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What Are Heuristics?

These mental shortcuts can help people make decisions more efficiently

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

Steven Gans, MD is board-certified in psychiatry and is an active supervisor, teacher, and mentor at Massachusetts General Hospital.

Verywell / Cindy Chung 

• History and Origins
• Heuristics vs. Algorithms
• Heuristics and Bias

How to Make Better Decisions

Heuristics are mental shortcuts that allow people to solve problems and make judgments quickly and efficiently. These rule-of-thumb strategies shorten decision-making time and allow people to function without constantly stopping to think about their next course of action.

However, there are both benefits and drawbacks of heuristics. While heuristics are helpful in many situations, they can also lead to  cognitive biases . Becoming aware of this might help you make better and more accurate decisions.

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The History and Origins of Heuristics

Nobel-prize winning economist and cognitive psychologist Herbert Simon originally introduced the concept of heuristics in psychology in the 1950s. He suggested that while people strive to make rational choices, human judgment is subject to cognitive limitations. Purely rational decisions would involve weighing all the potential costs and possible benefits of every alternative.

But people are limited by the amount of time they have to make a choice as well as the amount of information they have at their disposal. Other factors such as overall intelligence and accuracy of perceptions also influence the decision-making process.

During the 1970s, psychologists Amos Tversky and Daniel Kahneman presented their research on cognitive biases. They proposed that these biases influence how people think and the judgments people make.

As a result of these limitations, we are forced to rely on mental shortcuts to help us make sense of the world. Simon's research demonstrated that humans were limited in their ability to make rational decisions, but it was Tversky and Kahneman's work that introduced the study of heuristics and the specific ways of thinking that people rely on to simplify the decision-making process.

How Heuristics Are Used

Heuristics play important roles in both  problem-solving  and  decision-making , as we often turn to these mental shortcuts when we need a quick solution.

Here are a few different theories from psychologists about why we rely on heuristics.

• Attribute substitution : People substitute simpler but related questions in place of more complex and difficult questions.
• Effort reduction : People use heuristics as a type of cognitive laziness to reduce the mental effort required to make choices and decisions.
• Fast and frugal : People use heuristics because they can be fast and correct in certain contexts. Some theories argue that heuristics are actually more accurate than they are biased.

In order to cope with the tremendous amount of information we encounter and to speed up the decision-making process, our brains rely on these mental strategies to simplify things so we don't have to spend endless amounts of time analyzing every detail.

You probably make hundreds or even thousands of decisions every day. What should you have for breakfast? What should you wear today? Should you drive or take the bus? Fortunately, heuristics allow you to make such decisions with relative ease and without a great deal of agonizing.

There are many heuristics examples in everyday life. When trying to decide if you should drive or ride the bus to work, for instance, you might remember that there is road construction along the bus route. You realize that this might slow the bus and cause you to be late for work. So you leave earlier and drive to work on an alternate route.

Heuristics allow you to think through the possible outcomes quickly and arrive at a solution.

Are Heuristics Good or Bad?

Heuristics aren't inherently good or bad, but there are pros and cons to using them to make decisions. While they can help us figure out a solution to a problem faster, they can also lead to inaccurate judgments about other people or situations.

Types of Heuristics

There are many different kinds of heuristics. While each type plays a role in decision-making, they occur during different contexts. Understanding the types can help you better understand which one you are using and when.

Availability

The availability heuristic  involves making decisions based upon how easy it is to bring something to mind. When you are trying to make a decision, you might quickly remember a number of relevant examples. Since these are more readily available in your memory, you will likely judge these outcomes as being more common or frequently occurring.

For example, if you are thinking of flying and suddenly think of a number of recent airline accidents, you might feel like air travel is too dangerous and decide to travel by car instead. Because those examples of air disasters came to mind so easily, the availability heuristic leads you to think that plane crashes are more common than they really are.

Familiarity

The familiarity heuristic refers to how people tend to have more favorable opinions of things, people, or places they've experienced before as opposed to new ones. In fact, given two options, people may choose something they're more familiar with even if the new option provides more benefits.

Representativeness

The representativeness heuristic  involves making a decision by comparing the present situation to the most representative mental prototype. When you are trying to decide if someone is trustworthy, you might compare aspects of the individual to other mental examples you hold.

A soft-spoken older woman might remind you of your grandmother, so you might immediately assume that she is kind, gentle, and trustworthy. However, this is an example of a heuristic bias, as you can't know someone trustworthy based on their age alone.

The affect heuristic involves making choices that are influenced by the emotions that an individual is experiencing at that moment. For example, research has shown that people are more likely to see decisions as having benefits and lower risks when they are in a positive mood. Negative emotions, on the other hand, lead people to focus on the potential downsides of a decision rather than the possible benefits.

The anchoring bias involves the tendency to be overly influenced by the first bit of information we hear or learn. This can make it more difficult to consider other factors and lead to poor choices. For example, anchoring bias can influence how much you are willing to pay for something, causing you to jump at the first offer without shopping around for a better deal.

Scarcity is a principle in heuristics in which we view things that are scarce or less available to us as inherently more valuable. The scarcity heuristic is one often used by marketers to influence people to buy certain products. This is why you'll often see signs that advertise "limited time only" or that tell you to "get yours while supplies last."

Trial and Error

Trial and error is another type of heuristic in which people use a number of different strategies to solve something until they find what works. Examples of this type of heuristic are evident in everyday life. People use trial and error when they're playing video games, finding the fastest driving route to work, and learning to ride a bike (or learning any new skill).

Difference Between Heuristics and Algorithms

Though the terms are often confused, heuristics and algorithms are two distinct terms in psychology.

Algorithms are step-by-step instructions that lead to predictable, reliable outcomes; whereas heuristics are mental shortcuts that are basically best guesses. Algorithms always lead to accurate outcomes, whereas, heuristics do not.

Examples of algorithms include instructions for how to put together a piece of furniture or a recipe for cooking a certain dish. Health professionals also create algorithms or processes to follow in order to determine what type of treatment to use on a patient.

How Heuristics Can Lead to Bias

While heuristics can help us solve problems and speed up our decision-making process, they can introduce errors. As in the examples above, heuristics can lead to inaccurate judgments about how commonly things occur and about how representative certain things may be.

Just because something has worked in the past does not mean that it will work again, and relying on a heuristic can make it difficult to see alternative solutions or come up with new ideas.

Heuristics can also contribute to stereotypes and  prejudice . Because people use mental shortcuts to classify and categorize people, they often overlook more relevant information and create stereotyped categorizations that are not in tune with reality.

While heuristics can be a useful tool, there are ways you can improve your decision-making and avoid cognitive bias at the same time.

We are more likely to make an error in judgment if we are trying to make a decision quickly or are under pressure to do so. Whenever possible, take a few deep breaths . Do something to distract yourself from the decision at hand. When you return to it, you may find you have a fresh perspective, or notice something you didn't before.

Identify the Goal

We tend to focus automatically on what works for us and make decisions that serve our best interest. But take a moment to know what you're trying to achieve. Are there other people who will be affected by this decision? What's best for them? Is there a common goal that can be achieved that will serve all parties?

Process Your Emotions

Fast decision-making is often influenced by emotions from past experiences that bubble to the surface. Is your decision based on facts or emotions? While emotions can be helpful, they may affect decisions in a negative way if they prevent us from seeing the full picture.

Recognize All-or-Nothing Thinking

When making a decision, it's a common tendency to believe you have to pick a single, well-defined path, and there's no going back. In reality, this often isn't the case.

Sometimes there are compromises involving two choices, or a third or fourth option that we didn't even think of at first. Try to recognize the nuances and possibilities of all choices involved, instead of using all-or-nothing thinking .

Rachlin H. Rational thought and rational behavior: A review of bounded rationality: The adaptive toolbox . J Exp Anal Behav . 2003;79(3):409–412. doi:10.1901/jeab.2003.79-409

Shah AK, Oppenheimer DM. Heuristics made easy: An effort-reduction framework . Psychol Bull. 2008;134(2):207-22. doi:10.1037/0033-2909.134.2.207

Marewski JN, Gigerenzer G. Heuristic decision making in medicine .  Dialogues Clin Neurosci . 2012;14(1):77–89. PMID: 22577307

Schwikert SR, Curran T. Familiarity and recollection in heuristic decision making .  J Exp Psychol Gen . 2014;143(6):2341-2365. doi:10.1037/xge0000024

Finucane M, Alhakami A, Slovic P, Johnson S. The affect heuristic in judgments of risks and benefits . J Behav Decis Mak . 2000; 13(1):1-17. doi:10.1002/(SICI)1099-0771(200001/03)13:1<1::AID-BDM333>3.0.CO;2-S

Cheung TT, Kroese FM, Fennis BM, De Ridder DT. Put a limit on it: The protective effects of scarcity heuristics when self-control is low . Health Psychol Open . 2015;2(2):2055102915615046. doi:10.1177/2055102915615046

Mohr H, Zwosta K, Markovic D, Bitzer S, Wolfensteller U, Ruge H. Deterministic response strategies in a trial-and-error learning task . Inman C, ed. PLoS Comput Biol. 2018;14(11):e1006621. doi:10.1371/journal.pcbi.1006621

Lang JM, Ford JD, Fitzgerald MM.  An algorithm for determining use of trauma-focused cognitive-behavioral therapy .  Psychotherapy   (Chic) . 2010;47(4):554-69. doi:10.1037/a0021184

Bigler RS, Clark C. The inherence heuristic: A key theoretical addition to understanding social stereotyping and prejudice. Behav Brain Sci . 2014;37(5):483-4. doi:10.1017/S0140525X1300366X

del Campo C, Pauser S, Steiner E, et al.  Decision making styles and the use of heuristics in decision making .  J Bus Econ.  2016;86:389–412. doi:10.1007/s11573-016-0811-y

Marewski JN, Gigerenzer G. Heuristic decision making in medicine .  Dialogues Clin Neurosci . 2012;14(1):77-89. doi:10.31887/DCNS.2012.14.1/jmarewski

Zheng Y, Yang Z, Jin C, Qi Y, Liu X. The influence of emotion on fairness-related decision making: A critical review of theories and evidence .  Front Psychol . 2017;8:1592. doi:10.3389/fpsyg.2017.01592

Bazerman MH. Judgment and decision making. In: Biswas-Diener R, Diener E, eds.,  Noba Textbook Series: Psychology.  DEF Publishers.

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

Heuristics: Definition, Examples, And How They Work

Benjamin Frimodig

Science Expert

B.A., History and Science, Harvard University

Ben Frimodig is a 2021 graduate of Harvard College, where he studied the History of Science.

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Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

On This Page:

Every day our brains must process and respond to thousands of problems, both large and small, at a moment’s notice. It might even be overwhelming to consider the sheer volume of complex problems we regularly face in need of a quick solution.

While one might wish there was time to methodically and thoughtfully evaluate the fine details of our everyday tasks, the cognitive demands of daily life often make such processing logistically impossible.

Therefore, the brain must develop reliable shortcuts to keep up with the stimulus-rich environments we inhabit. Psychologists refer to these efficient problem-solving techniques as heuristics.

Heuristics can be thought of as general cognitive frameworks humans rely on regularly to reach a solution quickly.

For example, if a student needs to decide what subject she will study at university, her intuition will likely be drawn toward the path that she envisions as most satisfying, practical, and interesting.

She may also think back on her strengths and weaknesses in secondary school or perhaps even write out a pros and cons list to facilitate her choice.

It’s important to note that these heuristics broadly apply to everyday problems, produce sound solutions, and helps simplify otherwise complicated mental tasks. These are the three defining features of a heuristic.

While the concept of heuristics dates back to Ancient Greece (the term is derived from the Greek word for “to discover”), most of the information known today on the subject comes from prominent twentieth-century social scientists.

Herbert Simon’s study of a notion he called “bounded rationality” focused on decision-making under restrictive cognitive conditions, such as limited time and information.

This concept of optimizing an inherently imperfect analysis frames the contemporary study of heuristics and leads many to credit Simon as a foundational figure in the field.

Kahneman’s Theory of Decision Making

The immense contributions of psychologist Daniel Kahneman to our understanding of cognitive problem-solving deserve special attention.

