go off and use the big-gun tools. We need to understand the shape and scope of our problem before we start applying these massive and complex analytical approaches.

Simon London: Would you agree with that?

Hugo Sarrazin: I agree. I think there are so many wonderful heuristics. You need to start there before you go deep into the modeling exercise. There’s an interesting dynamic that’s happening, though. In some cases, for some types of problems, it is even better to set yourself up to maximize your learning. Your problem-solving methodology is test and learn, test and learn, test and learn, and iterate. That is a heuristic in itself, the A/B testing that is used in many parts of the world. So that’s a problem-solving methodology. It’s nothing different. It just uses technology and feedback loops in a fast way. The other one is exploratory data analysis. When you’re dealing with a large-scale problem, and there’s so much data, I can get to the heuristics that Charles was talking about through very clever visualization of data.

You test with your data. You need to set up an environment to do so, but don’t get caught up in neural-network modeling immediately. You’re testing, you’re checking—“Is the data right? Is it sound? Does it make sense?”—before you launch too far.

Simon London: You do hear these ideas—that if you have a big enough data set and enough algorithms, they’re going to find things that you just wouldn’t have spotted, find solutions that maybe you wouldn’t have thought of. Does machine learning sort of revolutionize the problem-solving process? Or are these actually just other tools in the toolbox for structured problem solving?

Charles Conn: It can be revolutionary. There are some areas in which the pattern recognition of large data sets and good algorithms can help us see things that we otherwise couldn’t see. But I do think it’s terribly important we don’t think that this particular technique is a substitute for superb problem solving, starting with good problem definition. Many people use machine learning without understanding algorithms that themselves can have biases built into them. Just as 20 years ago, when we were doing statistical analysis, we knew that we needed good model definition, we still need a good understanding of our algorithms and really good problem definition before we launch off into big data sets and unknown algorithms.

Simon London: Step six. You’ve done your analysis.

Charles Conn: I take six and seven together, and this is the place where young problem solvers often make a mistake. They’ve got their analysis, and they assume that’s the answer, and of course it isn’t the answer. The ability to synthesize the pieces that came out of the analysis and begin to weave those into a story that helps people answer the question “What should I do?” This is back to where we started. If we can’t synthesize, and we can’t tell a story, then our decision maker can’t find the answer to “What should I do?”

Simon London: But, again, these final steps are about motivating people to action, right?

Charles Conn: Yeah.

Simon London: I am slightly torn about the nomenclature of problem solving because it’s on paper, right? Until you motivate people to action, you actually haven’t solved anything.

Charles Conn: I love this question because I think decision-making theory, without a bias to action, is a waste of time. Everything in how I approach this is to help people take action that makes the world better.

Simon London: Hence, these are absolutely critical steps. If you don’t do this well, you’ve just got a bunch of analysis.

Charles Conn: We end up in exactly the same place where we started, which is people speaking across each other, past each other in the public square, rather than actually working together, shoulder to shoulder, to crack these important problems.

Simon London: In the real world, we have a lot of uncertainty—arguably, increasing uncertainty. How do good problem solvers deal with that?

Hugo Sarrazin: At every step of the process. In the problem definition, when you’re defining the context, you need to understand those sources of uncertainty and whether they’re important or not important. It becomes important in the definition of the tree.

You need to think carefully about the branches of the tree that are more certain and less certain as you define them. They don’t have equal weight just because they’ve got equal space on the page. Then, when you’re prioritizing, your prioritization approach may put more emphasis on things that have low probability but huge impact—or, vice versa, may put a lot of priority on things that are very likely and, hopefully, have a reasonable impact. You can introduce that along the way. When you come back to the synthesis, you just need to be nuanced about what you’re understanding, the likelihood.

Often, people lack humility in the way they make their recommendations: “This is the answer.” They’re very precise, and I think we would all be well-served to say, “This is a likely answer under the following sets of conditions” and then make the level of uncertainty clearer, if that is appropriate. It doesn’t mean you’re always in the gray zone; it doesn’t mean you don’t have a point of view. It just means that you can be explicit about the certainty of your answer when you make that recommendation.

Simon London: So it sounds like there is an underlying principle: “Acknowledge and embrace the uncertainty. Don’t pretend that it isn’t there. Be very clear about what the uncertainties are up front, and then build that into every step of the process.”

Hugo Sarrazin: Every step of the process.

Simon London: Yeah. We have just walked through a particular structured methodology for problem solving. But, of course, this is not the only structured methodology for problem solving. One that is also very well-known is design thinking, which comes at things very differently. So, Hugo, I know you have worked with a lot of designers. Just give us a very quick summary. Design thinking—what is it, and how does it relate?

Hugo Sarrazin: It starts with an incredible amount of empathy for the user and uses that to define the problem. It does pause and go out in the wild and spend an enormous amount of time seeing how people interact with objects, seeing the experience they’re getting, seeing the pain points or joy—and uses that to infer and define the problem.

Simon London: Problem definition, but out in the world.

Hugo Sarrazin: With an enormous amount of empathy. There’s a huge emphasis on empathy. Traditional, more classic problem solving is you define the problem based on an understanding of the situation. This one almost presupposes that we don’t know the problem until we go see it. The second thing is you need to come up with multiple scenarios or answers or ideas or concepts, and there’s a lot of divergent thinking initially. That’s slightly different, versus the prioritization, but not for long. Eventually, you need to kind of say, “OK, I’m going to converge again.” Then you go and you bring things back to the customer and get feedback and iterate. Then you rinse and repeat, rinse and repeat. There’s a lot of tactile building, along the way, of prototypes and things like that. It’s very iterative.

Simon London: So, Charles, are these complements or are these alternatives?

Charles Conn: I think they’re entirely complementary, and I think Hugo’s description is perfect. When we do problem definition well in classic problem solving, we are demonstrating the kind of empathy, at the very beginning of our problem, that design thinking asks us to approach. When we ideate—and that’s very similar to the disaggregation, prioritization, and work-planning steps—we do precisely the same thing, and often we use contrasting teams, so that we do have divergent thinking. The best teams allow divergent thinking to bump them off whatever their initial biases in problem solving are. For me, design thinking gives us a constant reminder of creativity, empathy, and the tactile nature of problem solving, but it’s absolutely complementary, not alternative.

Simon London: I think, in a world of cross-functional teams, an interesting question is do people with design-thinking backgrounds really work well together with classical problem solvers? How do you make that chemistry happen?

Hugo Sarrazin: Yeah, it is not easy when people have spent an enormous amount of time seeped in design thinking or user-centric design, whichever word you want to use. If the person who’s applying classic problem-solving methodology is very rigid and mechanical in the way they’re doing it, there could be an enormous amount of tension. If there’s not clarity in the role and not clarity in the process, I think having the two together can be, sometimes, problematic.

The second thing that happens often is that the artifacts the two methodologies try to gravitate toward can be different. Classic problem solving often gravitates toward a model; design thinking migrates toward a prototype. Rather than writing a big deck with all my supporting evidence, they’ll bring an example, a thing, and that feels different. Then you spend your time differently to achieve those two end products, so that’s another source of friction.

Now, I still think it can be an incredibly powerful thing to have the two—if there are the right people with the right mind-set, if there is a team that is explicit about the roles, if we’re clear about the kind of outcomes we are attempting to bring forward. There’s an enormous amount of collaborativeness and respect.

Simon London: But they have to respect each other’s methodology and be prepared to flex, maybe, a little bit, in how this process is going to work.

Hugo Sarrazin: Absolutely.

Simon London: The other area where, it strikes me, there could be a little bit of a different sort of friction is this whole concept of the day-one answer, which is what we were just talking about in classical problem solving. Now, you know that this is probably not going to be your final answer, but that’s how you begin to structure the problem. Whereas I would imagine your design thinkers—no, they’re going off to do their ethnographic research and get out into the field, potentially for a long time, before they come back with at least an initial hypothesis.

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Hugo Sarrazin: That is a great callout, and that’s another difference. Designers typically will like to soak into the situation and avoid converging too quickly. There’s optionality and exploring different options. There’s a strong belief that keeps the solution space wide enough that you can come up with more radical ideas. If there’s a large design team or many designers on the team, and you come on Friday and say, “What’s our week-one answer?” they’re going to struggle. They’re not going to be comfortable, naturally, to give that answer. It doesn’t mean they don’t have an answer; it’s just not where they are in their thinking process.

Simon London: I think we are, sadly, out of time for today. But Charles and Hugo, thank you so much.

Charles Conn: It was a pleasure to be here, Simon.

Hugo Sarrazin: It was a pleasure. Thank you.

Simon London: And thanks, as always, to you, our listeners, for tuning into this episode of the McKinsey Podcast . If you want to learn more about problem solving, you can find the book, Bulletproof Problem Solving: The One Skill That Changes Everything , online or order it through your local bookstore. To learn more about McKinsey, you can of course find us at McKinsey.com.

Charles Conn is CEO of Oxford Sciences Innovation and an alumnus of McKinsey’s Sydney office. Hugo Sarrazin is a senior partner in the Silicon Valley office, where Simon London, a member of McKinsey Publishing, is also based.

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Design thinking: problem-solving rooted in empathy.

Danielle Piccinini Black, academic lead for Johns Hopkins Executive Education’s Design Thinking for Innovation, discusses the benefits of utilizing design thinking as an empathy-centered approach to problem-solving.

At Johns Hopkins Carey Business School, we believe in a better business world through advanced education.

While volunteering with the Peace Corps in South Africa, Johns Hopkins Executive Education adjunct faculty member Danielle Piccinini Black (MBA/MPH ’16) experienced the complex challenges of creating effective and desirable solutions for global health initiatives.

Her time in South Africa inspired her to pursue an MPH/MBA dual degree from Johns Hopkins, confident that comprehensive public health and business skillsets would help create a niche for herself in the public health sector.

Today, Piccinini Black is the academic lead for Design Thinking for Innovation within Johns Hopkins Carey Business School’s Executive Education program. She also serves as an adjunct faculty member for design thinking courses at Carey, as well as the design innovation lead at Johns Hopkins Center for Communication Programs.

Her initial exposure to design thinking came during her time as an MBA student at Carey Business School. Now, an empathy-centered approach to problem-solving through design thinking is the basis of her career in both business and public health.

Post-graduation, Piccinini Black was hired at the Johns Hopkins Center for Communication Programs. Using her background in public health, she was brought onto a project to reinvigorate a commercial market for bed nets for malaria prevention in Ghana.

“This project was a great opportunity to apply the skills I gained in the design thinking course to a ‘real world’ project. I pitched the idea of using design thinking to design new bed nets for commercial sale and it stuck. That project was really the catalyst for my career,” she said.

Design thinking is a creative problem-solving process that’s rooted in empathy. By leveraging creativity, individuals can ultimately design and achieve novel solutions to complex problems and compete in today’s dynamic market.

“It’s a process to help create solutions that will actually meet the needs, desires, and constraints of its end users,” she said.

Piccinini Black leverages this human-centered mindset in the way she approaches and designs her design thinking research, workshops, and classes.

“I approach all my courses and design thinking work in an empathetic way. The design of my research processes and teaching approaches are rooted in a deep understanding of the participants, users, and key stakeholders,” she said. “I never conduct two processes or teach two courses the exact same way. It’s important to tailor each in order to respond to the realities of those involved.”

Breaking old habits

Piccinini Black says the pandemic created a space where organizations were forced to break out of old habits and become more creative in their approaches to problem-solving.

Looking for creative and effective approaches to problem-solving, working professionals from various industries are enrolling in Carey Business School’s Executive Education design thinking courses to help build their skillsets with hopes of bringing new, innovative solutions to their organizations. This approach to problem-solving can be leveraged for a variety of problems in different industries.

“Individuals want to revolutionize their problem-solving skills. Working professionals of all career levels participate in design thinking courses to better understand how to tackle business challenges and develop a more expansive human-centered mindset,” she said. “It is intended for individuals of different disciplines and backgrounds to learn how to solve complex problems in a more effective and strategic way.”