As context for his theory, Kahneman put forward the estimate that an individual makes around 35,000 decisions each day! To reach these resolutions, the mind relies on either “fast” or “slow” thinking.

The fast thinking pathway (system 1) operates mostly unconsciously and aims to reach reliable decisions with as minimal cognitive strain as possible.

While system 1 relies on broad observations and quick evaluative techniques (heuristics!), system 2 (slow thinking) requires conscious, continuous attention to carefully assess the details of a given problem and logically reach a solution.

Given the sheer volume of daily decisions, it’s no surprise that around 98% of problem-solving uses system 1.

Thus, it is crucial that the human mind develops a toolbox of effective, efficient heuristics to support this fast-thinking pathway.

Heuristics vs. Algorithms

Those who’ve studied the psychology of decision-making might notice similarities between heuristics and algorithms. However, remember that these are two distinct modes of cognition.

Heuristics are methods or strategies which often lead to problem solutions but are not guaranteed to succeed.

They can be distinguished from algorithms, which are methods or procedures that will always produce a solution sooner or later.

An algorithm is a step-by-step procedure that can be reliably used to solve a specific problem. While the concept of an algorithm is most commonly used in reference to technology and mathematics, our brains rely on algorithms every day to resolve issues (Kahneman, 2011).

The important thing to remember is that algorithms are a set of mental instructions unique to specific situations, while heuristics are general rules of thumb that can help the mind process and overcome various obstacles.

For example, if you are thoughtfully reading every line of this article, you are using an algorithm.

On the other hand, if you are quickly skimming each section for important information or perhaps focusing only on sections you don’t already understand, you are using a heuristic!

Why Heuristics Are Used

Heuristics usually occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind at the same moment

When studying heuristics, keep in mind both the benefits and unavoidable drawbacks of their application. The ubiquity of these techniques in human society makes such weaknesses especially worthy of evaluation.

More specifically, in expediting decision-making processes, heuristics also predispose us to a number of cognitive biases .

A cognitive bias is an incorrect but pervasive judgment derived from an illogical pattern of cognition. In simple terms, a cognitive bias occurs when one internalizes a subjective perception as a reliable and objective truth.

Heuristics are reliable but imperfect; In the application of broad decision-making “shortcuts” to guide one’s response to specific situations, occasional errors are both inevitable and have the potential to catalyze persistent mistakes.

For example, consider the risks of faulty applications of the representative heuristic discussed above. While the technique encourages one to assign situations into broad categories based on superficial characteristics and one’s past experiences for the sake of cognitive expediency, such thinking is also the basis of stereotypes and discrimination.

In practice, these errors result in the disproportionate favoring of one group and/or the oppression of other groups within a given society.

Indeed, the most impactful research relating to heuristics often centers on the connection between them and systematic discrimination.

The tradeoff between thoughtful rationality and cognitive efficiency encompasses both the benefits and pitfalls of heuristics and represents a foundational concept in psychological research.

When learning about heuristics, keep in mind their relevance to all areas of human interaction. After all, the study of social psychology is intrinsically interdisciplinary.

Many of the most important studies on heuristics relate to flawed decision-making processes in high-stakes fields like law, medicine, and politics.

Researchers often draw on a distinct set of already established heuristics in their analysis. While dozens of unique heuristics have been observed, brief descriptions of those most central to the field are included below:

Availability Heuristic

The availability heuristic describes the tendency to make choices based on information that comes to mind readily.

For example, children of divorced parents are more likely to have pessimistic views towards marriage as adults.

Of important note, this heuristic can also involve assigning more importance to more recently learned information, largely due to the easier recall of such information.

Representativeness Heuristic

This technique allows one to quickly assign probabilities to and predict the outcome of new scenarios using psychological prototypes derived from past experiences.

For example, juries are less likely to convict individuals who are well-groomed and wearing formal attire (under the assumption that stylish, well-kempt individuals typically do not commit crimes).

This is one of the most studied heuristics by social psychologists for its relevance to the development of stereotypes.

Scarcity Heuristic

This method of decision-making is predicated on the perception of less abundant, rarer items as inherently more valuable than more abundant items.

We rely on the scarcity heuristic when we must make a fast selection with incomplete information. For example, a student deciding between two universities may be drawn toward the option with the lower acceptance rate, assuming that this exclusivity indicates a more desirable experience.

The concept of scarcity is central to behavioral economists’ study of consumer behavior (a field that evaluates economics through the lens of human psychology).

Trial and Error

This is the most basic and perhaps frequently cited heuristic. Trial and error can be used to solve a problem that possesses a discrete number of possible solutions and involves simply attempting each possible option until the correct solution is identified.

For example, if an individual was putting together a jigsaw puzzle, he or she would try multiple pieces until locating a proper fit.

This technique is commonly taught in introductory psychology courses due to its simple representation of the central purpose of heuristics: the use of reliable problem-solving frameworks to reduce cognitive load.

Anchoring and Adjustment Heuristic

Anchoring refers to the tendency to formulate expectations relating to new scenarios relative to an already ingrained piece of information.

Put simply, this anchoring one to form reasonable estimations around uncertainties. For example, if asked to estimate the number of days in a year on Mars, many people would first call to mind the fact the Earth’s year is 365 days (the “anchor”) and adjust accordingly.

This tendency can also help explain the observation that ingrained information often hinders the learning of new information, a concept known as retroactive inhibition.

Familiarity Heuristic

This technique can be used to guide actions in cognitively demanding situations by simply reverting to previous behaviors successfully utilized under similar circumstances.

The familiarity heuristic is most useful in unfamiliar, stressful environments.

For example, a job seeker might recall behavioral standards in other high-stakes situations from her past (perhaps an important presentation at university) to guide her behavior in a job interview.

Many psychologists interpret this technique as a slightly more specific variation of the availability heuristic.

How to Make Better Decisions

Heuristics are ingrained cognitive processes utilized by all humans and can lead to various biases.

Both of these statements are established facts. However, this does not mean that the biases that heuristics produce are unavoidable. As the wide-ranging impacts of such biases on societal institutions have become a popular research topic, psychologists have emphasized techniques for reaching more sound, thoughtful and fair decisions in our daily lives.

Ironically, many of these techniques are themselves heuristics!

To focus on the key details of a given problem, one might create a mental list of explicit goals and values. To clearly identify the impacts of choice, one should imagine its impacts one year in the future and from the perspective of all parties involved.

Most importantly, one must gain a mindful understanding of the problem-solving techniques used by our minds and the common mistakes that result. Mindfulness of these flawed yet persistent pathways allows one to quickly identify and remedy the biases (or otherwise flawed thinking) they tend to create!

Further Information

• Shah, A. K., & Oppenheimer, D. M. (2008). Heuristics made easy: an effort-reduction framework. Psychological bulletin, 134(2), 207.
• Marewski, J. N., & Gigerenzer, G. (2012). Heuristic decision making in medicine. Dialogues in clinical neuroscience, 14(1), 77.
• Del Campo, C., Pauser, S., Steiner, E., & Vetschera, R. (2016). Decision making styles and the use of heuristics in decision making. Journal of Business Economics, 86(4), 389-412.

What is a heuristic in psychology?

A heuristic in psychology is a mental shortcut or rule of thumb that simplifies decision-making and problem-solving. Heuristics often speed up the process of finding a satisfactory solution, but they can also lead to cognitive biases.

Bobadilla-Suarez, S., & Love, B. C. (2017, May 29). Fast or Frugal, but Not Both: Decision Heuristics Under Time Pressure. Journal of Experimental Psychology: Learning, Memory, and Cognition .

Bowes, S. M., Ammirati, R. J., Costello, T. H., Basterfield, C., & Lilienfeld, S. O. (2020). Cognitive biases, heuristics, and logical fallacies in clinical practice: A brief field guide for practicing clinicians and supervisors. Professional Psychology: Research and Practice, 51 (5), 435–445.

Dietrich, C. (2010). “Decision Making: Factors that Influence Decision Making, Heuristics Used, and Decision Outcomes.” Inquiries Journal/Student Pulse, 2(02).

Groenewegen, A. (2021, September 1). Kahneman Fast and slow thinking: System 1 and 2 explained by Sue. SUE Behavioral Design. Retrieved March 26, 2022, from https://suebehaviouraldesign.com/kahneman-fast-slow-thinking/

Kahneman, D., Lovallo, D., & Sibony, O. (2011). Before you make that big decision .

Kahneman, D. (2011). Thinking, fast and slow . Macmillan.

Pratkanis, A. (1989). The cognitive representation of attitudes. In A. R. Pratkanis, S. J. Breckler, & A. G. Greenwald (Eds.), Attitude structure and function (pp. 71–98). Hillsdale, NJ: Erlbaum.

Simon, H.A., 1956. Rational choice and the structure of the environment. Psychological Review .

Tversky, A., & Kahneman, D. (1974). Judgment under Uncertainty: Heuristics and Biases. Science, 185 (4157), 1124–1131.

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Heuristic Method

Heuristic Method: this article explains the concept of the Heuristic Method , developed by George Pólya in a practical way. After reading it, you will understand the basics of this powerful Problem Solving tool.

What is the Heuristic Method?

A heuristic method is an approach to finding a solution to a problem that originates from the ancient Greek word ‘eurisko’, meaning to ‘find’, ‘search’ or ‘discover’. It is about using a practical method that doesn’t necessarily need to be perfect. Heuristic methods speed up the process of reaching a satisfactory solution.

Previous experiences with comparable problems are used that can concern problem situations for people, machines or abstract issues. One of the founders of heuristics is the Hungarian mathematician György (George) Pólya , who published a book about the subject in 1945 called ‘How to Solve It’. He used four principles that form the basis for problem solving.

Heuristic method: Four principles

Pólya describes the following four principles in his book:

• try to understand the problem
• make a plan
• carry out this plan
• evaluate and adapt

If this sequence doesn’t lead to the right solution, Pólya advises to first look for a simpler problem.

A solution may potentially be found by first looking at a similar problem that was possible to solve. With this experience, it’s possible to look at the current problem in another way.

First principle of the heuristic method: understand the problem

It’s more difficult than it seems, because it seems obvious. In truth, people are hindered when it comes to finding an initially suitable approach to the problem.

It can help to draw the problem and to look at it from another angle. What is the problem, what is happening, can the problem be explained in other words, is there enough information available, etc. Such questions can help with the first evaluation of a problem issue.

Second principle of the heuristic method: make a plan

There are many ways to solve problems. This section is about choosing the right strategy that best fits the problem at hand. The reversed ‘working backwards’ can help with this; people assume to have a solution and use this as a starting point to work towards the problem.

It can also be useful to make an overview of the possibilities, delete some of them immediately, work with comparisons, or to apply symmetry. Creativity comes into play here and will improve the ability to judge.

Third principle of the heuristic method: carry out the plan

Once a strategy has been chosen, the plan can quickly be implemented. However, it is important to pay attention to time and be patient, because the solution will not simply appear.

If the plan doesn’t go anywhere, the advice is to throw it overboard and find a new way.

Fourth principle of the heuristic method: evaluate and adapt

Take the time to carefully consider and reflect upon the work that’s already been done. The things that are going well should be maintained, those leading to a lesser solution, should be adjusted. Some things simply work, while others simply don’t.

There are many different heuristic methods, which Pólya also used. The most well-known heuristics are found below:

1. Dividing technique

The original problem is divided into smaller sub-problems that can be solved more easily. These sub-problems can be linked to each other and combined, which will eventually lead to the solving of the original problem.

2. Inductive method

This involves a problem that has already been solved, but is smaller than the original problem. Generalisation can be derived from the previously solved problem, which can help in solving the bigger, original problem.

3. Reduction method

Because problems are often larger than assumed and deal with different causes and factors, this method sets limits for the problem in advance. This reduces the leeway of the original problem, making it easier to solve.

4. Constructive method

This is about working on the problem step by step. The smallest solution is seen as a victory and from that point consecutive steps are taken. This way, the best choices keep being made, which will eventually lead to a successful end result.

5. Local search method

This is about the search for the most attainable solution to the problem. This solution is improved along the way. This method ends when improvement is no longer possible.