Piccinini Black explained that design thinking gives organizations a mechanism for engaging end users and key stakeholders at the beginning of and throughout the problem-solving process. And by doing so, it reduces risk ­­and failure of not meeting the needs of stakeholders.

“Individuals leverage empathy, research, ideation, and iteration to devise novel, human-centered solutions. We collaborate with companies and organizations to bring ‘real world’ challenges to our courses, so participants learn design thinking through experiential learning,” she said.

“Working professionals of all career levels participate in design thinking courses to better understand how to tackle business challenges and develop a more expansive human-centered mindset.” Danielle Piccinini Black

A promising future for design thinking

Piccinini Black has seen greater emphasis on design thinking approaches to problem-solving since the pandemic, giving her hope for the future of innovation and empathy-focused problem-solving and solutions.

“We have a global shared experience from the pandemic, which I believe has made people more empathetic. Design thinking is empathy-centric, and the process seems to resonate with people more now than ever. Because our world is ever-changing, as a society we recognize that we must challenge routines and solve problems while fostering an empathetic mindset,” she said.

While it may be challenging to apply design thinking effectively without study and practice, Piccinini Black says adopting a human-centered mindset is something individuals can do right away.

“Simply approach your work and problem-solving with empathy for a comprehensive understanding of those you are working with and designing for. The easiest way to do that is to simply engage in conversation from the beginning. Learn directly from them,” she said.

Those who are interested in building their knowledge and skills in design thinking, Piccinini Black says to explore the Johns Hopkins Executive Education certificate in Design Thinking for Innovation.

“Knowing design thinking is one thing. But knowing how to do design thinking effectively and having the confidence to implement it in your work and lives outside of the classroom is another. Earning a certificate will get you there.”

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• Introduction to Design Thinking
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Soft Skills for Leadership Success: Effective Communication, Emotional Intelligence, Adaptability, Problem-Solving, Empathy

• August 27, 2023
• Entrepreneurship & Startups

In the fast-paced world of leadership, the key to success lies in mastering a set of essential soft skills.

Effective communication, emotional intelligence, adaptability, problem-solving, and empathy are the building blocks of great leadership.

These skills empower leaders to connect, understand, and respond to the ever-changing needs of their teams and organizations.

By honing these skills, leaders can create a culture of innovation and drive transformative change.

Join us as we explore the power of these soft skills and discover how they can propel you towards leadership success.

Table of Contents

Key Takeaways

• Effective communication is crucial for leaders to clearly convey ideas and actively listen.
• Emotional intelligence helps leaders understand and manage emotions, build relationships, and make better decisions.
• Adaptability allows leaders to be flexible and open to change, enabling them to navigate challenges and seize opportunities.
• Strong problem-solving skills are essential for leaders to address issues and find innovative solutions.

The Importance of Effective Communication

Effective communication is a crucial soft skill for leadership success. It enables leaders to clearly convey ideas and actively listen to others. Active listening plays a vital role in effective communication as it shows respect and understanding towards individuals. By actively listening, leaders can gather valuable information, identify underlying concerns, and foster meaningful connections.

Additionally, developing effective body language skills is essential for effective communication. Non-verbal cues, such as facial expressions, gestures, and posture, can greatly impact the message being conveyed. Leaders who can effectively control their body language can enhance their communication skills and build trust with their audience.

In an innovative business environment, leaders must continuously hone their communication abilities. This is important to foster collaboration, inspire creativity, and drive successful outcomes.

Developing Emotional Intelligence as a Leader

Developing a strong sense of emotional intelligence allows leaders to understand and manage their own emotions, as well as connect with and support the emotions of others. It is a crucial skill for effective leadership in today’s innovative landscape.

To develop emotional intelligence, leaders can focus on three key areas:

Developing self-awareness: Leaders need to have a deep understanding of their own emotions, strengths, and weaknesses. This self-awareness helps them make better decisions and manage their reactions in challenging situations.

Fostering team collaboration: Emotional intelligence allows leaders to create a positive and inclusive work environment where team members feel valued and supported. By being empathetic and understanding, leaders can foster collaboration and encourage open communication among team members.

Building strong relationships: Emotional intelligence helps leaders build strong relationships based on trust and mutual respect. By recognizing and supporting the emotions of others, leaders can create a cohesive and motivated team that is more likely to achieve innovative solutions.

The Power of Adaptability in Leadership

Leaders who possess the ability to adapt to changing circumstances and embrace new opportunities have a significant advantage in leadership roles. In today’s rapidly evolving business landscape, being flexible and open to change is essential for success.

Strategies for adaptability include staying informed about industry trends, actively seeking feedback, and being willing to take calculated risks.

The benefits of flexible leadership are numerous. It allows leaders to quickly respond to challenges and seize opportunities, fostering innovation and growth. Additionally, adaptable leaders are more likely to inspire and motivate their teams, creating a culture of continuous learning and improvement.

Enhancing Problem-Solving Skills for Success

Enhancing problem-solving skills is crucial for success in professional endeavors. To excel in today’s fast-paced world, individuals must possess effective techniques and embrace creative approaches. Here are three key strategies to enhance problem-solving skills:

Embrace a growth mindset: Cultivate a mindset that embraces challenges and sees them as opportunities for growth. This mindset encourages individuals to seek new perspectives, explore unconventional solutions, and learn from failures.

Foster collaboration and diverse perspectives: Solving complex problems often requires input from multiple perspectives. By collaborating with others and seeking diverse viewpoints, individuals can tap into a wealth of knowledge and ideas, leading to more innovative solutions.

Practice critical thinking: Developing strong critical thinking skills is crucial for effective problem-solving. This involves analyzing and evaluating information, identifying assumptions, and making logical decisions.

Cultivating Empathy for Stronger Leadership

Cultivating empathy allows individuals to understand and connect with others, fostering stronger leadership and creating a positive work environment. Developing empathy is crucial for leaders who desire innovation and success.

By putting themselves in others’ shoes, leaders can better understand their team members’ perspectives, needs, and motivations. This understanding enables leaders to communicate effectively, build trust, and make informed decisions that consider the well-being of their team.

Fostering empathy also creates a supportive and inclusive work environment, where individuals feel valued and heard. When leaders prioritize empathy, they inspire their team to collaborate, share ideas, and work towards a common goal.

Empathy is not just a soft skill; it is a powerful tool that drives innovation, enhances teamwork, and leads to exceptional leadership.

Strategies for Improving Communication Skills

Improving communication skills involves actively listening, clearly conveying ideas, and fostering open dialogue for effective collaboration and understanding.

To enhance communication effectiveness, individuals can employ active listening techniques, such as maintaining eye contact, asking clarifying questions, and providing verbal and non-verbal cues to show understanding.

Additionally, utilizing effective feedback strategies can facilitate better communication. This includes providing specific and constructive feedback, focusing on behavior rather than personal traits, and offering suggestions for improvement.

By honing these skills, individuals can create an environment conducive to open and effective communication, leading to improved collaboration and understanding.

Employing active listening techniques and implementing effective feedback strategies are essential in fostering innovation and driving success in today’s fast-paced and constantly evolving business landscape.

Building Resilience Through Emotional Intelligence

Building resilience through emotional intelligence involves understanding and managing emotions to bounce back from challenges and setbacks. Developing resilience is crucial in today’s fast-paced and ever-changing business world, where leaders must navigate uncertainty and adversity.

Emotional intelligence is the ability to recognize and regulate emotions in oneself and others, allowing leaders to handle stress, build strong relationships, and make effective decisions. By building emotional intelligence, leaders can develop the resilience needed to overcome obstacles and thrive in the face of adversity.

This involves practicing self-awareness, self-regulation, empathy, and effective communication. Building emotional intelligence not only enhances personal well-being but also fosters a positive and innovative work culture, where individuals are motivated, adaptable, and capable of overcoming challenges to drive success.

Frequently Asked Questions

How can leaders use effective communication to build trust and create a positive work environment.

Leaders can build trust and create a positive work environment through effective communication. Building rapport and actively listening to employees fosters understanding and promotes collaboration, leading to increased engagement and productivity.

What Are Some Practical Ways for Leaders to Develop Their Emotional Intelligence?

To develop emotional intelligence, leaders can start by developing self-awareness and actively listening to others. Understanding one’s own emotions and empathizing with others can greatly enhance leadership effectiveness and foster positive relationships.

How Can Adaptability Help Leaders Navigate Challenges and Seize Opportunities?

Adaptability empowers leaders to navigate challenges and seize opportunities. By embracing change and being flexible, leaders can quickly adjust their strategies, make informed decisions, and stay ahead in a dynamic and competitive business environment.

What Strategies Can Leaders Use to Enhance Their Problem-Solving Skills and Find Innovative Solutions?

Leaders can enhance problem-solving skills and find innovative solutions by utilizing creative techniques and fostering a culture of innovation. This creates an environment where new ideas are encouraged, and collaboration leads to effective problem-solving.

How Does Cultivating Empathy as a Leader Contribute to Stronger Leadership and Better Team Dynamics?

Cultivating empathy as a leader fosters stronger leadership and better team dynamics. It creates an environment where individuals feel understood and valued, promoting collaboration and innovation for impactful results.

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Empathy in problem solving   , for projects and relationships.

Understanding other people, by thinking with empathy, is almost always essential for skillful design thinking, for solving problems.  You use design thinking (with empathy) for almost everything in life , so empathy can help you achieve a wide variety of objectives, in design projects and in relationships as described in an overview of using empathy in Design-Thinking Process by asking empathy questions — "What do THEY want?" and "What do I want?" and, combining these, "What do WE want?" — while you're trying to achieve win-win results.

In the following sections about empathy, later we'll explore the similarities between Empathy (to understand others) & Metacognition (to understand self) and will examine the Empathy-Ecology of a Classroom .

But we'll begin by asking...

What is empathy?

It's useful to think about — and think with, * and cultivate in yourself & others — different kinds of empathy :   Cognitive Empathy by cognitively understanding the feeling-and-thinking and behaviors of another person;   Emotional Empathy (aka Affective Empathy ) by feeling what another person feels;   Compassionate Empathy (aka Compassion or Empathic Concern or Compassionate Concern ) is a desire for the well-being of another person.

For most purposes, including education, it seems more useful to think about 2 kinds of empathy (Cognitive & Emotional) instead of 3, and to focus on the Cognitive Empathy that I think is more learn-able and generally is more beneficially useful for problem solving, for making things better. *    Why 2, not 3?  Instead of Compassionate Empathy, I prefer the term Empathic Concern because it places attention on the compassionate Concern (the Compassion ) that is produced by Cognitive Empathy (perhaps combined with Emotional Empathy ) and is motivated by Kindness .     /    *  There is wide variation in the terms used, and their definitions;  a comprehensive Literature Review about Empathy Training includes a recognition that "there are as many researchers acknowledging discrepancies in the use of the term, as there are inconsistent definitions."   many definitions of empathy(s)

also - How wide is the scope of "others"?  In addition to other humans, we also can have empathy for animals — such as a monkey or dolphin, dog or cat, parrot or lizard — although the accuracy of our empathy is limited by significant differences between us and them in our experiences of thinking & feeling, and our difficulties in communicating with them.

* Do we "think with" empathy?  Both kinds of empathy, cognitive and emotional, are important.  But this is a website about thinking that is productive for problem solving, so I'll be saying more about Cognitive Empathy, which is the ability to understand what another person is thinking-and-feeling.

Developing and Using a Growth Mindset for

Improving emotional-and-social intelligence.

As part of a whole-person education for ideas-and-skills & more a teacher can help students learn how to more effectively use both kinds of empathy, by improving their Cognitive Empathies and Emotional Empathies, and their skills in being aware (cognitively and emotionally) of the thinking & feeling of others in a wide variety of life-situations, and also (with metacognitive self-empathy ) of themselves.  These essential components of Emotional Intelligence* are closely related to Social Intelligence.   Students can improve all of their multiple intelligences (including emotional-and-social) when they develop-and-use a growth mindset by believing that their abilities are not fixed at the current levels, instead each ability can become better, can be “grown” when they invest intelligent effort to improve this kind of ability.

    * Psychology Today describes Emotional Intelligence as "the ability to identify and manage one’s own emotions, as well as the emotions of others.   Emotional intelligence is generally said to include at least three skills:  emotional awareness, or the ability to identify and name one's own emotions [by using self-empathy, and by using empathy to "identify and name" another person's emotions];  the ability to harness those emotions and apply them to tasks like thinking and [to "make things better" in ways that include improved relationships] problem solving;  and the ability to manage emotions, which includes both regulating one's own emotions when necessary, and helping others to do the same."  { em phasis and [comments] added by me}

Two closely related abilities – Social Intelligence and Emotional Intelligence – are combined in educational programs * to improve the Social-Emotional Learning (SEL) that is briefly defined by ca sel .org — "social and emotional learning (SEL) is the process through which children and adults understand and manage emotions, set and achieve positive goals, feel and show empathy for others, establish and maintain positive relationships, and make responsible decisions" — in the introduction for What is SEL?      { *   and people improve these skills informally by learning from their life-experiences }

As part of a school's Social-Emotional Learning to improve Social Intelligence and Emotional Intelligence , teachers can help students improve their Cognitive Empathy & Emotional Empathy and their Empathic Concern and Compassionate Action.

Compassion in Action:   A process that produces compassionate action occurs in a sequence:  cognitive empathy and/or emotional empathy, plus kindness, may produce empathic concern for a person, which may produce a desire to help them, and then action to help them.     /    The whole process can occur quickly, as with emergency action, or during a long period of time.  Or action may not occur at all, if the sequence is broken at any point.

Compassion in Design:   A process of design may lead to Compassionate Action if, for any area of life, * Empathic Concern is a motivating-and-guiding factor when you Define a Problem by Choosing an Objective and Defining Goal-Criteria.     { * compassionate action can be motivated by empathic concern in traditional design projects and in relationships }

Is empathy always useful?   In most design projects – even when you are not motivated mainly by compassion – it's very useful to think with empathy . { why do I say "most" projects, instead of “all”? }   And self-empathy , to understand yourself, is useful when your objective is a personal decision or a personal thinking strategy .   {more about empathy and self-empathy }

Human-Centered Design:   Because "empathy is the foundation of a human-centered design process," d.school (of Stanford) emphasizes the importance of a mode for Empathy by including it (when you search for "empath") in 19 of its 47 pages.  And one of their mindsets for design-thinking is to Focus on Human Values.    { Empathy in Design Thinking with d.school and DEEPdt}  { designing with empathy and self-empathy }

Accuracy in Empathy

Do you have an accurate understanding of people?  If you are surprised by a behavior — because your Observations (of how a person responds, in what they do or say) don't match your Predictions (your expectations) — something is wrong with your empathetic understanding of the way other people are thinking & feeling, of how they will respond in this situation.  Why?

When you do a Reality Check by comparing Predictions with Observations, a mis-match can occur due to...

    your inadequate Observations in the past, or     your incorrect interpretations of these Observations when you constructed an explanatory Theory/Model (used to make Predictions ) for this aspect of human feeling/thinking-and-behaving, in one of the areas (re: psychology, sociology, economics, marketing, politics,...) studied by Social Sciences.     Or maybe the other person(s) responded in an unusual way, not consistent with their previous feeling & thinking & actions.

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Empathy in design projects.

In all phases of a traditional Design Project — especially in Modes 1A and 1B when you Choose an Objective and Define Desired Goal-Properties for a product (or activity, strategy, theory) — it's important to think with empathy.   This is important for your Solution-Users and for those (you and maybe others) who are Solution-Designers.

Empathy for Solution-Users:   You learn about the thinking-and-behavior of potential users of a product by getting observations — old (already known by yourself or others) or new (from your own new studies) from customer interviews, focus groups, market surveys,... — that help you understand, with better insights into “how will they use the product? what do they need? and want?”  Ask users for feedback (positive & negative), for constructive criticism and suggestions.  By creatively imagining what it's like to “be a user and think like a user” from their perspective, make predictions. *   Also try to “think like a buyer” or (in another aspect of the project) to “think like a seller.”  These information-gathering activities will help you supplement your internal egocentric thinking with externally-oriented empathetic thinking for all stake - holders in a project, for everyone who will be involved in (or affected by) the project in any way, who will design, make, market, distribute, sell, buy, use, or service the product, or be involved or affected in other ways.

* Predictive Empathy:  Usually you'll try to "think like a buyer/user" in their future, which may differ from their thinking in the present.   For example, Helen Walters describes the "approach to customer research [of Steve Jobs, who said] ‘It isn't the consumers' job to know what they want.’  Jobs is comfortable hanging out in the world of the unknown, and this confidence allows him to take risks and make intuitive bets" by using empathy-based predictions of what buyers/users will want later, even if they don't yet want it now.

Relevant Empathy:  You can never fully understand another person.  Usually your main goal is relevant empathy, by trying to understand what is most important for a particular situation.  If you're designing a product, for example, you'll want to understand the thinking & feeling, the needing and wanting, of people who would use (or might buy) the product, in the context of their using the product and/or b uying it.   And for a relationship-situation, usually you focus on understanding what is most relevant in the context of that situation.

Empathy for Solution-Designers:   During a design project you'll want to develop empathy for solution-users (those you are serving), as described above .  And when you're co-designing as part of a group, you'll want to develop empathy for the other solution-designers in your team, to make your process of cooperative problem-solving more enjoyable and productive.   If members of a group improve their use of “collaborative empathy” this will improve their interactions, and will help them develop a cooperative community for creative collaboration .  This can occur in many contexts, including schools where better educational teamwork (by everyone involved in education ) will make the process more enjoyable for teachers, and more effective for students by increasing positives (in learning, performing, enjoying ) and decreasing negatives (like jealous attitudes & bullying behaviors).     { building empathy-ecology in a classroom }

Traditional and Relational:   Empathy is useful whenever you want to solve a problem by “making it better” with a traditional design project ( above ) — when you use empathy to produce a better solution (for your solution-users ) and a better process (if you're working in a team of solution-producers ) — and/or a relational design project (below) when your objective is to improve an interpersonal relationship.

Empathy in relationships  .

An Important Objective:   Originally I defined four general categories for problem-solving objectives – for when we decide to design a better product, strategy, activity, and/or theory.   Later I added relationships because our most important problems (our opportunities to make things better ) usually involve people, so improved relationships are among the most important objectives we can choose to improve.  How?  An essential foundation is developing...

Empathy and Self-Empathy to improve Two Understandings:   You can build a solid foundation for improving your relationships by improving two kinds of understandings (external and internal) with externally-oriented empathetic skills – to develop empathy (overall and also situation-specific relevant empathy ) based on external observations, trying to understand what others are feeling & thinking – and internally-oriented metacognitive skills (to develop self-empathy based on internal observations, trying to understand what you are feeling & thinking).   The practical value of these life-skills is a reason to define...

Educational Goals for Relationship Skills:   We can aim for whole-person education that will help students improve personally useful ideas & skills and more in their whole lives as whole people.  Our educational goals should include the important life-skill of building better relationships, with empathy & kindness and in other ways.  A very useful general strategy — for educating students (and yourself) in all of the multiple intelligences, including social-emotional intelligences — is to develop & consistently use a growth mindset .

Kindness plus Empathy:  When you want to be kind — and you combine your kindness with empathy — this will help you...

Choose a Win-Win Goal:   In many common life-situations, when you are trying to "make things better" your two understandings (external for others, and internal for self) are combined when you ask — while you are defining your goals — “what do they want?” (using empathy to understand others ) and (using self-empathy to understand yourself ) “what do I want?” and (if you choose to define your goal as an optimal win-win result ) “what do we want?”     /     You also make choices when you...

Define the Scope of Your Win-Win Goals:   How broadly do you define "they" when you're trying to achieve win-win results?  If you want to decrease the unfortunate tendency of positive teamwork to become negative tribalism, one strategy is for you (and those you influence) to increase your...

Understanding and Respect:   One of the many ways we can improve relationships is to develop better teamwork .  But one strategy for developing strong relationships among insiders (within a team) — by promoting hostile “us against them” attitudes toward outsiders (not in the team) — can convert positive teamwork into negative tribalism.   {   I'm calling it negative tribalism because tribe-like strong loyalties produce some positive effects and some negative effects.   }     One kind of educational activity that can help reduce the negative aspects of tribalism is examined in a page describing how my favorite high school teacher, by using informative debates in his civics class, helped us develop Accurate Understandings and Respectful Attitudes .  How?  After he helped us carefully-and-diligently study an issue, so our understandings of different position-perspectives were more accurate and thorough, usually we recognized that even when we have justifiable reasons to prefer one position, * people on other sides of an issue may also have justifiable reasons, both intellectual and ethical, for believing as they do, so we learned respectful attitudes.    { *   yes, he wanted us to find "justifiable reasons" because his educational goal was not a logically-fuzzy postmodern relativism , instead he promoted a logically appropriate humility with confidence that is not too little and not too much.}     When this kind of educational process is done well, it can produce a foundation of empathetic understanding that is useful for producing authentic understanding & respect, that helps us be more kind in our feeling & thinking & actions.

Empathy without Kindness:  This can be a bad combination, when it allows the use of empathetic thinking as a tool for manipulating others in harmful ways.

Empathy plus Kindness:   This is a good combination, when empathy (a useful skill) is accompanied by kindness (an essential aspect of good character).  Thinking with empathy is beneficial for other people when it's combined with kindness-and-caring in feeling & thinking & actions, when an attitude of caring for others (in feeling & thinking) leads to caring for others (in actions), with actions motivated by kindness, by genuinely caring for other people.

Kindness in Thinking-and-Actions:   More people will have better lives...  if more of us are more often motivated by kindness, with goals of trying to “make things better” for other people, wanting to affect their lives in ways that are beneficial for them, that make life better for them;   and if our empathy-based compassionate concerns were more often actualized with kindness in our actions.

A Wonderful Life produces Beneficial Effects:   A creative illustration of helping others is my favorite movie, It's a Wonderful Life.  I like it partly for its artistry (in plot, dialogue, acting, directing, photography) but mainly for the message:  each of us affects other people – as dramatized in the end-of-movie comparison of lives with & without George Bailey – and our own life is better when we affect others in ways that make their lives better, and help them achieve worthy goals in life.   We can help others enjoy what they do, and (when they “pass it on”) do more actions that benefit others, and more fully develop their whole-person potentials.

Helping Others achieve Their Goals:   For understanding how we can be more beneficial — by helping another person "enjoy..." and "more fully develop their whole-person potentials" so they are becoming a better version of themself, growing into the kind of “ideal person” they want to be, or they should be — a useful perspective is the Michelangelo Phenomenon;   this concept was developed by social psychologists, with Caryl Rusbult ( my wonderful sister ) being a main developer.  As described in a review article by Rusbult, Finkel, & Kumashiro: "close partners sculpt one another's selves, shaping one another's skills and traits [analogous to Michelangelo's Actions while shaping a piece of stone so it becomes a beautiful work of art] and promoting versus inhibiting one another's goal pursuits... of attaining his or her ideal-self goals" in the "dreams and aspirations, or the constellation of skills, traits, and resources that an individual ideally wishes to acquire."  When lovingly influential Michelangelo Actions are done well, the beneficial effects usually are lovingly appreciated, as we see in "Love" by Roy Croft:  "I love you, not only for what you have made of yourself, but for what you are making of me."   Or in the language of education, when feedback-actions help another person improve, this is formative feedback that helps them “form themselves” into a better person.   Of course, a beneficial shaping influence — a teaching influence that helps them develop a growth mindset about improving their skills with social-emotional intelligences and relational empathy — can come from a "close partner" and also others, including friends and family, counselors, fellow students & team members & co-workers, and teachers & coaches & supervisors.

Golden Rule with Empathy:   For building mutually beneficial relationships, one useful principle-for-life is a Golden Rule with Empathy that combines kindness with empathy, by treating others in ways THEY want to be treated, which may differ from what you would want. *   Treating others this way will be beneficial for them, and also for you (especially in the long run), in a wide variety of situations.     /     *   But it doesn't really "differ from what you would want," if we look more deeply.  Why?  You want others to empathetically understand you, and then treat you the way you want to be treated.   Other people also want this, so you should Seek First to Understand (with Habit 5 in The 7 Habits of Highly Effective People ) and then use a Golden Rule , e.g. "Do for others what you want them to do for you" by treating them the way THEY want to be treated.