Exact solutions versus the heuristic method

The heuristic approach is a mathmatical method with which proof of a good solution to a problem is delivered. There is a large number of different problems that could use good solutions. When the processing speed is equally as important as the obtained solution, we speak of a heuristic method.

The Heuristic Method only tries to find a good, but not necessarily optimal, solution. This is what differentiates heuristics from exact solution methods, which are about finding the optimal solution to a problem. However, that’s very time consuming, which is why a heuristic method may prove preferable. This is much quicker and more flexible than an exact method, but does have to satisfy a number of criteria.

It’s Your Turn

What do you think? Is the Heuristic Method applicable in your personal or professional environment? Do you recognize the practical explanation or do you have more suggestions? What are your success factors for solving problems

Share your experience and knowledge in the comments box below.

More information

• Groner, R., Groner, M., & Bischof, W. F. (2014). Methods of heuristics . Routledge .
• Newell, A. (1983). The heuristic of George Polya and its relation to artificial intelligence . Methods of heuristics, 195-243.
• Polya, G. (2014, 1945). How to solve it: A new aspect of mathematical method . Princeton university press .

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Published on: 29/05/2018 | Last update: 04/03/2022

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Patty Mulder

Patty Mulder is an Dutch expert on Management Skills, Personal Effectiveness and Business Communication. She is also a Content writer, Business Coach and Company Trainer and lives in the Netherlands (Europe). Note: all her articles are written in Dutch and we translated her articles to English!

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Heuristic Problem Solving: A comprehensive guide with 5 Examples

What are heuristics, advantages of using heuristic problem solving, disadvantages of using heuristic problem solving, heuristic problem solving examples, frequently asked questions.

• Speed: Heuristics are designed to find solutions quickly, saving time in problem solving tasks. Rather than spending a lot of time analyzing every possible solution, heuristics help to narrow down the options and focus on the most promising ones.
• Flexibility: Heuristics are not rigid, step-by-step procedures. They allow for flexibility and creativity in problem solving, leading to innovative solutions. They encourage thinking outside the box and can generate unexpected and valuable ideas.
• Simplicity: Heuristics are often easy to understand and apply, making them accessible to anyone regardless of their expertise or background. They don’t require specialized knowledge or training, which means they can be used in various contexts and by different people.
• Cost-effective: Because heuristics are simple and efficient, they can save time, money, and effort in finding solutions. They also don’t require expensive software or equipment, making them a cost-effective approach to problem solving.
• Real-world applicability: Heuristics are often based on practical experience and knowledge, making them relevant to real-world situations. They can help solve complex, messy, or ill-defined problems where other problem solving methods may not be practical.
• Potential for errors: Heuristic problem solving relies on generalizations and assumptions, which may lead to errors or incorrect conclusions. This is especially true if the heuristic is not based on a solid understanding of the problem or the underlying principles.
• Limited scope: Heuristic problem solving may only consider a limited number of potential solutions and may not identify the most optimal or effective solution.
• Lack of creativity: Heuristic problem solving may rely on pre-existing solutions or approaches, limiting creativity and innovation in problem-solving.
• Over-reliance: Heuristic problem solving may lead to over-reliance on a specific approach or heuristic, which can be problematic if the heuristic is flawed or ineffective.
• Lack of transparency: Heuristic problem solving may not be transparent or explainable, as the decision-making process may not be explicitly articulated or understood.
• Trial and error: This heuristic involves trying different solutions to a problem and learning from mistakes until a successful solution is found. A software developer encountering a bug in their code may try other solutions and test each one until they find the one that solves the issue.
• Working backward: This heuristic involves starting at the goal and then figuring out what steps are needed to reach that goal. For example, a project manager may begin by setting a project deadline and then work backward to determine the necessary steps and deadlines for each team member to ensure the project is completed on time.
• Breaking a problem into smaller parts: This heuristic involves breaking down a complex problem into smaller, more manageable pieces that can be tackled individually. For example, an HR manager tasked with implementing a new employee benefits program may break the project into smaller parts, such as researching options, getting quotes from vendors, and communicating the unique benefits to employees.
• Using analogies: This heuristic involves finding similarities between a current problem and a similar problem that has been solved before and using the solution to the previous issue to help solve the current one. For example, a salesperson struggling to close a deal may use an analogy to a successful sales pitch they made to help guide their approach to the current pitch.
• Simplifying the problem: This heuristic involves simplifying a complex problem by ignoring details that are not necessary for solving it. This allows the problem solver to focus on the most critical aspects of the problem. For example, a customer service representative dealing with a complex issue may simplify it by breaking it down into smaller components and addressing them individually rather than simultaneously trying to solve the entire problem.

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A heuristic is a mental shortcut that allows an individual to make a decision, pass judgment, or solve a problem quickly and with minimal mental effort. While heuristics can reduce the burden of decision-making and free up limited cognitive resources, they can also be costly when they lead individuals to miss critical information or act on unjust biases.

• Understanding Heuristics
• Different Heuristics
• Problems with Heuristics

As humans move throughout the world, they must process large amounts of information and make many choices with limited amounts of time. When information is missing, or an immediate decision is necessary, heuristics act as “rules of thumb” that guide behavior down the most efficient pathway.

Heuristics are not unique to humans; animals use heuristics that, though less complex, also serve to simplify decision-making and reduce cognitive load.

Generally, yes. Navigating day-to-day life requires everyone to make countless small decisions within a limited timeframe. Heuristics can help individuals save time and mental energy, freeing up cognitive resources for more complex planning and problem-solving endeavors.

The human brain and all its processes—including heuristics— developed over millions of years of evolution . Since mental shortcuts save both cognitive energy and time, they likely provided an advantage to those who relied on them.

Heuristics that were helpful to early humans may not be universally beneficial today . The familiarity heuristic, for example—in which the familiar is preferred over the unknown—could steer early humans toward foods or people that were safe, but may trigger anxiety or unfair biases in modern times.

The study of heuristics was developed by renowned psychologists Daniel Kahneman and Amos Tversky. Starting in the 1970s, Kahneman and Tversky identified several different kinds of heuristics, most notably the availability heuristic and the anchoring heuristic.

Since then, researchers have continued their work and identified many different kinds of heuristics, including:

Familiarity heuristic

Fundamental attribution error

Representativeness heuristic

Satisficing

The anchoring heuristic, or anchoring bias , occurs when someone relies more heavily on the first piece of information learned when making a choice, even if it's not the most relevant. In such cases, anchoring is likely to steer individuals wrong .

The availability heuristic describes the mental shortcut in which someone estimates whether something is likely to occur based on how readily examples come to mind . People tend to overestimate the probability of plane crashes, homicides, and shark attacks, for instance, because examples of such events are easily remembered.

People who make use of the representativeness heuristic categorize objects (or other people) based on how similar they are to known entities —assuming someone described as "quiet" is more likely to be a librarian than a politician, for instance. 

Satisficing is a decision-making strategy in which the first option that satisfies certain criteria is selected , even if other, better options may exist.

Heuristics, while useful, are imperfect; if relied on too heavily, they can result in incorrect judgments or cognitive biases. Some are more likely to steer people wrong than others.

Assuming, for example, that child abductions are common because they’re frequently reported on the news—an example of the availability heuristic—may trigger unnecessary fear or overprotective parenting practices. Understanding commonly unhelpful heuristics, and identifying situations where they could affect behavior, may help individuals avoid such mental pitfalls.

Sometimes called the attribution effect or correspondence bias, the term describes a tendency to attribute others’ behavior primarily to internal factors—like personality or character— while attributing one’s own behavior more to external or situational factors .

If one person steps on the foot of another in a crowded elevator, the victim may attribute it to carelessness. If, on the other hand, they themselves step on another’s foot, they may be more likely to attribute the mistake to being jostled by someone else .

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What Are Heuristics?

Understanding heuristics.

• Pros and Cons
• Examples in Behavioral Economics

Heuristics and Psychology

The bottom line.

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Heuristics: Definition, Pros & Cons, and Examples

James Chen, CMT is an expert trader, investment adviser, and global market strategist.

Heuristics are mental shortcuts that help people make quick decisions. They are rules or methods that help people use reason and past experience to solve problems efficiently. Commonly used to simplify problems and avoid cognitive overload, heuristics are part of how the human brain evolved and is wired, allowing individuals to quickly reach reasonable conclusions or solutions to complex problems. These solutions may not be optimal ones but are often sufficient given limited timeframes and calculative capacity.

These cognitive shortcuts feature prominently in behavioral economics .

Key Takeaways

• Heuristics are mental shortcuts for solving problems in a quick way that delivers a result that is sufficient enough to be useful given time constraints.
• Investors and financial professionals use a heuristic approach to speed up analysis and investment decisions.
• Heuristics can lead to poor decision-making based on a limited data set, but the speed of decisions can sometimes make up for the disadvantages.
• Behavioral economics has focused on heuristics as one limitation of human beings behaving like rational actors.
• Availability, anchoring, confirmation bias, and the hot hand fallacy are some examples of heuristics people use in their economic lives.

Investopedia / Danie Drankwalter

People employ heuristics naturally due to the evolution of the human brain. The brain can only process so much information at once and therefore must employ various shortcuts or practical rules of thumb . We would not get very far if we had to stop to think about every little detail or collect every piece of available information and integrate it into an analysis.

Heuristics therefore facilitate timely decisions that may not be the absolute best ones but are appropriate enough. Individuals are constantly using this sort of intelligent guesswork, trial and error, process of elimination, and past experience to solve problems or chart a course of action. In a world that is increasingly complex and overloaded with big data, heuristic methods make decision-making simpler and faster through shortcuts and good-enough calculations.

First identified in economics by the political scientist and organizational scholar Herbert Simon in his work on bounded rationality, heuristics have now become a cornerstone of behavioral economics.

Rather than subscribing to the idea that economic behavior was rational and based upon all available information to secure the best possible outcome for an individual ("optimizing"), Simon believed decision-making was about achieving outcomes that were "good enough" for the individual based on their limited information and balancing the interests of others. Simon called this " satisficing ," a portmanteau of the words "satisfy" and "suffice."

Advantages and Disadvantages of Using Heuristics

The main advantage to using heuristics is that they allow people to make good enough decisions without having all of the information and without having to undertake complex calculations.

Because humans cannot possibly obtain or process all the information needed to make fully rational decisions, they instead seek to use the information they do have to produce a satisfactory result, or one that is good enough. Heuristics allow people to go beyond their cognitive limits.

Heuristics are also advantageous when speed or timeliness matters—for example, deciding to enter a trade or making a snap judgment about some important decision. Heuristics are thus handy when there is no time to carefully weigh all options and their merits.

Disadvantages

There are also drawbacks to using heuristics. While they may be quick and dirty, they will likely not produce the optimal decision and can also be wrong entirely. Quick decisions without all the information can lead to errors in judgment, and miscalculations can lead to mistakes.

Moreover, heuristics leave us prone to biases that tend to lead us toward irrational economic behavior and sway our understanding of the world. Such heuristics have been identified and cataloged by the field of behavioral economics.

Quick & easy

Allows decision-making that goes beyond our cognitive capacity

Allows for snap judgments when time is limited

Often inaccurate

Can lead to systemic biases or errors in judgment

Example of Heuristics in Behavioral Economics

Representativeness.

A popular shortcut method in problem-solving identified in behavioral economics is called representativeness heuristics. Representativeness uses mental shortcuts to make decisions based on past events or traits that are representative of or similar to the current situation.

Say, for example, Fast Food ABC expanded its operations to India and its stock price soared. An analyst noted that India is a profitable venture for all fast-food chains. Therefore, when Fast Food XYZ announced its plan to explore the Indian market the following year, the analyst wasted no time in giving XYZ a "buy" recommendation.

Although their shortcut approach saved reviewing data for both companies, it may not have been the best decision. Fast Food XYZ may have food that is not appealing to Indian consumers, which research would have revealed.

Anchoring and Adjustment

Anchoring and adjustment is another prevalent heuristic approach. With anchoring and adjustment, a person begins with a specific target number or value—called the anchor—and subsequently adjusts that number until an acceptable value is reached over time. The major problem with this method is that if the value of the initial anchor is not the true value, then all subsequent adjustments will be systematically biased toward the anchor and away from the true value.