Empathy for Society:   I.O.U. – This paragraph might be written before mid-2023, with ideas from John Rawls:  imagine you are part of a group in Original Position (before you're born) that is designing a society with the goal of making life optimal for all,  and you are self-interested in "all" because – with a Veil of Ignorance – you don't know “who you will be” when you are born, re: your multiple intelligences, looks, race, health, wealth, status, location,... ;   in reality we cannot be “ignorant of our situation” now, during life as it really is, but we can use empathy + kindness/compassion in our thinking about society.    {for more, an article by Richard Beck, Empathy, the Veil of Ignorance, and Justice }

Clever and Kind:   Abraham Heschel, sharing an insightful observation based on self-empathy, wisely said "When I was young, I admired clever people.  Now that I am old, I admire kind people."   Teachers can help students, while they are still young, appreciate the value of being truly clever (with skills in creative-and-critical productive thinking to solve problems to make things better) and also kind.

Empathy and Metacognition

These related ways of thinking – helping you understand others , and understand yourself – are very useful in all areas of life, including education.  This section — first in Goals & Perspectives, then in RESULTS and PROCESS , and Using Empathetic Feedback in a Classroom — will examine ideas & strategies that can help a teacher and students develop better empathy-ecology in their classroom .

Goals & Perspectives

Empathy and Metacognition have similar goals (to understand thinking & feeling) but different orientation-perspectives, re: external and internal.

    • With empathy you try to understand the thinking & feeling of others, who are external to you.     {  two empathies and a result : cognitive empathy (used "to understand" thinking & feeling) plus emotional empathy (to feel) can produce empathic concern.  }     • With metacognition ( self-empathy ) you try to understand your own internal thinking (& feeling).     { In its basic definition, with metacognition you "think about your thinking. "  But in practice, thinking and feeling are related, often with strong mutual influences.  Therefore, typically it's useful to “think about your thinking AND feeling . ” }

External & Internal, for You and Others:

    everyone – you and others – thinks with externally-oriented empathy, to understand the thinking & feeling of other people;     everyone – you and others – thinks with internally-oriented metacognition, to understand your own thinking & feeling.

The external & internal understandings constructed by you are summarized in the 1st & 2nd rows-of-cells in this table.

The 3rd & 4th cell-rows describe the external & internal understandings constructed by another person .

Metacognition and Self-Empathy:  These terms have the same meaning, in this page.  More generally, when these terms are used by others, typically with metacognition the emphasis is more heavily on thinking, and with self-empathy it's on feeling (but also thinking).

other terms:  a metacognitive understanding is aka personal metacognitive knowledge that is one aspect of a person's overall general-and-personal metacognitive knowledge .  By analogy, empathetic understanding also can be called empathetic knowledge, although the term metacognitive knowledge is used much more often.

RESULTS  —  Perspectives and Understandings

By comparing understandings of YOU in the 2nd & 3rd cell-rows, or of THEM in the 1st & 4th rows, you can see how understandings ( of YOU , or of THEM ) depend on point-of-view perspectives (on whether the constructing is done by you , or by them ).

two pov-perspectives on YOU, in rows 2 & 3:  You use internal metacognition (self-empathy) to construct your understanding of YOUR thinking & feeling.  And another person uses external empathy to construct their understanding of YOUR thinking & feeling.  It can be interesting to compare these two understandings, asking “How do I view me? How do they view me?” and “What are the similarities? and differences?” and “Why do the differences occur?” and “Which understanding is more accurate ? and in what ways?”

three pov-perspectives on ANOTHER PERSON, in rows 1 & 4 & _:  You also can make comparisons and ask questions (about similarities & differences, and accuracy), re: understandings of ANOTHER PERSON – “How do I view THEM ? How does this person view THEMSELF ?  And, not shown in the table, how do other people view THEM ?”

When we compare empathy (to understand others) with metacognition (to understand self), we see many similarities and analogous relationships in the PROCESS used (below) and (above) the RESULT produced .

PROCESS  —  constructing Empathy & Metacognition

Now we'll shift attention from RESULTS to PROCESS.

We construct our understandings (of others & self) in a social context, so it's useful to distinguish between...

Understanding and Feedback:  We construct (i.e. we develop) feedback in a two-step process.  First we use empathy or metacognition to construct understanding that we use, after evaluative filtering, to provide feedback for others, with communication.   { Understanding and Feedback, Part 2 }

You construct your external EMPATHY (it's your understanding of ANOTHER PERSON ) when you internally interpret all of the evidence you find.   You can use three kinds of evidence:  your observations of the person ;  feedback about the person from other people;  feedback about self from the person.

You construct your internal SELF-EMPATHY (to get your understanding of YOURSELF ) when you internally interpret all of the evidence you find.   You can use two kinds of evidence:  your observations of yourself ;  and feedback about you from others.

{an option: If the table below is too wide for easy reading in your browser window, you can temporarily view this page in a new full-width window . }

The first 4 rows in the tables above (for RESULTS) and below (for PROCESS) are matched, re: who is trying to understand WHO .  Below,

    The 1st and 2nd rows summarize-and-organize the processes you use to construct your understandings of ANOTHER and YOURSELF .     The 3rd and 4th rows describe how, using the same processes, another person constructs their other-understanding of YOU , and their self-understanding of THEMSELF .  The 5th row shows how they construct their other-understanding of ANOTHER PERSON, of someone who isn't YOU or THEM, and thus is a THIRD PERSON .

Did you notice that the 3rd & 5th rows are analogous but with one difference?   (what is it? the 5th-row process can include one extra evidence that is "feedback-about-third from you")

Understanding and Feedback  —  These are related, but different.  They occur in sequence:

    1. First you use empathy and observations-of-performance, trying to get accurate understandings of another person(s), and of their performance(s).     2. Then if you want to provide helpful feedback, * you will wisely filter your understandings by not saying everything you are thinking, but only what will be helpful.   You do this by deciding, for each person or group, what to say (and not say), when and how, or whether to say nothing.  The goal is to be helpful by providing formative feedback with an intention, and hopefully a result, of being kind and beneficial .   /   *  Unfortunately, sometimes (if a person doesn't want to be kind-and-beneficial) the feedback is intended to be un-helpful.     1-during-2:  An empathetic understanding (developed in Step 1) is used (in Step 2) during the process of filtering, when you're deciding the details (the what/when/how-and-whether) of providing feedback that will be helpful.

MORE - Other useful strategies for providing helpful feedback are in two places:  Developing a Creative (and critical) Community by trying to minimize any "harshness" in feedback-providing and feedback-receiving;  Evaluation is Argumentation that in a group requires "the social skills of communication" when you combine Evaluative Thinking with a Persuasion Strategy and Communication Skills, along with productive Attitudes while Arguing.

Using Empathetic Feedback in a Classroom

The three * s — above in the table-for-process and below in descriptions of each * — are three kinds of "feedback... from you ."  Imagine that you are a teacher , and two of your students are Sue (" a person ", aka " them ") and John (" a third person ", aka " third ").

How will you use these 3 kinds of empathy-based feedbacks?  If you're an effective teacher, then (in cell-Rows 4, 5, and 3)...

    * You want to provide feedback that will help Sue construct a better self-understanding of HERSELF .  (This is her SELF-EMPATHY, aka her METACOGNITION, in Row 4.)   /   a new term: Sue's own internal METACOGNITION (by "thinking about Sue's thinking) is being supplemented by your feedback-to-her about her, which is aka external metacognition because it's the "thinking about Sue's thinking" that is externally supplied by you, as an empathetic observer.     * You want to provide feedback that will help Sue (and other students) construct a better other-understanding of JOHN .  (This is her EMPATHY for A THIRD PERSON in Row 5.)   /  You can provide feedback-to-others about all of your students, individually and collectively, to influence each student's other-understandings of their fellow students, and attitudes toward them.     * You want to provide feedback that will help Sue construct a better other-understanding of YOU .  (This is her EMPATHY for YOU in Row 3.) 

With a particular feedback, you want to help a student understand themself (Row 4), or another student (Row 5), or you (Row 3).

Building an Ecology of Empathy in a Classroom

All of these * -feedbacks are one part of the complex personal interactions (simplistically symbolized in the diagram) that occur in every classroom.  In this context, "better self-understanding" and "better other-understanding" will help all of you — Teacher , Student (like Sue or John), and students (in the whole class, or in smaller groups) — develop a better ecology of empathy in your classroom.

In the interactions-diagram, arrows indicate a variety of interactions, including communications that are verbal (with * -feedbacks and in other ways) and non-verbal:

    two arrows point away from the Teacher (you) who can communicate with only one Student (like Sue) or with two or more students .     two arrows point away from the Student (Sue) who can communicate with you , or with one or more other students .     two arrows point away from students (John & others) who can communicate with you , or with any other Student (s).   {note: A complex diagram that is more-complete would show more kinds of interactions between students, as individuals and in groups.}

A skilled teacher will provide guidance for students in how to " wisely filter " their communications (using feedback and in other ways) with the teacher and each other, so their interactions will be helpful.   A wise evaluating-and-filtering should be based on a foundation of healthy interpersonal motivations, with each student wanting to be kind, wanting to affect others in beneficial ways.

Shared Goals and Individual Goals:  In ideal educational teamwork the teacher and all students will have shared educational goals of “greatest good for the greatest number” with optimal learning-performing-enjoying for everyone in the classroom.  But each student also will have their own personal goals that include wanting to improve their interpersonal relationships and personal education .

Habit 5 of Highly Effective People is "Seek first to understand, then to be understood. "  As a teacher, you can use this habit/principle in (at least) two ways:

    When you provide feedback , in Step 1 you try to understand Sue, as a foundation for Step 2 when you help her understand your view of her and what she is doing and how she can improve.   {your feedback is one aspect of stimulating and guiding students}     In the third * -feedback you try to understand Sue, so (with your * -feedback about yourself) you can help her understand you .

Building Empathy-Ecology for a Classroom

I.O.U. - Below are some ideas that eventually, maybe by mid-2019, will be developed more fully.

a humble disclaimer:  This section is just ideas, and most of the ideas (maybe all of them) aren't really new.  I'm just describing some goals of skilled teachers, and some strategies they already are using to effectively pursue their goals.

Important foundational ideas, essential for this section, are in other parts of the website:

• empathy-ecology performs a valuable function in a system of strategies for teaching by helping a teacher provide formative feedback that will help students improve their performing-enjoying-learning and their system of self-perceptions and...

    more generally, will help guide our goal-directed designing of coordinated curriculum & instruction .

• definitions for empathy(s) & metacognition and their Process (of construction) & Result (in understanding) and their uses (by teacher & students) in developing a classroom ecology .  /  [[here are ideas that will be developed later: motivational teamwork for cooperation-collaboration in education, at all levels, including Teaching Strategies for students (re: how they influence the learning of other students, directly with peer teaching, and indirectly/unofficially);  being motivated, as on a sports team, to establish an education-culture for better learning/performing/enjoying;  a HMW for students, in activity where they ask "How Might We" design our own ideal culture/environment for optimal learning, to pursue a “greatest good for the greatest number of students” and for the teacher.]]

strategies for thinking (in a wide variety of contexts ) by learning from experience , and...

    related strategies for teaching .

based on their understanding of personal motivation teachers can use motivational persuasion to help students recognize that school experiences (when they're well designed) can help them learn for life so they will want to adopt a problem-solving approach (to "make it better" in their life) for their own personal education .  When students are personally motivated to learn, it will be much easier for teachers & students to build educational teamwork in a classroom and a school.