An example of anchoring and adjustment is a car salesman beginning negotiations with a very high price (that is arguably well above the  fair value ). Because the high price is an anchor, the final price will tend to be higher than if the car salesman had offered a fair or low price to start.

Availability (Recency) Heuristic

The availability (or recency) heuristic is an issue where people give too much weight to the probability of an event happening again if it recently has occurred. For instance, if a shark attack is reported in the news, those headlines make the event salient and can lead people to stay away from the water, even though shark attacks remain very rare.

Another example is the case of the " hot hand ," or the sense that following a string of successes, an individual is likely to continue being successful. Whether at the casino, in the markets, or playing basketball, the hot hand has been debunked. A string of recent good luck does not alter the overall probability of events occurring.

Confirmation Bias

Confirmation bias is a well-documented heuristic whereby people give more weight to information that fits with their existing worldviews or beliefs. At the same time, information that contradicts these beliefs is discounted or rejected.

Investors should be aware of their own tendency toward confirmation bias so that they can overcome poor decision-making, missing chances, and avoid falling prey to bubbles . Seeking out contrarian views and avoiding affirmative questions are two ways to counteract confirmation bias.

Hindsight Bias

Hindsight is always 20/20. However, the hindsight bias leads us to forget that we made incorrect predictions or estimates prior to them occurring. Rather, we become convinced that we had accurately predicted an event before it occurred, even when we did not. This can lead to overconfidence for making future predictions, or regret for not taking past opportunities.

Stereotypes

Stereotypes are a kind of heuristic that allows us to form opinions or judgments about people whom we have never met. In particular, stereotyping takes group-level characteristics about certain social groups—often ones that are racist, sexist, or otherwise discriminatory—and casts those characteristics onto all of the members in that group, regardless of their individual personalities, beliefs, skills, or behaviors.

By imposing oversimplified beliefs onto people, we can quickly judge potential interactions with them or individual outcomes of those people. However, these judgments are often plain wrong, derogatory, and perpetuate social divisions and exclusions.

Heuristics were first identified and taken seriously by scholars in the middle of the 20th century with the work of Herbert Simon, who asked why individuals and firms don't act like rational actors in the real world, even with market pressures punishing irrational decisions. Simon found that corporate managers do not usually optimize but instead rely on a set of heuristics or shortcuts to get the job done in a way that is good enough (to "satisfice").

Later, in the 1970s and '80s, psychologists Amos Tversky and Daniel Kahneman working at the Hebrew University in Jerusalem, built off of Herbert Simon's work and developed what is known as Prospect Theory . A cornerstone of behavioral economics, Prospect Theory catalogs several heuristics used subconsciously by people as they make financial evaluations.

One major finding is that people are loss-averse —that losses loom larger than gains (i.e., the pain of losing $50 is far more than the pleasure of receiving $50). Here, people adopt a heuristic to avoid realizing losses, sometimes spurring them to take excessive risks in order to do so—but often leading to even larger losses.

More recently, behavioral economists have tried to develop policy measures or "nudges" to help correct people's irrational use of heuristics in order to help them achieve more optimal outcomes—for instance, by having people enroll in a retirement savings plan by default instead of having to opt in.

What Are the Types of Heuristics?

To date, several heuristics have been identified by behavioral economics—or else developed to aid people in making otherwise complex decisions. In behavioral economics, representativeness, anchoring and adjustment, and availability (recency) are among the most widely cited. Heuristics may be categorized in many ways, such as cognitive versus emotional biases or errors in judgment versus errors in calculation.

What Is Heuristic Thinking?

Heuristic thinking uses mental shortcuts—often unconsciously—to quickly and efficiently make otherwise complex decisions or judgments. These can be in the form of a "rule of thumb" (e.g., saving 5% of your income in order to have a comfortable retirement) or cognitive processes that we are largely unaware of like the availability bias.

What Is Another Word for Heuristic?

Heuristic may also go by the following terms: rule of thumb; mental shortcut; educated guess; or satisfice.

How Does a Heuristic Differ From an Algorithm?

An algorithm is a step-by-step set of instructions that are followed to achieve some goal or outcome, often optimizing that outcome. They are formalized and can be expressed as a formula or "recipe." As such, they are reproducible in the sense that an algorithm will always provide the same output, given the same input.

A heuristic amounts to an educated guess or gut feeling. Rather than following a set of rules or instructions, a heuristic is a mental shortcut. Moreover, it often produces sub-optimal and even irrational outcomes that may differ even when given the same input.

What Are Computer Heuristics?

In computer science, a heuristic refers to a method of solving a problem that proves to be quicker or more efficient than traditional methods. This may involve using approximations rather than precise calculations or techniques that circumvent otherwise computationally intensive routines.

Heuristics are practical rules of thumb that manifest as mental shortcuts in judgment and decision-making. Without heuristics, our brains would not be able to function given the complexity of the world, the amount of data to process, and the calculative abilities required to form an optimal decision. Instead, heuristics allow us to make quick, good-enough choices.

However, these choices may also be subject to inaccuracies and systemic biases, such as those identified by behavioral economics.

Simon, Herbert. " Herbert Simon, Innovation, and Heuristics ." Mind & Society, vol. 17, 2019, pp. 97-109.

Kahneman, Daniel, and Tversky, Amos. " Prospect Theory: An Analysis of Decision Under Risk ." The Econometric Society, vol. 47, no. 2, 1979, pp. 263-292.

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7.3 Problem-Solving

Learning objectives.

By the end of this section, you will be able to:

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving

   People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.

PROBLEM-SOLVING STRATEGIES

   When people are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them (table below). For example, a well-known strategy is trial and error. The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

   Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.

Additional Problem Solving Strategies :

• Abstraction – refers to solving the problem within a model of the situation before applying it to reality.
• Analogy – is using a solution that solves a similar problem.
• Brainstorming – refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.
• Divide and conquer – breaking down large complex problems into smaller more manageable problems.
• Hypothesis testing – method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.
• Lateral thinking – approaching problems indirectly and creatively by viewing the problem in a new and unusual light.
• Means-ends analysis – choosing and analyzing an action at a series of smaller steps to move closer to the goal.
• Method of focal objects – putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.
• Morphological analysis – analyzing the outputs of and interactions of many pieces that together make up a whole system.
• Proof – trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.
• Reduction – adapting the problem to be as similar problems where a solution exists.
• Research – using existing knowledge or solutions to similar problems to solve the problem.
• Root cause analysis – trying to identify the cause of the problem.

The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.

One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :

Missionary-Cannibal Problem

Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.

Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.

The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:

• 1. Only one disk can be moved at a time.
• 2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
• 3. No disc may be placed on top of a smaller disk.

  Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.

Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.

The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.

GESTALT PSYCHOLOGY AND PROBLEM SOLVING

As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.

As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage  (1990) suggesting that while collecting data for what would later be his book  The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.

While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as  insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).

While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.

Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground.  Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).

Solving puzzles.

   Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (see figure) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

   Here is another popular type of puzzle (figure below) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

   Take a look at the “Puzzling Scales” logic puzzle below (figure below). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

What steps did you take to solve this puzzle? You can read the solution at the end of this section.

Pitfalls to problem solving.

   Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

   Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in the table below.

Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.

   Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

References:

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology

Review Questions:

1. A specific formula for solving a problem is called ________.

a. an algorithm

b. a heuristic

c. a mental set

d. trial and error

2. Solving the Tower of Hanoi problem tends to utilize a  ________ strategy of problem solving.

a. divide and conquer

b. means-end analysis

d. experiment

3. A mental shortcut in the form of a general problem-solving framework is called ________.

4. Which type of bias involves becoming fixated on a single trait of a problem?

a. anchoring bias

b. confirmation bias

c. representative bias

d. availability bias

5. Which type of bias involves relying on a false stereotype to make a decision?

6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.

a. social adjustment

b. student load payment options

c. emotional learning

d. insight learning

7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.

a. functional fixedness

c. working memory

Critical Thinking Questions:

1. What is functional fixedness and how can overcoming it help you solve problems?

2. How does an algorithm save you time and energy when solving a problem?

Personal Application Question:

1. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

anchoring bias

availability heuristic

confirmation bias

functional fixedness

hindsight bias

problem-solving strategy

representative bias

trial and error

working backwards

Answers to Exercises

algorithm:  problem-solving strategy characterized by a specific set of instructions

anchoring bias:  faulty heuristic in which you fixate on a single aspect of a problem to find a solution

availability heuristic:  faulty heuristic in which you make a decision based on information readily available to you

confirmation bias:  faulty heuristic in which you focus on information that confirms your beliefs

functional fixedness:  inability to see an object as useful for any other use other than the one for which it was intended

heuristic:  mental shortcut that saves time when solving a problem

hindsight bias:  belief that the event just experienced was predictable, even though it really wasn’t

mental set:  continually using an old solution to a problem without results

problem-solving strategy:  method for solving problems

representative bias:  faulty heuristic in which you stereotype someone or something without a valid basis for your judgment

trial and error:  problem-solving strategy in which multiple solutions are attempted until the correct one is found

working backwards:  heuristic in which you begin to solve a problem by focusing on the end result

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• Published: 17 February 2023

A brief history of heuristics: how did research on heuristics evolve?

• Mohamad Hjeij   ORCID: orcid.org/0000-0003-4231-1395 1 &
• Arnis Vilks 1  

Humanities and Social Sciences Communications volume  10 , Article number:  64 ( 2023 ) Cite this article

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Heuristics are often characterized as rules of thumb that can be used to speed up the process of decision-making. They have been examined across a wide range of fields, including economics, psychology, and computer science. However, scholars still struggle to find substantial common ground. This study provides a historical review of heuristics as a research topic before and after the emergence of the subjective expected utility (SEU) theory, emphasising the evolutionary perspective that considers heuristics as resulting from the development of the brain. We find it useful to distinguish between deliberate and automatic uses of heuristics, but point out that they can be used consciously and subconsciously. While we can trace the idea of heuristics through many centuries and fields of application, we focus on the evolution of the modern notion of heuristics through three waves of research, starting with Herbert Simon in the 1950s, who introduced the notion of bounded rationality and suggested the use of heuristics in artificial intelligence, thereby paving the way for all later research on heuristics. A breakthrough came with Daniel Kahneman and Amos Tversky in the 1970s, who analysed the biases arising from using heuristics. The resulting research programme became the subject of criticism by Gerd Gigerenzer in the 1990s, who argues that an ‘adaptive toolbox’ consisting of ‘fast-and-frugal’ heuristics can yield ‘ecologically rational’ decisions.

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Introduction.

Over the past 50 years, the notion of ‘heuristics’ has considerably gained attention in fields as diverse as psychology, cognitive science, decision theory, computer science, and management scholarship. While for 1970, the Scopus database finds a meagre 20 published articles with the word ‘heuristic’ in their title, the number has increased to no less than 3783 in 2021 (Scopus, 2022 ).

We take this to be evidence that many researchers in the aforementioned fields find the literature that refers to heuristics stimulating and that it gives rise to questions that deserve further enquiry. While there are some review articles on the topic of heuristics (Gigerenzer and Gaissmaier, 2011 ; Groner et al., 1983 ; Hertwig and Pachur, 2015 ; Semaan et al., 2020 ), a somewhat comprehensive and non-partisan historical review seems to be missing.

While interest in heuristics is growing, the very notion of heuristics remains elusive to the point that, e.g., Shah and Oppenheimer ( 2008 ) begin their paper with the statement: ‘The word “heuristic” has lost its meaning.’ Even if one leaves aside characterizations such as ‘rule of thumb’ or ‘mental shortcut’ and considers what Kahneman ( 2011 ) calls ‘the technical definition of heuristic,’ namely ‘a simple procedure that helps find adequate, though often imperfect, answers to difficult questions,’ one is immediately left wondering how simple it has to be, what an adequate, but the imperfect answer is, and how difficult the questions need to be, in order to classify a procedure as a heuristic. Shah and Oppenheimer conclude that ‘the term heuristic is vague enough to describe anything’.