Educational Ecologies (in Educational Ecosystems) occur at many levels, in large-scale systems — in a nation, state, district, school, department — and , on a smaller scale,

in a classroom with its ecosystem of interactions between each Student and other students and the Teacher , as shown simplistically in this diagram, to produce 6 kinds of formative feedback — from one person (or group ) to another — based on empathetic understandings of what others are feeling & thinking in their hearts & minds.   Each person also tries to understand, with metacognitive self-empathy, their own feeling & thinking, their own life-goals and life-strategies, for what they want (in their goals ) and how to get it (with their strategies ).   { a process of developing classroom ecology should be based on a foundation of kind attitudes and compassionate intentions to be benefically helpful}

Ideally, the shared goal when building empathy-ecology in a classroom will be improving the total school experience to produce an optimal performing-enjoying-learning overall, with “greatest good for the greatest number” but also respect for all individuals.  For each student, and the teacher(s), the shared mutual objective is to build educational teamwork that will be helpful in achieving individual goals, and group goals.  All can work together in creative collaboration to construct a classroom community with a learning-friendly atmosphere, so students can learn in the ways they want to learn and are able to learn.

I.O.U. reminder - Soon, maybe in mid-2023, these ideas (and related ideas) "will be developed more fully," including my exploration of what others are doing — in principle and in applications — with different aspects of educational ecology.

Is empathy always needed?

This section responds to a question:  Is thinking-with-empathy useful in ALL design projects?

A high quality of thinking with empathy (so your understanding is relevant, accurate, and deep) is extremely important for defining and solving most problems.   But not all problems, because empathy is not very important (or at least it's different) for problem-solving objectives in two categories, when your problem either (1) involves mainly you, or  (2) does not directly involve any people,  when...

1) ...when you want to “make life better” by achieving an objective that is mainly for your own benefit, not for other people, *  and you do most of the problem solving (or all of it) by yourself.   This focus-on-self occurs for some personal decisions and for many of your thinking strategies .  To do each of these well, you need to know yourself, with self-empathy for your own thinking & feeling .  You can use the benefits of different perspectives by supplementing your own understanding (from internal self-observation & self-empathy by yourself) with other understandings (from external observations & empathy by other people).    { perspectives - internal & external, metacognition & empathy }

* Even when a problem-solving project does not "directly involve people" (as in 2a below) or "...other people" (in 1 above), usually some people will be affected in some way, so typically we are describing an objective that requires less empathy, rather than no empathy.

2a) ...when the objective is mostly technical, so it does not directly involve people.  This can occur because a wide variety of objectives (for designing a better object, activity, or strategy in General Design) require a wide variety of empathy, with less needed for a few objectives (those in 2a) than for most objectives.   { IOU - Later, maybe in May, some of these variations-in-empathy will be examined in an appendix, as outlined in the final paragraph of this page.

2b) ...when your functional responsibility in a problem-solving process is to solve a purely technical problem, in a sub-project within the overall project.  For example, you might be asked to design a new piece of equipment (or to repair it) after the technical goal-specifications already have been clearly defined by others in a part of the design project ( Defining a Problem ) that usually requires empathy. }

2c) ...when your objective in Science-Design is an explanatory theory about NON-HUMAN aspects of nature (as in chemistry, physics, or astronomy), not about HUMAN nature (as in psychology, sociology, political science, economics, marketing,...).    { If you ask “is science-design authentic design?”, we can discuss the pros & cons of using definitions (for problem, design, design thinking,...) that are broad or narrow. }

Empathy for Collaboration:  During any design project (including 1, 2a, 2b, 2c), if you're working collaboratively it's important to have empathy for your colleagues, so you can understand ( intellectually and emotionally ) what they are thinking & feeling, to help all of you work together more effectively and enjoyably.

I.O.U. - The ideas below are in gray text because they need to be developed and revised:

In this website, the importance of empathy is emphasized (as in mc-em.htm#empathy - ws.htm#dpmo1ab - ws.htm#dpmo2aem - ws.htm#mcts ) but some other models-for-process (like d.school and DEEPdt) emphasize it more strongly, as described here .

The fact that creative thinking is necessary to imagine projects requiring "no empathy (or very little)" shows that empathy is essential (or at least is extremely useful) for understanding-and-improving almost all problem-situations. — especially for "design projects" (which include almost everything we do in life) that are worthwhile.

maybe responses will be indicated by text-highlighting the objectives where empathy is extremely important and very important and not as important.

for a problem that only you can solve, analogous to solo mountain climbing when you are “on your own” so you must do everything by yourself. 

A larger project is making a detailed appendix (maybe in May) by asking, for many objectives (across a wide range of objectives ), "How useful is thinking with empathy when you define a problem (by learning about a problem-situation, defining an objective, defining goals for a solution) and solve the problem (by designing a solution that satisfactorily achieves your goals)?"

If you want to discuss any of these ideas, you can contact me, <craigru178-att-yahoo-daut-caum> ; Craig Rusbult, Ph.D. - my life on a road less traveled

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The Art of Empathetic Problem Solving

Empathetic problem solving is the ability to really understand and feel another’s perspective in a conflict or issue. Empathetic problem solving is about what you do in communication while solving a problem but also about what you don’t do .

What is deep listening? Deep listening is a way of listening where we are fully present without trying to immediately control or judge a situation. This can be hard for us leaders because we have so much responsibility and can be so accustomed to putting out fires. With deep listening, we do our best to stay in the moment and not jump ahead and define or solve the problem before we have more information. We also try to push away our preconceived notions about the situation or the people involved. For example, not letting our mind immediately go to fault finding when dealing with a problem employee. Or not assuming a customer that frequently complains is just blowing off steam. Rather we do our best to limit our assumptions and really tune in for precisely what someone is trying to tell us. Telling, on the other hand, is when we jump in and try to tell someone what happened before getting his or her perspective. When this happens, people tend to shut down and be resistant to solutions, even very good ones, because they don’t feel they were really heard.

Questioning is about asking questions to understand what happened so that you can arrive at a workable solution. The other side of the coin is blame. Blame is about figuring out ‘who did it.’ Your questions should be as neutral and judgment free as possible. For example, it is better to ask, “What happened between you and Bob?” than “Why were you shouting at Bob?” This kind of neutral questioning can get the information rather than shutting someone down because they feel your judgment. Real questioning should be about revealing obstacles and uncovering alternate paths ahead. Again, this can be challenging because quite often we probably know what happened and we can bring our own feelings of anger, frustration and disappointment to these conflicts.  

With enhanced perspective, the most effective leaders are able to help an individual embrace a more open perspective of the situation or conflict they are imbued in. Enhancing perspective is akin to ‘see it how I see it’ but more subtle and done together rather than delivered straightaway. When you enhance someone’s perspective, you reframe the issue pointing out other perspectives and possibilities. You light the path and then allow someone to walk down it.

Inspiring someone to make the choice you want is always better than an autocratic power play. Whether its employees or children, gaining their agreement on what you want them to do always works better than making demands from up on high. While it may work with Nike, ‘Just Do It’ rarely works for long with people. Maybe they do something they don’t want to do because they want to please you. Perhaps in seeing your fairness and lack of blame placing, they are inspired to be more conciliatory with a difficult colleague. 

Even though this kind of engaged problem solving really requires stamina and mindfulness from a leader, it also can gain us the respect and trust our people. They see how we work to be fair, really listen, value problem solving over blame placing. And when issues arise, and they will, they will trust us, come to us and try to work through an issue rather than resort to a CYA or worse.

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PBL That Fosters Empathy and Community

Project-based learning can cultivate collaboration, creativity, and critical thinking across the grades.

In today’s fast-paced and interconnected world, fostering collaborative, empathy-driven learning experiences is crucial for equipping students with the skills they need to navigate an increasingly complex future. Combining the power of community partners , collaboration, authentic problem-solving, and a focus on understanding, project-based learning (PBL) experiences offer valuable insights into how education can shape compassionate and socially responsible individuals.

Here we explore two innovative PBL projects developed through a partnership between multiple schools within Wappingers Central School District and Maria Fareri Children’s Healthcare Services at MidHudson Regional Hospital, a member of WCMHealth . “Happy Little Accidents” and “What’s the Matter?” sought to cultivate creativity, critical thinking, and empathy among students while addressing real-world challenges.  

Our role was to support our colleagues with curriculum design through planning meetings and serving as liaisons connecting our community partner with the district,  teachers, and students. We modeled PBL techniques, including differentiated instruction, feedback, reflection, assessment, and evaluation. We shared resources, supported the integration of technology, and fostered community building with different teachers and students. 

In this article, through a review of the outcomes, as well as an examination of the design and implementation, we explore the transformative potential of PBL.

The Outcomes

Maria Fareri Children’s Healthcare Services offers specialized care for infants and children who may be seriously ill. As part of Westchester Medical Center, they provide world-renowned health care services to the most fragile in our community.

During the 2021–22 school year, the Wappingers Central School District students worked on a PBL project, “Happy Little Accidents.” The students inspired, designed, fabricated, and donated a Rube Goldberg machine to the hospital to provide much-needed entertainment and potential therapeutic benefits during difficult times.

Kindergarten and fourth-grade students used their physical science knowledge to inspire original prototype designs for the machine. Kindergarten students transferred their knowledge of pushes, pulls, and collisions into their prototype designs. Fourth-grade students utilized their knowledge of energy, energy transfer, and motion for their prototype designs.

High school students then reviewed 94 different designs from the elementary students. They thought critically, planned meticulously, and solved problems along the way. They analyzed cause-and-effect relationships, had to troubleshoot issues, and made adjustments to ensure the successful chain reaction.

The Rube Goldberg machine at the hospital continues to entertain and provide therapeutic benefits to children. Yet, it has limitations. It’s a single self-contained portable device that can serve only one child at a time. After collaborating further with our community partner, we understood their new needs: multiple games for many children.

During the 2022–23 school year, we helped establish the PBL experience titled  “What’s the Matter?” As with “Happy Little Accidents,” elementary students worked with high school students to inspire the designs and fabrications. The public product for this PBL included eight tabletop games (interactive tic-tac-toe and mini-catapult).

Due to the nature of the public product and the users, grade five and high school students were sensitive to the properties of matter, particulate nature of matter, and conservation of matter. They created games that prioritized the safety, comfort, accessibility, and emotional well-being of sick children in order to contribute to a positive and enriching play experience.

• Brainstorming and planning: Every PBL experience starts by thinking about our community partners and their needs. We align their needs with relevant standards and our content curriculum. We utilize Gold Standard Design Elements and think about how we’ll use the design thinking process with our students so they can develop empathy while creating something for someone .  
• Storylines and driving questions: Each experience launches with a Storyline , a narrative structure that engages students, contextualizes learning, stimulates creativity, and creates an emotional connection with the subject matter. Out of our storylines come our driving questions—open-ended, thought-provoking questions that guide the project and stimulate students’ inquiry. We typically use Tubric 2.0 to easily generate our driving questions.
• Turning points: Turning points serve as important checkpoints in the learning and the project’s progression. They help teachers and students track progress, stay organized, and ensure that they’re on track to achieve the project goals. With each turning point, students are using their content knowledge and creating elements that contribute to their public product. This ensures that the project is the learning, not a product that is only completed at the end. See our turning point template for What’s the Matter?
• Design thinking:  We employ design thinking at relevant turning points, which promotes a human-centered (empathy), iterative problem-solving process.

The Implementation

We delivered our instruction aligned to Gold Standard PBL Teaching Practices , New York State Science Learning Standards , and our curriculum. 

• Culture: Because of the scope of the projects, it was important to make sure we established a proper culture. All of the students had to collaborate within their classes and virtually with other classes, utilize empathy, be independent learners, and function within an inquiry-based learning environment. Additionally, they all had to collaborate with employees from our community partner. To achieve this, we utilized open dialogue, active listening, and empathy toward diverse perspectives with students. We also facilitated collaborative activities and group work that promoted teamwork and the exchange of ideas. Students worked in science teams; engaged in authentic, real-world science experiments; and had to consider multiple viewpoints in their work. 
• Sustained inquiry: We used student-generated need-to-know questions to support student inquiry. These provided a starting point for students and helped them delve deeper into the projects and guide the learning journey. As they progressed, students generated additional questions specific to each turning point. These need-to-know questions became refined and guided their inquiry and shaped their learning experiences. 
• Scaffold student learning: To support all students in reaching their PBL  goals, we employed a variety of lessons, tools, and instructional strategies at different points during the teaching and learning. We utilized the 5E Model, explicit direct instruction with a gradual release, small group lessons, and differentiation.  
• Assessment tools and strategies: We used a variety of assessment tools and strategies, including observations, science notebooks, investigations, feedback, and revision of designs, as well as digital tools. Using formative assessment methods throughout the projects provided a view of student progress and allowed for timely intervention.