However, one feature does distinguish heuristics from certain other, typically more elaborate procedures: heuristics are problem-solving methods that do not guarantee an optimal solution. The use of heuristics is, therefore, inevitable where no method to find an optimal solution exists or is known to the problem-solver, in particular where the problem and/or the optimality criterion is ill-defined. However, the use of heuristics may be advantageous even where the problem to be solved is well-defined and methods do exist which would guarantee an optimal solution. This is because definitions of optimality typically ignore constraints on the process of solving the problem and the costs of that process. Compared to infallible but elaborate methods, heuristics may prove to be quicker or more efficient.

Nevertheless, the range of what has been called heuristics is very broad. Application of a heuristic may require intuition, guessing, exploration, or experience; some heuristics are rather elaborate, others are truly shortcuts, some are described in somewhat loose terms, and others are well-defined algorithms.

One procedure of decision-making that is commonly not regarded as a heuristic is the application of the full-blown theory of subjective expected utility (SEU) in the tradition of Ramsey ( 1926 ), von Neumann and Morgenstern ( 1944 ), and Savage ( 1954 ). This theory is arguably spelling out what an ideally rational decision would be, but was already seen by Savage (p. 16) to be applicable only in what he called a ‘small world’. Quite a few approaches that have been called heuristics have been explicitly motivated by SEU imposing demands on the decision-maker, which are utterly impractical (cf., e.g., Klein, 2001 , for a discussion). As a second defining feature of the heuristics we want to consider, therefore, we take them to be procedures of decision-making that differ from the ‘gold standard’ of SEU by being practically applicable in at least a number of interesting cases. Along with SEU, we also leave aside the rules of deductive logic, such as Aristotelian syllogisms, modus ponens, modus tollens, etc. While these can also be seen as rules of decision-making, and the universal validity of some of them is not quite uncontroversial (see, e.g., Priest, 2008 , for an introduction to non-classical logic), they are widely regarded as ‘infallible’. By stark contrast, it seems characteristic for heuristics that their application may fail to yield a ‘best’ or ‘correct’ result.

By taking heuristics to be practically applicable, but fallible, procedures for problem-solving, we will also neglect the literature that focuses on the adjective ‘heuristic’ instead of on the noun. When, e.g., Suppes ( 1983 ) characterizes axiomatic analyses as ‘heuristic’, he is not suggesting any rule, but he is saying that heuristic axioms ‘seem intuitively to organize and facilitate our thinking about the subject’ (p. 82), and proceeds to give examples of both heuristic and nonheuristic axioms. It may of course be said that many fundamental equations in science, such as Newton’s force = mass*acceleration, have some heuristic value in the sense indicated by Suppes, but the research we will review is not about the property of being heuristic.

Given that heuristics can be assessed against the benchmark of SEU, one may distinguish broadly between heuristics suggested pre-SEU, i.e., before the middle of the 20th century, and the later research on heuristics that had to face the challenge of an existing theory of allegedly rational decision-making. We will review the former in the section “Deliberate heuristics—the art of invention” below, and devote sections “Herbert Simon: rationality is bounded”, “Heuristics in computer science” and “Daniel Kahneman and Amos Tversky: heuristics and biases” to the latter.

To cover the paradigmatic cases of what has been termed ‘heuristics’ in the literature, we have to take ‘problem-solving’ in a broad sense that includes decision-making and judgement, but also automatic, instinctive behaviour. We, therefore, feel that an account of research on heuristics should also review the main views on how observable behaviour patterns in humans—or maybe animals in general—can be explained. This we do in the section “Automatic heuristics: learnt or innate?”.

While our brief history cannot aim for completeness, we selected the scholars to be included based on their influence and contributions to different fields of research related to heuristics. Our focus, however, will be on the more recent research that may be said to begin with Herbert Simon.

That problem-solving according to SEU will, in general, be impractical, was clearly recognized by Herbert Simon, whose notion of bounded rationality we look at in the section “Herbert Simon: rationality is bounded”. In the section “Heuristics in computer science”, we also consider heuristics in computer science, where the motivation to use heuristics is closely related to Simon’s reasoning. In the section “Daniel Kahneman and Amos Tversky: heuristics and biases”, we turn to the heuristics identified and analysed by Kahneman and Tversky; while their assessment was primarily that the use of those heuristics often does not conform to rational decision-making, the approach by Gigerenzer and his collaborators, reviewed in the section “Gerd Gigerenzer: fast-and-frugal heuristics” below, takes a much more affirmative view on the use of heuristics. Section “Critiques” explains the limitations and critiques of the corresponding ideas. The final section “Conclusion” contains the conclusion, discussion, and avenues for future research.

The evolutionary perspective

While we focus on the history of research on heuristics, it is clear that animal behaviour patterns evolved and were shaped by evolutionary forces long before the human species emerged. Thus ‘heuristics’ in the mere sense of behaviour patterns have been used long before humans engaged in any kind of conscious reflection on decision-making, let alone systematic research. However, evolution endowed humans with brains that allow them to make decisions in ways that are quite different from animal behaviour patterns. According to Gibbons ( 2007 ), the peculiar evolution of the human brain started thousands of years ago when the ancient human discovered fire and started cooking food, which reduced the amount of energy the body needed for digestion. This paved the way for a smaller intestinal tract and implied that the excess calories led to the development of larger tissues and eventually a larger brain. Through this organ, intelligence increased exponentially, resulting in advanced communication that allowed Homo sapiens to collaborate and form relationships that other primates at the time could not match. According to Dunbar ( 1998 ), it was in the time between 400,000 and 100,000 years ago that abilities to hunt more effectively took humans from the middle of the food chain right to the top.

It does not seem to be known when and how exactly the human brain developed the ability to reflect on decisions made consciously, but it is now widely recognized that in addition to the fast, automatic, and typically nonconscious type of decision-making that is similar to animal behaviour, humans also employ another, rather a different type of decision-making that can be characterized as slow, conscious, controlled, and reflective. The former type is known as ‘System 1’ or ‘the old mind’, and the latter as ‘System 2’ or ‘the new mind’ (Evans, 2010 ; Kahneman, 2011 ), and both systems have clearly evolved side by side throughout the evolution of the human brain. According to Gigerenzer ( 2021 ), humans as well as other organisms evolved to acquire what he calls ‘embodied heuristics’ that can be both innate or learnt rules of thumb, which in turn supply the agility to respond to the lack of information by fast judgement. The ‘embodied heuristics’ use the mental capacity that includes the motor and sensory abilities that start to develop from the moment of birth.

While a detailed discussion of the ‘dual-process theories’ of the mind is beyond the scope of this paper, we find it helpful to point out that one may distinguish between ‘System 1 heuristics’ and ‘System 2 heuristics’ (Kahneman 2011 , p. 98). While some ‘rules of decision-making’ may be hard-wired into the human species by its genes and physiology, others are complicated enough that their application typically requires reflection and conscious mental effort. Upon reflection, however, the two systems are not as separate as they may seem. For example, participants in the Mental Calculation World Cup perform mathematical tasks instantly, whereas ordinary people would need a pen and paper or a calculator. Today, many people cannot multiply large numbers or calculate a square root using only a pen and paper but can easily do this using the calculator app on their smartphone. Thus, what can be done by spontaneous effortless calculation by some, may for others require the application of a more or less complicated theory.

Nevertheless, one can loosely characterize the heuristics that have been explained and recommended for more or less well-specified purposes over the course of history as System 2 or deliberate heuristics.

Deliberate heuristics—the art of invention

Throughout history, scholars have investigated methods to solve complex tasks. In this section, we review those attempts to formulate ‘operant and voluntary’ heuristics to solve demanding problems—in particular, to generate new insights or do research in more or less specified fields. Most of the heuristics in this section have been suggested before the emergence of the SEU theory and the associated modern definition of rationality, and none of them deals with the kind of decision problems that are assumed as ‘given’ in the SEU model. The reader will notice that some historical heuristics were suggested for problems that, today, may seem too general to be solved. However, through the development of such attempts, later scholars were inspired to develop a more concrete understanding of the notion of heuristics.

The Greek origin

The term heuristic originates from the Greek verb heurísko , which means to discover or find out. The Greek word heúrēka , allegedly exclaimed by Archimedes when discovering how to measure the volume of a random object through water, derives from the same verb and can be translated as I found it! (Pinheiro and McNeill, 2014 ). Heuristics can thus be said to be etymologically related to the discipline of discovery, the branch of knowledge based on investigative procedures, and are naturally associated with trial techniques, including what-if scenarios and simple trial and error.

While the term heurísko does not seem to be used in this context by Aristotle, his notion of induction ( epagôgê ) can be seen as a method to find, but not prove, true general statements and thus as a heuristic. At any rate, Aristotle considered inductive reasoning as leading to insights and as distinct from logically valid syllogisms (Smith, 2020 ).

Pappus (4th century)

While a brief, somewhat cryptic, mention of analysis and synthesis appears in Book 13 of some, but not all, editions of Euclid’s Elements, a clearer explanation of the two methods was given in the 4th century by the Greek mathematician and astronomer Pappus of Alexandria (cf. Heath, 1926 ; Polya, 1945 ; Groner et al., 1983 ). While synthesis is what today would be called deduction from known truths, analysis is a method that can be used to try and find proof. Two slightly different explanations are given by Pappus. They boil down to this: in order to find proof for a statement A, one can deduce another statement B from A, continue by deducing yet another statement C from B, and so on, until one comes upon a statement T that is known to be true. If all the inferences are convertible, the converse deductions evidently constitute a proof of A from T. While Pappus did not mention the condition that the inferences must be convertible, his second explanation of analysis makes it clear that one must be looking for deductions from A which are both necessary and sufficient for A. In Polya’s paraphrase of Pappus’ text: ‘We enquire from what antecedent the desired result could be derived; then we enquire again what could be the antecedent of that antecedent, and so on, until passing from antecedent to antecedent, we come eventually upon something already known or admittedly true.’ Analysis thus described is hardly a ‘shortcut’ or ‘rule of thumb’, but quite clearly it is a heuristic: it may help to find a proof of A, but it may also fail to do so…

Al-Khawarizmi (9th century)

In the 9th century, the Persian thinker Mohamad Al-Khawarizmi, who resided in Baghdad’s centre of knowledge or the House of Wisdom , used stepwise methods for problem-solving. Thus, after his name and findings, the algorithm concept was derived (Boyer, 1991 ). Although a heuristic orientation has sometimes been contrasted with an algorithmic one (Groner and Groner, 1991 ), it is worth noting that an algorithm may well serve as a heuristic—certainly in the sense of a shortcut, and also in the sense of a fallible method. After all, an algorithm may fail to produce a satisfactory result. We will return to this issue in the section “Heuristics in computer science” below.

Zairja (10th century)

Heuristic methods were created by medieval polymaths in their attempts to find solutions for the complex problems they faced—science not yet being divorced from what today would appear as theology or astrology. Perhaps the first tangible example of a heuristic based on a mechanical device was using an ancient tool called a zairja , which Arab astrologers employed before the 11th century (Ritchey, 2022 ). It was designed to reconfigure notions into ideas through randomization and resonance and thus to produce answers to questions mechanically (Link, 2010 ). The word zairja may have originated from the Persian combination zaicha-daira , which means horoscope-circle. According to Ibn Khaldoun, ‘zairja is the technique of finding out answers from questions by means of connections existing between the letters of the expressions used in the question; they imagine that these connections can form the basis for knowing the future happenings they want to know’ (Khaldun, 1967 ).

Ramon Llull (1305)

The Majorcan philosopher Ramon Llull (or Raimundus Lullus), who was exposed to the Arabic culture, used the zairja as a starting point for his ars inveniendi veritatem that was meant to complement the ars demonstrandi of medieval Scholastic logic and on which he worked from around 1270–1305 (Link, 2010 ; Llull, 1308 ; Ritchey, 2022 ) when he finished his Ars Generalis Ultima (or Ars Magna ). Llull transformed the astrological and combinatorial components of the zairja into a religious system that took the fundamental ideas of the three Abrahamic faiths of Islam, Christianity, and Judaism and analysed them through symbolic and numeric reasoning. Llull tried to broaden his theory across all fields of knowledge and combine all sciences into a single science that would address all human problems. His thoughts impacted great thinkers, such as Leibniz, and even the modern theory of computation (Fidora and Sierra, 2011 ). Llull’s approach may be considered a clear example of heuristic methods applied to complicated and even theological questions (Hertwig and Pachur, 2015 ).