The two PBL experiences described highlight the power of collaborative, empathy-driven projects to inspire and empower students. By embracing the principles of PBL and engaging with the community, students not only develop essential academic and social and emotional skills but also make a positive difference in the lives of others. These experiences serve as a testament to the transformative potential of PBL in creating empathetic, engaged, and community-minded learners.

Problem Solving Skills & Steps

When you truly want to fix a problem between two parties or multi parties the solution is communication.

For communication to be authentic, the parties involved must respect each other as equals and comprehend the words with empathy.

Empathy creates a connection that is the core of any truly resolved problem.

Problem Solving is a skill needed in all the roles we play in life. It could be in our personal and marital relationships, as parents of young children or children of aged parents, and even in our workspaces.

The human need to connect, be seen, understood, and belong is universal in all walks of life. Honoring that need is the basis of connection, cooperation, and ultimately peace.

Today we will talk about problem solving in three particular areas :

• Parents of School Going to Teen kids
• Personal Relationships

Before we get into Problem Solving let’s see the 4 skills essential to successful problem-solving.

4 Skills For Problem Solving

1. active listening (empathy).

Active listening is when your usually cheerful kid or partner comes back home with a long face and slouched body and you say :

” Looks like you had a rough day buddy, let’s have a cup of cocoa/tea and talk about it”.

And when they do say – you listen with all your attention and describe what they must be feeling. Validate and support those feelings.

” Oh, thats seems tough! “

” I understand, my darling – that must have made you so mad!”

” That is a terrible feeling my dear ….”

And the same goes for positive & happy news! When your kid comes bounding up & down to tell you about a recent victory – your level of enthusiasm in your response will make him/her feel seen or not seen.

For more information on how to actively listen and respond please read the article: What is the Key To Happy Relationships?

Active Listening is the key step to empathy . You need to truly listen to another to understand how they are feeling.

2. Perspective Taking (Keeping An Open Mind)

Another skill pertinent for problem-solving is cognitive empathy or understanding another’s point of view.

Putting yourself in another’s shoes and being open to immerse yourself in their world unlocks your mind to new perspectives. This is a valuable skill to understand the situation as to how your partner, co-worker, or family member sees it and maybe challenging your own belief or mindset.

To know more about the idea please read the article: The Art & Craft Of Conversation

3. Being Respectful (I Statements)

In a conversation, tone of voice is everything. When the people accept each other as equals in a conversation, what is said is accepted with understanding.

In such a setting, when you want to discuss an issue you have with someone it helps to lead with the ‘I statements’.

For example:

” I feel very angry when you do not finish your chores.”

” I would like it better if you can be an active listener and support me when I feel low.”

“I feel very tired doing so much cleaning in the house and would like some help.”

These statements refrain from pointing fingers and putting blame and shame on others. You are not assuming anything, just stating what it is to you and looking for a viable solution to your upsetting feelings.

4. Being Creative (Bricolage)

Issuing consequences is an age-old system to ‘discipline’ a child. But where consequences are one solution, problem-solving is many.

Using your joint creativity to find tailor-made creative solutions for your family or workplace is the goal of problem-solving. When you hit an impasse you need bricolage to get through.

Bricolage literally means bouncing back. In the modern sense, bricolage is the kind of inventiveness, creativity, or out-of-the-box thinking to improvise on the solution of a problem without the proper tools or materials. It is where the proverb comes true – ‘Necessity is the mother of all invention’.

It is also an important step in resilience building. To know more please read the article: Resilience & COVID – 19

So with empathy, an open mind, a respectful tone, and bricolage, we can come to solutions that make everyone happy.

Steps Of Problem Solving

Now that we have laid the groundwork for a conducive atmosphere for effective problem-solving let’s dive into the actual process.

Step 1: Identify the problem

The first step is to identify the main ideas or problems to be discussed. All members involved can use a whiteboard/paper/blackboard or any common medium to write down the topics to be discussed.

If holding weekly meetings, you can ask participants to write topics throughout the week to discuss on a designated day. Also, everyone can decide if each member gets to choose one or more topics per week.

Here is where we can use the ‘I statements’ to address our needs.

Step 2: Listening To Needs

All behavior is communication. All behavior arises from an unmet need. So listen actively to understand the need of the speaker so you can provide solutions that fulfill them. Here is where we need to address everyone else’s needs.

The above diagram may be child based but it is true for adults too. Many of us do have an inner child who has the exact same needs.

For a family conference, it could be paying attention to the tone of voice, body language and referring to the above chart to understand where is this need arising from.

For couples connection and safety are the basic needs. They are the stem of most issues and honoring them is the beginning of deep and satisfying relationships.

In the work environment, this would look like listening attentively to the speaker and asking follow-up questions to get a better understanding of their perspective.

The above diagram shows the competency model of iceberg theory where you have to listen to your co-worker or boss with these aspects in mind. And also when you try to think of a viable solution.

Step 3: Listing Out Ideas

Once all the problems have been addressed and needs to be understood it is time to brainstorm ideas as possible solutions.

While thinking of ideas ask follow up questions:

“Does this work for you?”

“Let’s start with this week and connect upon this for any further distress/renegotiation next week.”

” How does this sound? Do you think we can give it a try?”

Here is where we need to keep an open mind and be creative. Start from what you know and reach where you all want to be – together.

Write down all solutions and you can pick and choose parts, modify some areas so everyone’s needs are met, and even put the solution in steps. So you start small and address it weekly or monthly as things grow or change.

Step 4 – Choosing A Trial Solution

Once a current solution or plan is devised please write it on the drawing/white or blackboard. Preferably it can stay up there for the whole week. Even messaging or emailing the decided plan is an option.

These modes serve as a motivator and reminder to all concerned for the week ahead. Planning is one part but following it up with action is key.

Do not be disheartened if things do not go as planned. It may just mean you need to make amends. That is why a check back later date is important to write under all determined solutions.

For children, if they are breaking set rules then the need is not met. All you have to do is go back to the drawing board and listen more before devising another solution.

For co-workers, if they are not being able to maintain the designated plan then it needs some tweaking. They are not ready yet and you need to tailor it to everyone’s abilities. A true leader makes a plan according to the competencies of his/her teammates, not himself/herself.

For couples, if the fights continue means that they need to be more honest with their needs and vulnerable while sharing. Once the trust is there, long-lasting solutions and friendships follow.

To conclude, problem-solving without connection and empathy is like climbing a steep mountain. You keep on struggling and are usually filled with negative emotions.

Problem-solving with empathy is like a downhill joyride. Once there is a connection, there may be twists and turns but overall it’s filled with lots of fun & learning!

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Do You Understand the Problem You’re Trying to Solve?

To solve tough problems at work, first ask these questions.

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Problem solving skills are invaluable in any job. But all too often, we jump to find solutions to a problem without taking time to really understand the dilemma we face, according to Thomas Wedell-Wedellsborg , an expert in innovation and the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

In this episode, you’ll learn how to reframe tough problems by asking questions that reveal all the factors and assumptions that contribute to the situation. You’ll also learn why searching for just one root cause can be misleading.

Key episode topics include: leadership, decision making and problem solving, power and influence, business management.

HBR On Leadership curates the best case studies and conversations with the world’s top business and management experts, to help you unlock the best in those around you. New episodes every week.

• Listen to the original HBR IdeaCast episode: The Secret to Better Problem Solving (2016)
• Find more episodes of HBR IdeaCast
• Discover 100 years of Harvard Business Review articles, case studies, podcasts, and more at HBR.org .

HANNAH BATES: Welcome to HBR on Leadership , case studies and conversations with the world’s top business and management experts, hand-selected to help you unlock the best in those around you.

Problem solving skills are invaluable in any job. But even the most experienced among us can fall into the trap of solving the wrong problem.

Thomas Wedell-Wedellsborg says that all too often, we jump to find solutions to a problem – without taking time to really understand what we’re facing.

He’s an expert in innovation, and he’s the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

  In this episode, you’ll learn how to reframe tough problems, by asking questions that reveal all the factors and assumptions that contribute to the situation. You’ll also learn why searching for one root cause can be misleading. And you’ll learn how to use experimentation and rapid prototyping as problem-solving tools.

This episode originally aired on HBR IdeaCast in December 2016. Here it is.

SARAH GREEN CARMICHAEL: Welcome to the HBR IdeaCast from Harvard Business Review. I’m Sarah Green Carmichael.

Problem solving is popular. People put it on their resumes. Managers believe they excel at it. Companies count it as a key proficiency. We solve customers’ problems.

The problem is we often solve the wrong problems. Albert Einstein and Peter Drucker alike have discussed the difficulty of effective diagnosis. There are great frameworks for getting teams to attack true problems, but they’re often hard to do daily and on the fly. That’s where our guest comes in.

Thomas Wedell-Wedellsborg is a consultant who helps companies and managers reframe their problems so they can come up with an effective solution faster. He asks the question “Are You Solving The Right Problems?” in the January-February 2017 issue of Harvard Business Review. Thomas, thank you so much for coming on the HBR IdeaCast .

THOMAS WEDELL-WEDELLSBORG: Thanks for inviting me.

SARAH GREEN CARMICHAEL: So, I thought maybe we could start by talking about the problem of talking about problem reframing. What is that exactly?

THOMAS WEDELL-WEDELLSBORG: Basically, when people face a problem, they tend to jump into solution mode to rapidly, and very often that means that they don’t really understand, necessarily, the problem they’re trying to solve. And so, reframing is really a– at heart, it’s a method that helps you avoid that by taking a second to go in and ask two questions, basically saying, first of all, wait. What is the problem we’re trying to solve? And then crucially asking, is there a different way to think about what the problem actually is?

SARAH GREEN CARMICHAEL: So, I feel like so often when this comes up in meetings, you know, someone says that, and maybe they throw out the Einstein quote about you spend an hour of problem solving, you spend 55 minutes to find the problem. And then everyone else in the room kind of gets irritated. So, maybe just give us an example of maybe how this would work in practice in a way that would not, sort of, set people’s teeth on edge, like oh, here Sarah goes again, reframing the whole problem instead of just solving it.

THOMAS WEDELL-WEDELLSBORG: I mean, you’re bringing up something that’s, I think is crucial, which is to create legitimacy for the method. So, one of the reasons why I put out the article is to give people a tool to say actually, this thing is still important, and we need to do it. But I think the really critical thing in order to make this work in a meeting is actually to learn how to do it fast, because if you have the idea that you need to spend 30 minutes in a meeting delving deeply into the problem, I mean, that’s going to be uphill for most problems. So, the critical thing here is really to try to make it a practice you can implement very, very rapidly.

There’s an example that I would suggest memorizing. This is the example that I use to explain very rapidly what it is. And it’s basically, I call it the slow elevator problem. You imagine that you are the owner of an office building, and that your tenants are complaining that the elevator’s slow.

Now, if you take that problem framing for granted, you’re going to start thinking creatively around how do we make the elevator faster. Do we install a new motor? Do we have to buy a new lift somewhere?

The thing is, though, if you ask people who actually work with facilities management, well, they’re going to have a different solution for you, which is put up a mirror next to the elevator. That’s what happens is, of course, that people go oh, I’m busy. I’m busy. I’m– oh, a mirror. Oh, that’s beautiful.

And then they forget time. What’s interesting about that example is that the idea with a mirror is actually a solution to a different problem than the one you first proposed. And so, the whole idea here is once you get good at using reframing, you can quickly identify other aspects of the problem that might be much better to try to solve than the original one you found. It’s not necessarily that the first one is wrong. It’s just that there might be better problems out there to attack that we can, means we can do things much faster, cheaper, or better.

SARAH GREEN CARMICHAEL: So, in that example, I can understand how A, it’s probably expensive to make the elevator faster, so it’s much cheaper just to put up a mirror. And B, maybe the real problem people are actually feeling, even though they’re not articulating it right, is like, I hate waiting for the elevator. But if you let them sort of fix their hair or check their teeth, they’re suddenly distracted and don’t notice.

But if you have, this is sort of a pedestrian example, but say you have a roommate or a spouse who doesn’t clean up the kitchen. Facing that problem and not having your elegant solution already there to highlight the contrast between the perceived problem and the real problem, how would you take a problem like that and attack it using this method so that you can see what some of the other options might be?

THOMAS WEDELL-WEDELLSBORG: Right. So, I mean, let’s say it’s you who have that problem. I would go in and say, first of all, what would you say the problem is? Like, if you were to describe your view of the problem, what would that be?

SARAH GREEN CARMICHAEL: I hate cleaning the kitchen, and I want someone else to clean it up.

THOMAS WEDELL-WEDELLSBORG: OK. So, my first observation, you know, that somebody else might not necessarily be your spouse. So, already there, there’s an inbuilt assumption in your question around oh, it has to be my husband who does the cleaning. So, it might actually be worth, already there to say, is that really the only problem you have? That you hate cleaning the kitchen, and you want to avoid it? Or might there be something around, as well, getting a better relationship in terms of how you solve problems in general or establishing a better way to handle small problems when dealing with your spouse?

SARAH GREEN CARMICHAEL: Or maybe, now that I’m thinking that, maybe the problem is that you just can’t find the stuff in the kitchen when you need to find it.

THOMAS WEDELL-WEDELLSBORG: Right, and so that’s an example of a reframing, that actually why is it a problem that the kitchen is not clean? Is it only because you hate the act of cleaning, or does it actually mean that it just takes you a lot longer and gets a lot messier to actually use the kitchen, which is a different problem. The way you describe this problem now, is there anything that’s missing from that description?

SARAH GREEN CARMICHAEL: That is a really good question.

THOMAS WEDELL-WEDELLSBORG: Other, basically asking other factors that we are not talking about right now, and I say those because people tend to, when given a problem, they tend to delve deeper into the detail. What often is missing is actually an element outside of the initial description of the problem that might be really relevant to what’s going on. Like, why does the kitchen get messy in the first place? Is it something about the way you use it or your cooking habits? Is it because the neighbor’s kids, kind of, use it all the time?

There might, very often, there might be issues that you’re not really thinking about when you first describe the problem that actually has a big effect on it.

SARAH GREEN CARMICHAEL: I think at this point it would be helpful to maybe get another business example, and I’m wondering if you could tell us the story of the dog adoption problem.

THOMAS WEDELL-WEDELLSBORG: Yeah. This is a big problem in the US. If you work in the shelter industry, basically because dogs are so popular, more than 3 million dogs every year enter a shelter, and currently only about half of those actually find a new home and get adopted. And so, this is a problem that has persisted. It’s been, like, a structural problem for decades in this space. In the last three years, where people found new ways to address it.

So a woman called Lori Weise who runs a rescue organization in South LA, and she actually went in and challenged the very idea of what we were trying to do. She said, no, no. The problem we’re trying to solve is not about how to get more people to adopt dogs. It is about keeping the dogs with their first family so they never enter the shelter system in the first place.

In 2013, she started what’s called a Shelter Intervention Program that basically works like this. If a family comes and wants to hand over their dog, these are called owner surrenders. It’s about 30% of all dogs that come into a shelter. All they would do is go up and ask, if you could, would you like to keep your animal? And if they said yes, they would try to fix whatever helped them fix the problem, but that made them turn over this.

And sometimes that might be that they moved into a new building. The landlord required a deposit, and they simply didn’t have the money to put down a deposit. Or the dog might need a $10 rabies shot, but they didn’t know how to get access to a vet.

And so, by instigating that program, just in the first year, she took her, basically the amount of dollars they spent per animal they helped went from something like $85 down to around $60. Just an immediate impact, and her program now is being rolled out, is being supported by the ASPCA, which is one of the big animal welfare stations, and it’s being rolled out to various other places.

And I think what really struck me with that example was this was not dependent on having the internet. This was not, oh, we needed to have everybody mobile before we could come up with this. This, conceivably, we could have done 20 years ago. Only, it only happened when somebody, like in this case Lori, went in and actually rethought what the problem they were trying to solve was in the first place.

SARAH GREEN CARMICHAEL: So, what I also think is so interesting about that example is that when you talk about it, it doesn’t sound like the kind of thing that would have been thought of through other kinds of problem solving methods. There wasn’t necessarily an After Action Review or a 5 Whys exercise or a Six Sigma type intervention. I don’t want to throw those other methods under the bus, but how can you get such powerful results with such a very simple way of thinking about something?

THOMAS WEDELL-WEDELLSBORG: That was something that struck me as well. This, in a way, reframing and the idea of the problem diagnosis is important is something we’ve known for a long, long time. And we’ve actually have built some tools to help out. If you worked with us professionally, you are familiar with, like, Six Sigma, TRIZ, and so on. You mentioned 5 Whys. A root cause analysis is another one that a lot of people are familiar with.

Those are our good tools, and they’re definitely better than nothing. But what I notice when I work with the companies applying those was those tools tend to make you dig deeper into the first understanding of the problem we have. If it’s the elevator example, people start asking, well, is that the cable strength, or is the capacity of the elevator? That they kind of get caught by the details.

That, in a way, is a bad way to work on problems because it really assumes that there’s like a, you can almost hear it, a root cause. That you have to dig down and find the one true problem, and everything else was just symptoms. That’s a bad way to think about problems because problems tend to be multicausal.

There tend to be lots of causes or levers you can potentially press to address a problem. And if you think there’s only one, if that’s the right problem, that’s actually a dangerous way. And so I think that’s why, that this is a method I’ve worked with over the last five years, trying to basically refine how to make people better at this, and the key tends to be this thing about shifting out and saying, is there a totally different way of thinking about the problem versus getting too caught up in the mechanistic details of what happens.

SARAH GREEN CARMICHAEL: What about experimentation? Because that’s another method that’s become really popular with the rise of Lean Startup and lots of other innovation methodologies. Why wouldn’t it have worked to, say, experiment with many different types of fixing the dog adoption problem, and then just pick the one that works the best?

THOMAS WEDELL-WEDELLSBORG: You could say in the dog space, that’s what’s been going on. I mean, there is, in this industry and a lot of, it’s largely volunteer driven. People have experimented, and they found different ways of trying to cope. And that has definitely made the problem better. So, I wouldn’t say that experimentation is bad, quite the contrary. Rapid prototyping, quickly putting something out into the world and learning from it, that’s a fantastic way to learn more and to move forward.

My point is, though, that I feel we’ve come to rely too much on that. There’s like, if you look at the start up space, the wisdom is now just to put something quickly into the market, and then if it doesn’t work, pivot and just do more stuff. What reframing really is, I think of it as the cognitive counterpoint to prototyping. So, this is really a way of seeing very quickly, like not just working on the solution, but also working on our understanding of the problem and trying to see is there a different way to think about that.

If you only stick with experimentation, again, you tend to sometimes stay too much in the same space trying minute variations of something instead of taking a step back and saying, wait a minute. What is this telling us about what the real issue is?

SARAH GREEN CARMICHAEL: So, to go back to something that we touched on earlier, when we were talking about the completely hypothetical example of a spouse who does not clean the kitchen–

THOMAS WEDELL-WEDELLSBORG: Completely, completely hypothetical.

SARAH GREEN CARMICHAEL: Yes. For the record, my husband is a great kitchen cleaner.

You started asking me some questions that I could see immediately were helping me rethink that problem. Is that kind of the key, just having a checklist of questions to ask yourself? How do you really start to put this into practice?

THOMAS WEDELL-WEDELLSBORG: I think there are two steps in that. The first one is just to make yourself better at the method. Yes, you should kind of work with a checklist. In the article, I kind of outlined seven practices that you can use to do this.

But importantly, I would say you have to consider that as, basically, a set of training wheels. I think there’s a big, big danger in getting caught in a checklist. This is something I work with.

My co-author Paddy Miller, it’s one of his insights. That if you start giving people a checklist for things like this, they start following it. And that’s actually a problem, because what you really want them to do is start challenging their thinking.

So the way to handle this is to get some practice using it. Do use the checklist initially, but then try to step away from it and try to see if you can organically make– it’s almost a habit of mind. When you run into a colleague in the hallway and she has a problem and you have five minutes, like, delving in and just starting asking some of those questions and using your intuition to say, wait, how is she talking about this problem? And is there a question or two I can ask her about the problem that can help her rethink it?

SARAH GREEN CARMICHAEL: Well, that is also just a very different approach, because I think in that situation, most of us can’t go 30 seconds without jumping in and offering solutions.

THOMAS WEDELL-WEDELLSBORG: Very true. The drive toward solutions is very strong. And to be clear, I mean, there’s nothing wrong with that if the solutions work. So, many problems are just solved by oh, you know, oh, here’s the way to do that. Great.

But this is really a powerful method for those problems where either it’s something we’ve been banging our heads against tons of times without making progress, or when you need to come up with a really creative solution. When you’re facing a competitor with a much bigger budget, and you know, if you solve the same problem later, you’re not going to win. So, that basic idea of taking that approach to problems can often help you move forward in a different way than just like, oh, I have a solution.

I would say there’s also, there’s some interesting psychological stuff going on, right? Where you may have tried this, but if somebody tries to serve up a solution to a problem I have, I’m often resistant towards them. Kind if like, no, no, no, no, no, no. That solution is not going to work in my world. Whereas if you get them to discuss and analyze what the problem really is, you might actually dig something up.

Let’s go back to the kitchen example. One powerful question is just to say, what’s your own part in creating this problem? It’s very often, like, people, they describe problems as if it’s something that’s inflicted upon them from the external world, and they are innocent bystanders in that.

SARAH GREEN CARMICHAEL: Right, or crazy customers with unreasonable demands.

THOMAS WEDELL-WEDELLSBORG: Exactly, right. I don’t think I’ve ever met an agency or consultancy that didn’t, like, gossip about their customers. Oh, my god, they’re horrible. That, you know, classic thing, why don’t they want to take more risk? Well, risk is bad.

It’s their business that’s on the line, not the consultancy’s, right? So, absolutely, that’s one of the things when you step into a different mindset and kind of, wait. Oh yeah, maybe I actually am part of creating this problem in a sense, as well. That tends to open some new doors for you to move forward, in a way, with stuff that you may have been struggling with for years.

SARAH GREEN CARMICHAEL: So, we’ve surfaced a couple of questions that are useful. I’m curious to know, what are some of the other questions that you find yourself asking in these situations, given that you have made this sort of mental habit that you do? What are the questions that people seem to find really useful?

THOMAS WEDELL-WEDELLSBORG: One easy one is just to ask if there are any positive exceptions to the problem. So, was there day where your kitchen was actually spotlessly clean? And then asking, what was different about that day? Like, what happened there that didn’t happen the other days? That can very often point people towards a factor that they hadn’t considered previously.

SARAH GREEN CARMICHAEL: We got take-out.

THOMAS WEDELL-WEDELLSBORG: S,o that is your solution. Take-out from [INAUDIBLE]. That might have other problems.

Another good question, and this is a little bit more high level. It’s actually more making an observation about labeling how that person thinks about the problem. And what I mean with that is, we have problem categories in our head. So, if I say, let’s say that you describe a problem to me and say, well, we have a really great product and are, it’s much better than our previous product, but people aren’t buying it. I think we need to put more marketing dollars into this.

Now you can go in and say, that’s interesting. This sounds like you’re thinking of this as a communications problem. Is there a different way of thinking about that? Because you can almost tell how, when the second you say communications, there are some ideas about how do you solve a communications problem. Typically with more communication.

And what you might do is go in and suggest, well, have you considered that it might be, say, an incentive problem? Are there incentives on behalf of the purchasing manager at your clients that are obstructing you? Might there be incentive issues with your own sales force that makes them want to sell the old product instead of the new one?