Joachim Jungius (1622)

Arguably, the German mathematician and philosopher Joachim Jungius was the first to use the terminology heuretica in a call to establish a research society in 1622. Jungius distinguished between three degrees or levels of learning and cognition: empirical, epistemic, and heuristic. Those who have reached the empirical level believe that what they have learned is true because it corresponds to experience. Those who have reached the epistemic level know how to derive their knowledge from principles with rigorous evidence. But those who have reached the highest level, the heuristic level, have a method of solving unsolved problems, finding new theorems, and introducing new methods into science (Ritter et al., 2017 ).

René Descartes (1637)

In 1637, the French philosopher René Descartes published his Discourse on Method (one of the first major works not written in Latin). Descartes argued that humans could utilize mathematical reasoning as a vehicle for progress in knowledge. He proposed four simple steps to follow in problem-solving. First, to accept as true only what is indubitable. Next, divide the problem into as many smaller subproblems as possible and helpful. After that, to conduct one’s thoughts in an orderly fashion, beginning with the simplest and gradually ascending to the most complex. And finally, to make enumerations so complete that one is assured of having omitted nothing (Descartes, 1998 ). In reference to his other methods, Descartes ( 1908 ) started working on the proper heuristic rules to transform every problem, when possible, into algebraic equations, thus creating a mathesis universalis or universal science. In his unfinished ‘Rules for the Direction of the Mind’ or Regulae ad directionem ingenii , Descartes suggested 21 heuristic rules (of planned 36) for scientific research like simplifying the problem, rewriting the problem in geometrical shape, and identifying the knowns and the unknowns. Although Leibniz criticized the rules of Descartes for being too general (Leibniz, 1880 ), this treatise outlined the basis for later work on complex problems in several disciplines.

Gottfried Wilhelm Leibniz (1666)

Influenced by the ideas of Llull, Jungius, and Descartes, the Prussian–German polymath Gottfried Wilhelm Leibniz suggested an original approach to problem-solving in his Dissertatio de Arte Combinatoria , published in Leipzig in 1666. His aim was to create a new universal language into which all problems could be translated and a standard solving procedure that could be applied regardless of the type of the problem. Leibniz also defined an ars inveniendi as a method for finding new truths, distinguishing it from an ars iudicandi , a method to evaluate the validity of alleged truths. Later, in 1673, he invented the calculating machine that could execute all four arithmetic operations and thus find ‘new’ arithmetic truths (Pombo, 2002 ).

Bernard Bolzano ( 1837 )

In 1837, the Czech mathematician and philosopher Bernard Bolzano published his four-volume Wissenschaftslehre (Theory of Science). The fourth part of his theory he called ‘Erfindungskunst’ or the art of invention, mentions in the introductory section 322 that ‘heuristic’ is just the Greek translation. Bolzano explains that the rules he is going to state are not at all entirely new, but instead have always been used ‘by the talented’—although mostly not consciously. He then explains 13 general and 33 special rules one should follow when trying to find new truths. Among the general rules are, e.g., that one should first decide on the question one wants to answer, and the kind of answer one is looking for (section 325), or that one should choose suitable symbols to represent one’s ideas (section 334). Unlike the general rules, the special ones are meant to be helpful for special mental tasks only. E.g., in order to solve the task of finding the reason for any given truth, Bolzano advises first to analyse or dissect the truth into its parts and then use those to form truths which are simpler than the given one (section 378). Another example is Bolzano’s special rule 28, explained in section 386, which is meant to help identify the intention behind a given action. To do so, Bolzano advises exploring the agent’s beliefs about the effects of his action at the time he decided to act, and explains that this will require investigating the agent’s knowledge, his degree of attention and deliberation, any erroneous beliefs the agent may have had, and ‘many other circumstances’. Bolzano continues to point out that any effect the agent may have expected to result from his action will not be an intended one if he considered it neither as an obligation nor as advantageous. While Bolzano’s rules can hardly be considered as ‘shortcuts’, he mentions again and again that they may fail to solve the task at hand adequately (cf. Hertwig and Pachur, 2015 ; Siitonen, 2014 ).

Frank Ramsey ( 1926 )

In Ramsey’s pathbreaking paper on ‘Truth and Probability’ which laid the foundation of subjective probability theory, a final section that has received little attention in the literature is devoted to inductive logic. While he does not use the word ‘heuristic’, he characterizes induction as a ‘habit of the mind,’ explaining that he uses ‘habit in the most general possible sense to mean simply rule or the law of behaviour, including instinct,’ but also including ‘acquired rules.’ Ramsey gives the following pragmatic justification for being convinced by induction: ‘our conviction is reasonable because the world is so constituted that inductive arguments lead on the whole to true opinions,’ and states more generally that ‘we judge mental habits by whether they work, i.e., whether the opinions they lead to are for the most part true, or more often true than those which alternative habits would lead to’ (Ramsey, 1926 ). In modern terminology, Ramsey was pointing out that mental habits—such as inductive inference—may be more or less ‘ecologically rational’.

Karl Duncker ( 1935 )

Karl Duncker was a pioneer in the experimental investigation of human problem-solving. In his 1935 book Zur Psychologie des produktiven Denkens , he discussed both heuristics that help to solve problems, but also hindrances that may block the solution of a problem—and reported on a number of experimental findings. Among the heuristics was a situational analysis with the aim of uncovering the reasons for the gap between the status quo and the problem-solvers goal, analysis of the goal itself, and of sacrifices the problem-solver is willing to make, of prerequisites for the solution, and several others. Among the hindrances to problem-solving was what Duncker called functional fixedness, illustrated by the famous candle problem, in which he asked the participants to fix a candle to the wall and light it without allowing the wax to drip. The available tools were a candle, matches, and a box filled with thumbtacks. The solution was to empty the box of thumbtacks, fix the empty box to the wall using the thumbtacks, put the candle in the box, and finally light the candle. Participants who were given the empty box as a separate item could solve this problem, while those given the box filled with thumbtacks struggled to find a solution. Through this experiment, Duncker illustrated an inability to think outside the box and the difficulty in using a device in a way that is different from the usual one (Glaveanu, 2019 ). Duncker emphasized that success in problem-solving depends on a complementary combination of both the internal mind and the external problem structure (cf. Groner et al., 1983 ).

George Polya ( 1945 )

The Hungarian mathematician George Polya can be aptly called the father of problem-solving in modern mathematics and education. In his 1945 book, How to Solve it , Polya writes that ‘heuristic…or ‘ ars inveniendi ’ was the name of a certain branch of study…often outlined, seldom presented in detail, and as good as forgotten today’ and he attempts to ‘revive heuristic in a modern and modest form’. According to his four principles of mathematical problem-solving, it is first necessary to understand the problem, then plan the execution, carry out the plan, and finally, reflect and search for improvement opportunities. Among the more detailed suggestions for problem-solving explained by Polya are to ask questions such as ‘can you find the solution to a similar problem?’, to use inductive reasoning and analogy, or to choose a suitable notation. Procedures inspired by Polya’s ( 1945 ) book and several later ones (e.g., Induction and Analogy in Mathematics of 1954 ) also informed the field of artificial intelligence (AI) (Hertwig and Pachur, 2015 ).

Johannes Müller (1968)

In 1968, the German scientist Johannes Müller introduced the concept of systematic heuristics while working on his postdoctoral thesis at the Chemnitz University of Technology. Systematic heuristics is a framework for improving the efficiency of intellectual work using problem-solving processes in the fields of science and technology.

The main idea of systematic heuristics is to solve repeated problems with previously validated solutions. These methods are called programmes and are gathered in a library that can be accessed by the main programme, which receives the requirements, prepares the execution plan, determines the required procedures, executes the plan, and finally evaluates the results. Müller’s team was dismissed for ideological reasons, and his programme was terminated after a few years, but his findings went on to be successfully applied in many projects across different industries (Banse and Friedrich, 2000 ).

Imre Lakatos ( 1970 )

In his ‘Methodology of Scientific Research Programmes’ that turned out to be a major contribution to the Popper–Kuhn controversy about the rationality of non-falsifiable paradigms in the natural sciences, Lakatos introduced the interesting distinction between a ‘negative heuristic’ that is given by the ‘hard core’ of a research programme and the ‘positive heuristic’ of the ‘protective belt’. While the latter suggests ways to develop the research programme further and to predict new facts, the ‘hard core’ of the research programme is treated as irrefutable ‘by the methodological decision of its protagonists: anomalies must lead to changes only in the ‘protective’ belt’ of auxiliary hypotheses. The Lakatosian notion of a negative heuristic seems to have received little attention outside of the Philosophy of Science community but may be important elsewhere: when there are too many ways to solve a complicated problem, excluding some of them from consideration may be helpful.

Gerhard Kleining ( 1982 )

The German sociologist Gerhard Kleining suggested a qualitative heuristic as the appropriate research method for qualitative social science. It is based on four principles: (1) open-mindedness of the scientist who should be ready to revise his preconceptions about the topic of study, (2) openness of the topic of study, which is initially defined only provisionally and allowed to be modified in course of the research, (3) maximal variation of the research perspective, and (4) identification of similarities within the data (Kleining, 1982 , 1995 ).

Automatic heuristics: learnt or innate?

Unlike the deliberate, and in some cases quite elaborate, heuristics reviewed above, at least some System 1 heuristics are often applied automatically, without any kind of deliberation or conscious reflection on the task that needs to be performed or the question that needs to be answered. One may view them as mere patterns of behaviour, and as such their scientific examination has been a long cumulative process through different disciplines, even though explicit reference to heuristics was not often made.

Traditionally, examining the behaviour patterns of any living creature, any study concerning thoughts, feelings, or cognitive abilities was regarded as the task of biologists. However, the birth of psychology as a separate discipline paved the way for an alternative outlook. Evolutionary psychology views human behaviour as being shaped through time and experience to promote survival throughout the long history of human struggle with nature. With many factors to consider, scholars have been interested in the evolution of the human brain, patterns of behaviour, and problem-solving (Buss and Kenrick, 1998 ).

Charles Darwin (1873)

Charles Darwin himself maybe qualifies for the title of first evolutionary psychologist, as his perceptions laid the foundations for this field that would continue to grow over a century later (Ghiselin, 1973 ).

In 1873, Darwin claimed that the brain’s articulations regarding expressions and emotions have probably developed similarly to its physical traits (Baumeister and Vohs, 2007 ). He acknowledged that personal demonstrations or expressions have a high capacity for interaction with different peers from the same species. For example, an aggressive look flags an eagerness to battle yet leaves the recipient with the option of retreating without either party being harmed. Additionally, Darwin, as well as his predecessor Lamarck, constantly emphasized the role of environmental factors in ‘the struggle for existence’ that could shape the organism’s traits in response to changes in their corresponding environments (Sen, 2020 ). The famous example of giraffes that grew long necks in response to trees growing taller is an illustration of a major environmental effect. Similarly, cognitive skills, including heuristics, must have also been shaped by the environments to evolve and keep humans surviving and reproducing.

Darwin’s ideas impacted the early advancement of brain science, psychology, and all related disciplines, including the topic of cognitive heuristics (Smulders, 2009 ).

William James (1890)

A few years later, in 1890, the father of American psychology, William James, introduced the notion of evolutionary psychology in his 1200-page text The Principles of Psychology , which later became a reference on the subject and helped establish psychology as a science. In its core content, James reasoned that many actions of the human being demonstrate the activity of instincts, which are the evolutionary embedded inclinations to react to specific incentives in adaptive manners. With this idea, James added an important building block to the foundation of heuristics as a scientific topic.

A simple example of such hard-wired behaviour patterns would be a sneeze, the preprogrammed reaction of convulsive nasal expulsion of air from the lungs through the nose and mouth to remove irritants (Baumeister and Vohs, 2007 ).