So literally, just identifying what type of problem does this person think about, and is there different potential way of thinking about it? Might it be an emotional problem, a timing problem, an expectations management problem? Thinking about what label of what type of problem that person is kind of thinking as it of.

SARAH GREEN CARMICHAEL: That’s really interesting, too, because I think so many of us get requests for advice that we’re really not qualified to give. So, maybe the next time that happens, instead of muddying my way through, I will just ask some of those questions that we talked about instead.

THOMAS WEDELL-WEDELLSBORG: That sounds like a good idea.

SARAH GREEN CARMICHAEL: So, Thomas, this has really helped me reframe the way I think about a couple of problems in my own life, and I’m just wondering. I know you do this professionally, but is there a problem in your life that thinking this way has helped you solve?

THOMAS WEDELL-WEDELLSBORG: I’ve, of course, I’ve been swallowing my own medicine on this, too, and I think I have, well, maybe two different examples, and in one case somebody else did the reframing for me. But in one case, when I was younger, I often kind of struggled a little bit. I mean, this is my teenage years, kind of hanging out with my parents. I thought they were pretty annoying people. That’s not really fair, because they’re quite wonderful, but that’s what life is when you’re a teenager.

And one of the things that struck me, suddenly, and this was kind of the positive exception was, there was actually an evening where we really had a good time, and there wasn’t a conflict. And the core thing was, I wasn’t just seeing them in their old house where I grew up. It was, actually, we were at a restaurant. And it suddenly struck me that so much of the sometimes, kind of, a little bit, you love them but they’re annoying kind of dynamic, is tied to the place, is tied to the setting you are in.

And of course, if– you know, I live abroad now, if I visit my parents and I stay in my old bedroom, you know, my mother comes in and wants to wake me up in the morning. Stuff like that, right? And it just struck me so, so clearly that it’s– when I change this setting, if I go out and have dinner with them at a different place, that the dynamic, just that dynamic disappears.

SARAH GREEN CARMICHAEL: Well, Thomas, this has been really, really helpful. Thank you for talking with me today.

THOMAS WEDELL-WEDELLSBORG: Thank you, Sarah.  

HANNAH BATES: That was Thomas Wedell-Wedellsborg in conversation with Sarah Green Carmichael on the HBR IdeaCast. He’s an expert in problem solving and innovation, and he’s the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

We’ll be back next Wednesday with another hand-picked conversation about leadership from the Harvard Business Review. If you found this episode helpful, share it with your friends and colleagues, and follow our show on Apple Podcasts, Spotify, or wherever you get your podcasts. While you’re there, be sure to leave us a review.

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Promote Empathy Early: 5 Strategies That Work

Try these practical methods to promote empathic responding..

Posted October 9, 2019 | Reviewed by Kaja Perina

• The Importance of Empathy
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Following the introduction is a guest post by Dr. Lisa Dissinger, Lower School Psychologist at The Agnes Irwin School, an All-Girls Pre-K-12 Independent School in Rosemont, Pennsylvania.

It's a fall day, and you and a friend are at the neighborhood playground for a 2-year-old playdate. Your children are running around when one trips, falls, and begins to cry. It's clear from the soft landing that there are no major injuries, yet you are surprised to see that your child begins to hold her leg in the same place as her toddling friend. This small moment is what psychologists call empathic distress.

By the age of 2, children respond to others' distress with concerned attention and comforting behavior. But even before this age, there is evidence that human beings are wired for empathy and prosocial behaviors. Empathic responding begins in infancy; empathic comforting increases in the preschool years and becomes more complex as emotion regulation and cognitive functioning develops. Empathic responding is defined as the human capacity to see the world from others' perspectives, to delight in their joy or feel their pain echo within oneself, and to respond to others' needs with sensitivity and care (Stern, Botdorf, Cassidy & Riggins, 2019).

Read on to discover ways to promote empathy early.

Promote Empathy

Many studies have shown that young children are very sensitive to the feelings of others. In fact, empathy appears to be an inborn trait for most preschoolers, but it can be lost over time without thoughtful nurturing.

Empathy starts with putting yourself in someone else’s shoes, a key step in understanding perspectives that differ from your own. Like a muscle, empathy gets stronger and stronger with practice and age. This is the muscle that allows you to stand up for something and to help others in need.

Empathy also fuels connections. When a person learns to understand and share the feelings of another, this creates better relationships, closer friendships, and ultimately stronger communities.

As a school psychologist and parent coach, I often see empathy as one of the most important school supplies to stock up on at the beginning of the year. What can parents do to help fill their child's hypothetical empathy backpack? First and foremost, parents need to lead by example.

Parents have to model empathy and compassion, inside and outside of the family. Express your feelings clearly, simply, and in a non-threatening way. You can say, “I’m angry at you right now,” instead of yelling and losing control. When you demonstrate emotional honesty, your child learns to nurture those feelings in themselves.

Do not use physical punishment or withdrawal of affection as discipline techniques. Discipline should help a child feel safe and calm, rather than agitated or rejected. When you make a mistake and lose your temper, which will happen, practice the technique of rupture and repair. Make time to repair the hurt feelings in the relationship, because if a child feels rejected, it will be harder for them to show empathy toward others.

Make caring for others a part of your family life, as well. Get involved in a community project as a family and volunteer with your children. As they grow, have your children donate their toys, books, and/or clothing. This action encourages children to begin to “see” that others have needs too.

In order to empathize with others, young children must first recognize their own feelings and believe these emotions are accepted and understood. To build this emotional vocabulary, parents need to use feeling words like “sad,” “scared,” “excited,” and “frustrated” on a daily basis, even when the child is very young. Parents can use bibliotherapy (fancy word for reading books to children on specific topics) to build a child’s emotional vocabulary and empathy. Books like Today I Feel Silly and Other Moods That Make My Day by Jamie Lee Curtis and How Do I Stand in Your Shoes? by Dr. Susan DeBell are helpful.

When your child expresses their feelings, just listen. Do not try to shut your child’s feelings down. Think of yourself as their emotional container. Reflect back what you think they are feeling. Let them know all feelings are OK. Give them appropriate ways to express these feelings, like “Use your words, not your hands”; “Take some time and come back when you are ready”; or “Show me how you feel in a drawing.”

Another way to build empathy is to use a positive parenting approach that promotes problem solving and empathy building. Dr. Ross Greene articulates this approach in his 2016 book Raising Human Beings: Creating A Collaborative Partnership With Your Child. In his book, Dr. Ross explains how to cultivate a better parent-child relationship while also nurturing empathy, honesty, resilience , and independence.

Dr. Ross sees parents as problem-solving partners. Help kids solve problems collaboratively, not unilaterally. The three steps in this problem-solving approach are the empathy step, “define adult concerns” step, and the invitation step.

The empathy step focuses on understanding your child’s perspective or point of view by listening to the problem (no teaching or preaching here!). This empathy step of gathering information begins with words like “I’ve noticed that…” and ends with “What’s up?” For example, “I’ve noticed you and your sister have not been getting along lately. What’s up?” After completing the empathy step, a parent can voice their own concerns and point of view. This is the “define adult concerns” step. Finally, the invitation step encourages the parent to work with their child toward a realistic and mutually satisfactory solution.

If a child is struggling to develop empathy, the parents may need to more directly instruct their child to follow a five-step process.

Watch and listen: What is the other person saying? What is their body language telling you?

Remember: When did you feel the same way?

Imagine: How does the other person feel? How would you feel in that situation

Ask: Ask what the person is feeling.

Show: Show you care with words and actions

Post these five steps on your refrigerator or in the child’s room as a visual reminder. Continue to teach the five-step process, sometimes for several years, until the child has internalized the steps.

Finally, encourage your child to become friends with others who are different. This is the simplest way to develop empathy. We do not always need to see the world in the same way as others, but we can promote prosocial behaviors that value the dignity and worth of all human beings.

Greene, R. (2017). Raising Human Beings: Creating a Collaborative Partnership with Your Child. New York: New York. Scribner.

Stern, J. A., Botdorf, M., Cassidy, J., & Riggins, T. (2019). Empathic responding and hippocampal volume in young children. Developmental Psychology, 55, 1908–1920. http://dx.doi.org/10.1037/dev0000684

Elizabeth Elizardi is an educational leader and Positive Psychology practitioner with passionate interest in the intersection of Positive Psychology and Parenting.

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

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

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

Embrace Uncertainty

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

Seek Diverse Perspectives

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

Simplify the Complex

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

Adopt a Growth Mindset

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

Question Assumptions

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

Think in Reverse

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

Embrace Failure as a Teacher

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

Harness the Power of Daydreaming

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

Practice Empathy

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

Set Clear Goals

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

Stay Curious

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

Use Analogies

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

Focus on the Process, Not Just the Outcome

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

Prioritize Effectively

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

Build Resilience

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

Cultivate Patience

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

Practice Reflection

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

Encourage Collaboration

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

Visualize Success

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

Adapt and Evolve

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

Maintain a Positive Attitude

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

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• Open access
• Published: 10 April 2024

A hybrid particle swarm optimization algorithm for solving engineering problem

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

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

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• Computational science
• Mechanical engineering

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

Introduction

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

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

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

Literature review

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

Metaheuristic algorithms

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

Improved PSO algorithms

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

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

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

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

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

Particle swarm optimization (PSO)

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

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

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

Improved particle swarm optimization algorithm

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

Improvement strategies

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Spiral updating position.

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

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

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

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

The main procedure of NDWPSO.

Comparing the distribution of inertia weight parameters

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

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

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

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

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

Experiment and discussion

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

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

Experiments on benchmark functions between NDWPSO, and other PSO variants

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Evolution curve of NDWPSO and other PSO algorithms for f23.

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

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

Comparison experiments between NDWPSO and other intelligent algorithms

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Evolution curve of NDWPSO and other algorithms for f23.

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

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

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

Experiments on classical engineering problems

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

Welded beam design

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

Welded beam design.

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

Pressure vessel design

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

Pressure vessel design.

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

Three-bar truss design

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

Three-bar truss design.

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

Conclusions and future works

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

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

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

Data availability

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

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Acknowledgements

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

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School of Mechanical and Automotive Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan, 250353, China

Jinwei Qiao, Guangyuan Wang, Zhi Yang, Jun Chen & Pengbo Liu

Shandong Institute of Mechanical Design and Research, Jinan, 250353, China

School of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

Xiaochuan Luo

Fushun Supervision Inspection Institute for Special Equipment, Fushun, 113000, China

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Z.Y., J.Q., and G.W. wrote the main manuscript text and prepared all figures and tables. J.C., P.L., K.L., and X.L. were responsible for the data curation and software. All authors reviewed the manuscript.

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Qiao, J., Wang, G., Yang, Z. et al. A hybrid particle swarm optimization algorithm for solving engineering problem. Sci Rep 14 , 8357 (2024). https://doi.org/10.1038/s41598-024-59034-2

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DOI : https://doi.org/10.1038/s41598-024-59034-2

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Title: chatglm-math: improving math problem-solving in large language models with a self-critique pipeline.

Abstract: Large language models (LLMs) have shown excellent mastering of human language, but still struggle in real-world applications that require mathematical problem-solving. While many strategies and datasets to enhance LLMs' mathematics are developed, it remains a challenge to simultaneously maintain and improve both language and mathematical capabilities in deployed LLM this http URL this work, we tailor the Self-Critique pipeline, which addresses the challenge in the feedback learning stage of LLM alignment. We first train a general Math-Critique model from the LLM itself to provide feedback signals. Then, we sequentially employ rejective fine-tuning and direct preference optimization over the LLM's own generations for data collection. Based on ChatGLM3-32B, we conduct a series of experiments on both academic and our newly created challenging dataset, MathUserEval. Results show that our pipeline significantly enhances the LLM's mathematical problem-solving while still improving its language ability, outperforming LLMs that could be two times larger. Related techniques have been deployed to ChatGLM\footnote{\url{ this https URL }}, an online serving LLM. Related evaluation dataset and scripts are released at \url{ this https URL }.

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