Ivan Pavlov (1897)

Triggered by scientific curiosity or the instinct for research, as he called it, the first Russian Nobel laureate, Ivan Pavlov, introduced classical conditioning, which occurs when a stimulus is used that has a predictive relationship with a reinforcer, resulting in a change in response to the stimulus (Schreurs, 1989 ). This learning process was demonstrated through experiments conducted with dogs. In the experiments, a bell (a neutral stimulus) was paired with food (a potent stimulus), resulting ultimately in the dogs salivating at the ringing of the bell—a conditioned response. Pavlov’s experiments remain paradigmatic cases of the emergence of behaviour patterns through association learning.

William McDougall (1909)

At the start of the 20th century, the Anglo-American psychologist William McDougall was one of the first to write about the instinct theory of motivation. McDougall argued that instincts trigger many critical social practices. He viewed instincts as extremely sophisticated faculties in which specific provocations such as social impediments can drive a person’s state of mind in a particular direction, for example, towards a state of hatred, envy, or anger, which in turn may increase the probability of specific practices such as hostility or violence (McDougall, 2015 ).

However, in the early 1920s, McDougall’s perspective about human behaviour being driven by instincts faded remarkably as scientists supporting the concept of behaviourism started to get more attention with original ideas (Buss and Kenrick, 1998 ).

John B. Watson (1913)

The pioneer of the psychological school of behaviourism, John B. Watson, who conducted the controversial ‘Little Albert’ experiment by imposing a phobia on a child to evidence classical conditioning in humans (Harris, 1979 ), argued against the ideas of McDougall, even within public debates (Stephenson, 2003 ). Unlike McDougall, Watson considered the brain an empty page ( tabula rasa as described by Aristotle). According to him. all personality traits and behaviours directly result from the accumulated experience that starts from birth. Thus, the story of the human mind is a continuous writing process featured by surrounding events and factors. This perception was supported in the following years of the 20th century by anthropologists who revealed many very different social standards in different societies, and numerous social researchers argued that the wide variety of cross-cultural differences should lead to the conclusion that there is no mental content built-in from birth, and that all knowledge, therefore, comes from individual experience or perception (Farr, 1996 ). In stark contrast to McDougall, Watson suggested that human intuitions and behaviour patterns are the product of a learning process that starts blank.

B. F. Skinner (1938)

Inspired by the work of Pavlov, the American psychologist B.F. Skinner took the classical conditioning approach to a more advanced level by modifying a key aspect of the process. According to Skinner, human behaviour is dependent on the outcome of past activities. If the outcome is bad, the action will probably not be repeated; however, if the outcome is good, the likelihood of the activity being repeated is relatively high. Skinner called this process reinforcement learning (Schacter et al., 2011 ). Based on reinforcement learning, Skinner also introduced the concept of operant conditioning, a type of associative learning process through which the strength of a behaviour is adjusted by reinforcement or punishment. Considering, for example, a parent’s response to a child’s behaviour, the probability of the child repeating an action will be highly dependent on the parent’s reaction (Zilio, 2013 ). Effectively, Skinner argues that the intuitive System 1 may get edited and that a heuristical cue may become more or less ‘hard-wired’ in the subject’s brain as a stimulus leading to an automatic response.

The DNA and its environment (1953 onwards)

Today, there seems to be wide agreement that behaviour patterns in humans and other species are to some extent ‘in the DNA’, the structure of which was discovered by Francis Crick and James Watson in 1953, but that they also to some extent depend on ‘the environment’—including the social environment in which the agent lives and has problems to solve. Today, it seems safe to say, therefore, that the methods of problem-solving that humans apply are neither completely innate nor completely the result of environmental stimuli—but rather the product of the complex interaction between genes and the environment (Lerner, 1978 ).

Herbert Simon: rationality is bounded

Herbert Simon is well known for his contributions to several fields, including economics, psychology, computer science, and management. Simon proposed a remarkable theory that led him to be awarded the Nobel Prize for Economics in 1978.

Bounded rationality and satisficing

In the mid-1950s, Simon published A Behavioural Model of Rational Choice, which focused on bounded rationality: the idea that people must make decisions with limited time, mental resources, and information (Simon, 1955 ). He clearly states the triangle of limitations in every decision-making process—the availability of information, time, and cognitive ability (Bazerman and Moore, 1994 ). The ideas of Simon are considered an inspiring foundation for many technologies in use today.

Instead of conforming to the idea that economic behaviour can be seen as rational and dependent on all accessible data (i.e., as optimization), Simon suggested that the dynamics of decision-making were essentially ‘satisficing,’ a notion synthesized from ‘satisfy’ and ‘suffice’ (Byron, 1998 ). During the 1940s, scholars noticed the frequent failure of two assumptions required for ‘rational’ decision-making. The first is that data is never enough and may be far from perfect, while people dependably make decisions based on incomplete data. Second, people do not assess every feasible option before settling on a decision. This conduct is highly correlated with the cost of data collection since data turns out to be progressively harder and costlier to accumulate. Rather than trying to find the ideal option, people choose the first acceptable or satisfactory option they find. Simon described this procedure as satisficing and concluded that the human brain in the decision-making process would, at best, exhibit restricted abilities (Barros, 2010 ).

Since people can neither obtain nor process all the data needed to make a completely rational decision, they use the limited data they possess to determine an outcome that is ‘good enough’—a procedure later refined into the take-the-best heuristic. Simon’s view that people are bounded by their cognitive limits is usually known as the theory of bounded rationality (cf. Gigerenzer and Selten, 2001 ).

Herbert Simon and AI

With the cooperation of Allen Newell of the RAND Corporation, Simon attempted to create a computer simulator for human decision-making. In 1956, they created a ‘thinking’ machine called the ‘Logic Theorist’. This early smart device was a computer programme with the ability to prove theorems in symbolic logic. It was perhaps the first man-made programme that simulated some human reasoning abilities to solve actual problems (Gugerty, 2006 ). After a few years, Simon, Newell, and J.C. Shaw proposed the General Problem Solver or GPS, the first AI-based programme ever invented. They actually aimed to create a single programme that could solve all problems with the same unified algorithm. However, while the GPS was efficient with sufficiently well-structured problems like the Towers of Hanoi (a puzzle with 3 rods and different-sized disks to be moved), it could not solve real-life scenarios with all their complexities (A. Newell et al., 1959 ).

By 1965, Simon was confident that ‘machines will be capable of doing any work a man can do’ (Vardi, 2012 ). Therefore, Simon dedicated most of the remainder of his career to the advancement of machine intelligence. The results of his experiments showed that, like humans, certain computer programmes make decisions using trial-and-error and shortcut methods (Frantz, 2003 ). Quite explicitly, Simon and Newell ( 1958 , p. 7) referred to heuristics being used by both humans and intelligent machines: ‘Digital computers can perform certain heuristic problem-solving tasks for which no algorithms are available… In doing so, they use processes that are closely parallel to human problem-solving processes’.

Additionally, the importance of the environment was also clearly observed in Newell and Simon’s ( 1972 ) work:

‘Just as scissors cannot cut paper without two blades, a theory of thinking and problem-solving cannot predict behaviour unless it encompasses both an analysis of the structure of task environments and an analysis of the limits of rational adaptation to task requirements’ (p. 55).

Accordingly, the term ‘task environment’ describes the formal structure of the universe of choices and results for a specific problem. At the same time, Newell and Simon do not treat the agent and the environment as two isolated entities, but rather as highly related. Consequently, they tend to believe that agents with different cognitive abilities and choice repertoires will inhabit different task environments even though their physical surroundings and intentions might be the same (Agre and Horswill, 1997 ).

Heuristics in computer science

Computer science as a discipline may have the biggest share of deliberately applied heuristics. As heuristic problem-solving has often been contrasted with algorithmic problem-solving—even by Simon and Newell ( 1958 )—it is worth recalling that the very notion of ‘algorithm’ was clarified only in the first half of the 20th century, when Alan Turing ( 1937 ) defined what was later named ‘Turing-machine’. Basically, he defined ‘mechanical’ computation as a computation that can be done by a—stylized—machine. ‘Mechanical’ being what is also known today as algorithmic, one can say that any procedure that can be performed by a digital computer is algorithmic. Nevertheless, many of them are also heuristics because an algorithm may fail to produce an optimal solution to the problem it is meant to solve. This may be so either because the problem is ill-defined or because the computations required to produce the optimal solution may not be feasible with the available resources. If the problem is ill-defined—as it often is, e.g., in natural language processing—the algorithm that does the processing has to rely on a well-defined model that does not capture the vagueness and ambiguities of the real-life problem—a problem typically stated in natural language. If the problem is well-defined, but finding the optimal solution is not feasible, algorithms that would find it may exist ‘in principle’, but require too much time or memory to be practically implemented.

In fact, there is today a rich theory of complexity classes that distinguishes between types of (well-defined) problems according to how fast the time or memory space required to find the optimal solution increases with increasing problem size. E.g., for problem types of the complexity class P, any deterministic algorithm that produces the optimal solution has a running time bounded by a polynomial function of the input size, whereas, for problems of complexity class EXPTIME, the running time is bounded by an exponential function of the input size. In the jargon of computer science, problems of the latter class are considered intractable, although the input size has to become sufficiently large before the computation of the optimal solution becomes practically infeasible (cf. Harel, 2000 ; Hopcroft et al., 2007 ). Research indicates that the computational complexity of problems can also reduce the quality of human decision-making (Bossaerts and Murawski, 2017 ).

Shortest path algorithms

A classic optimization problem that may serve to illustrate the issues of optimal solution, complexity, and heuristics goes by the name of the travelling salesman problem (TSP), which was first introduced in 1930. In this problem, several cities with given distances between each two are considered, and the goal is to find the shortest possible path through all cities and return to the starting point. For a small input size, i.e., for a small number of cities, the ‘brute-force’ algorithm is easy to use: write down all the possible paths through all the cities, calculate their lengths, and choose the shortest. However, the number of steps that are required by this procedure quickly increases with the number of cities. The TSP is today known to belong to the complexity class NP which is in between P and EXPTIME Footnote 1 ). To solve the TSP, Jon Bentley ( 1982 ) proposed the greedy (or nearest-neighbour) algorithm that will yield an acceptable result, but not necessarily the optimal one, within a relatively short time. This approach always picks the nearest neighbour as the next city to visit without regard to possible later non-optimal steps. Hence, it is considered a good-enough solution with fast results. Bentley argued that there may be better solutions, but that it approximates the optimal solution. Many other heuristic algorithms have been explored later on. There is no assurance that the solution found by a heuristic algorithm will be an ideal answer for the given problem, but it is acceptable and adequate (Pearl, 1984 ).

Heuristic algorithms of the shortest path are utilized nowadays by GPS frameworks and self-driving vehicles to choose the best route from any point of departure to any destination (for example, A* Search Algorithm). Further developed algorithms can also consider additional elements, including traffic, speed limits, and quality of roads, they may yield the shortest routes in terms of distance and the fastest ones in terms of driving time.

Computer chess

While the TSP consists of a whole set of problems which differ by the number of cities and the distances between them, determining the optimal strategy for chess is just one problem of a given size. The rules of chess make it a finite game, and Ernst Zermelo proved in 1913 that it is ‘determined’: if it were played between perfectly rational players, it would always end with the same outcome: either White always wins, or Black always wins, or it always ends with a draw (Zermelo, 1913 ). Up to the present day, it is not known which of the three is true, which points to the fact that a brute-force algorithm that would go through all possible plays of chess is practically infeasible: it would have to explore too many potential moves, and the required memory would quickly run out of space (Schaeffer et al., 2007 ). Inevitably, a chess-playing machine has to use algorithms that are ‘shortcuts’—which can be more or less intelligent.

While Simon and Newell had predicted in 1958 that within ten years the world chess champion would be a computer, it took until 1997, when a chess-playing machine developed by IBM under the name Deep Blue defeated grandmaster Garry Kasparov. Although able to analyse millions of possibilities due to their computing powers, today’s chess-playing machines apply a heuristic approach to eliminate unlikely moves and focus on those with a high probability of defeating their opponent (Newborn, 1997 ).

Machine learning

One of the main features of machine learning is the ability of the model to predict a future outcome based on past data points. Machine learning algorithms build a knowledge base similar to human experience from previous experiences in the dataset provided. From this knowledge base, the model can derive educated guesses.

A good demonstration of this is the card game Top Trumps in which the model can learn to play and keep improving to dominate the game. It does so by undertaking a learning path through a sequence of steps in which it picks two random cards from the deck and then analyses and compares them with random criteria. According to the winning result, the model iteratively updates its knowledge base in the same manner as a human, following the rule that ‘practice makes perfect.’ Hence the model will play, collect statistics, update, and iterate while becoming more accurate with each increment (Volz et al., 2016 ).

Natural language processing

In the world of language understanding, current technologies are far from perfect. However, models are becoming more reliable by the minute. When analysing and dissecting a search phrase entered into the Google search engine, a background model tries to make sense of the search criteria. Stemming words, context analysis, the affiliation of phrases, previous searches, and autocorrect/autocomplete can be applied in a heuristic algorithm to display the most relevant result in less than a second. Heuristic methods can be utilized when creating certain algorithms to understand what the user is trying to express when searching for a phrase. For example, using word affiliation, an algorithm tries to narrow down the meaning of words as much as possible toward the user’s intention, particularly when a word has more than one meaning but changes with the context. Therefore, a search for apple pie allows the algorithm to deduce that the user is highly interested in recipes and not in the technology company (Sullivan, 2002 ).

Search and big data

Search is a good example to appreciate the value of time, as one of the most important criteria is retrieving acceptable results in an acceptable timeframe. In a full search algorithm, especially in large datasets, retrieving optimal results can take a massive amount of time, making it necessary to apply heuristic search.

Heuristic search is a type of search algorithm that is used to find solutions to problems in a faster way than an exhaustive search. It uses specific criteria to guide the search process and focuses on more favourable areas of the search space. This can greatly reduce the number of nodes required to find a solution, especially for large or complex search trees.

Heuristic search algorithms work by evaluating the possible paths or states in a search tree and selecting the better ones to explore further. They use a heuristic function, which is a measure of how close a given state is to the goal state, to guide the search. This allows the algorithm to prioritize certain paths or states over others and avoid exploring areas of the search space that are unlikely to lead to a solution. The reached solution is not necessarily the best, however, a ‘good enough’ one is found within a ‘fast enough’ time. This technique is an example of a trade-off between optimality and speed (Russell et al., 2010 ).

Today, there is a rich literature on heuristic methods in computer science (Martí et al., 2018 ). As the problem to be solved may be the choice of a suitable heuristic algorithm, there are also meta-heuristics that have been explored (Glover and Kochenberger, 2003 ), and even hyper-heuristics which may serve to find or generate a suitable meta-heuristic (Burke et al., 2003 ). As Sörensen et al. ( 2018 ) point out, the term ‘metaheuristic’ may refer either to an ‘algorithmic framework that provides a set of guidelines or strategies to develop heuristic optimization algorithms’—or to a specific algorithm that is based on such a framework. E.g., a metaheuristic to find a suitable search algorithm may be inspired by the framework of biological evolution and use its ideas of mutation, reproduction and selection to produce a particular search algorithm. While this algorithm will still be a heuristic one, the fact that it has been generated by an evolutionary process indicates its superiority over alternatives that have been eliminated in the course of that process (cf. Vikhar, 2016 ).

Daniel Kahneman and Amos Tversky: heuristics and biases

Inspired by the concepts of Herbert Simon, psychologists Daniel Kahneman and Amos Tversky initiated the heuristics and biases research programme in the early 1970s, which emphasized how individuals make judgements and the conditions under which those judgements may be inaccurate (Kahneman and Klein, 2009 ).

In addition, Kahneman and Tversky emphasized information processing to elaborate on how real people with limitations can decide, choose, or estimate (Kahneman, 2011 ).

The remarkable article Judgement under Uncertainty: Heuristics and Biases , published in 1974, is considered the turning key that opened the door wide to research on this topic, although it was and still is considered controversial (Kahneman, 2011 ). In their research, Kahneman and Tversky identified three types of heuristics by which probabilities are often assessed: availability, representativeness, and anchoring and adjustment. In passing, Kahneman and Tversky mention that other heuristics are used to form non-probabilistic judgements; for example, the distance of an object may be assessed according to the clarity with which it is seen. Other researchers subsequently introduced different types of heuristics. However, availability, representativeness, and anchoring are still considered fundamental heuristics for judgements under uncertainty.

Availability

According to the psychological definition, availability or accessibility is the ease with which a specific thought comes to mind or can be inferred. Many people use this type of heuristic when judging the probability of an event that may have happened or will happen in the future. Hence, people tend to overestimate the likelihood of a rare event if it easily comes to mind because it is frequently mentioned in daily discussions (Kahneman, 2011 ). For instance, individuals overestimate their probability of being victims of a terrorist attack while the real probability is negligible. However, since terrorist attacks are highly available in the media, the feeling of a personal threat from such an attack will also be highly available during our daily life (Kahneman, 2011 ).

This concept is also present in business, as we remember the successful start-ups whose founders quit college for their dreams, such as Steve Jobs and Mark Zuckerberg, and ignore the thousands of ideas, start-ups, and founders that failed. This is because successful companies are considered a hot topic and receive broad coverage in the media, while failures do not. Similarly, broad media coverage is known to create top-of-mind awareness (TOMA) (Farris et al., 2010 ). Moreover, the availability type of heuristics was offered as a clarification for fanciful connections or irrelevant correlations in which individuals wrongly judge two events to be related to each other when they are not. Tversky and Kahneman clarified that individuals judge relationships based on the ease of envisioning the two events together (Tversky and Kahneman, 1973 ).

Representativeness

The representativeness heuristic is applied when individuals assess the probability that an object belongs to a particular class or category based on how much it resembles the typical case or prototype representing this category (Tversky and Kahneman, 1974 ). Conceptually, this heuristic can be decomposed into three parts. The first one is that the ideal case or prototype of the category is considered representative of the group. The second part judges the similarity between the object and the representative prototype. The third part is that a high degree of similarity indicates a high probability that the object belongs to the category, and a low degree of similarity indicates a low probability.

While the heuristic is often applied automatically within an instant and may be compelling in many cases, Tversky and Kahneman point out that the third part of the heuristic will often lead to serious errors or, at any rate, biases.

In particular, the representativeness heuristic can give rise to what is known as the base rate fallacy. As an example, Tversky and Kahneman consider an individual named Steve, who is described as shy, withdrawn, and somewhat pedantic, and report that people who have to assess, based on this description, whether Steve is more likely to be a librarian or a farmer, invariably consider it more likely that he is a librarian—ignoring the fact that there are many more farmers than librarians, the fact that an estimate of the probability that Steve is a librarian or a farmer, respectively, must take into account.

Another example is that a taxicab was engaged in an accident. The data indicates that 85% of the taxicabs are green and 15% blue. An eyewitness claims that the involved cab was blue. The court then evaluates the witness for reliability because he is 80% accurate and 20% inaccurate. So now, what would be the probability of the involved cab being blue, given that the witness identified it as blue as well?

To evaluate this case correctly, people should consider the base rate, 15% of the cabs being blue, and the witness accuracy rate, 80%. Of course, if the number of cabs is equally split between colours, then the only factor in deciding is the reliability of the witness, which is an 80% probability.

However, regardless of the colours’ distribution, most participants would select 80% to respond to this enquiry. Even participants who wanted to take the base rate into account estimated a probability of more than 50%, while the right answer is 41% using the Bayesian inference (Kahneman, 2011 ).

In relation to the representativeness heuristic, Kahnemann ( 2011 ) illustrated the ‘conjunction fallacy’ in the following example: based only on a detailed description of a character named Linda, doctoral students in the decision science programme of the Stanford Graduate School of Business, all of whom had taken several advanced courses in probability, statistics, and decision theory, were asked to rank various other descriptions of Linda according to their probability. Even Kahneman and Tversky were surprised to find that 85% of the students ranked Linda as a bank teller active in the feminist movement as more likely than Linda as a bank teller.

From these and many other examples, one must conclude that even sophisticated humans use the representativeness heuristic to make probability judgements without referring to what they know about probability.

Representativeness is used to make probability judgements and judgements about causality. The similarity of A and B neither indicates that A causes B nor that B causes A. Nevertheless, if A precedes B and is similar to B, it is often judged to be B’s cause.

Adjustment and anchoring

Based on Tversky and Kahneman’s interpretations, the anchor is the first available number introduced in a question forming the centre of a circle whose radius (up or down) is an acceptable range within which lies the best answer (Baron, 2000 ). This is used and tested in several academic and real-world scenarios and in business negotiations where parties anchor their prices to formulate the range of acceptance through which they can close the deal, deriving the ceiling and floor from the anchor. The impact is more dominant when parties lack time to analyse actions thoroughly.

Significantly, even if the anchor is way beyond logical boundaries, it can still bias the estimated numbers by all parties without them even realizing that it does (Englich et al., 2006 ).

In one of their experiments, Tversky and Kahneman ( 1974 ) asked participants to quickly calculate the product of numbers from 1 to 8 and others to do so from 8 to 1. Since the time was limited to 5 min, they needed to make a guess. The group that started from 1 had an average of 512, while the group that started from 8 had an average of 2250. The right answer was 40,320.

Perhaps this is one of the most unclear cognitive heuristics introduced by Kahneman and Tversky that can be interchangeably considered as a bias instead of a heuristic. The problem is that the mind tends to fixate on the anchor and adjust according to it, whether it was introduced implicitly or explicitly. Some scholars even believe that such bias/heuristic is unavoidable. For instance, in one study, participants were asked if they believed that Mahatma Gandhi died before or after nine years old versus before or after 140 years old. Unquestionably, these anchors were considered unrealistic by the audience. However, when the participants were later asked to give their estimate of Gandhi’s age of death, the group which was anchored to 9 years old speculated the average age to be 50, while the group anchored to the highest value estimated the age of death to be as high as 67 (Strack and Mussweiler, 1997 ).

Gerd Gigerenzer: fast-and-frugal heuristics

The German psychologist Gerd Gigerenzer is one of the most influential figures in the field of decision-making, with a particular emphasis on the use of heuristics. He has built much of his research on the theories of Herbert Simon and considers that Simon’s theory of bounded rationality was unfinished (Gigerenzer, 2015 ). As for Kahneman and Tversky’s work, Gigerenzer has a different approach and challenges their ideas with various arguments, facts, and numbers.

Gigerenzer explores how people make sense of their reality with constrained time and data. Since the world around us is highly uncertain, complex, and volatile, he suggests that probability theory cannot stand as the ultimate concept and is incapable of interpreting everything, particularly when probabilities are unknown. Instead, people tend to use the effortless approach of heuristics. Gigerenzer introduced the concept of the adaptive toolbox, which is a collection of mental shortcuts that a person or group of people can choose from to solve a current problem (Gigerenzer, 2000 ). A heuristic is considered ecologically rational if adjusted to the surrounding ecosystem (Gigerenzer, 2015 ).

A daring argument of Gigerenzer, which very much opposes the heuristics and biases approach of Kahneman and Tversky, is that heuristics cannot be considered irrational or inferior to a solution by optimization or probability calculation. He explicitly argues that heuristics are not gambling shortcuts that are faster but riskier (Gigerenzer, 2008 ), but points to several situations where less is more, meaning that results from frugal heuristics, which neglect some data, were nevertheless more accurate than results achieved by seemingly more elaborate multiple regression or Bayesian methods that try to incorporate all relevant data. While researchers consider this counterintuitive since a basic rule in research seems to be that more data is always better than less, Gigerenzer points out that the less-is-more effect (abbreviated as LIME) could be confirmed by computer simulations. Without denying that in some situations, the effect of using heuristics may be biased (Gigerenzer and Todd, 1999 ), Gigerenzer emphasizes that fast-and-frugal heuristics are basic, task-oriented choice systems that are a part of the decision-maker’s toolbox, the available collection of cognitive techniques for decision-making (Goldstein and Gigerenzer, 2002 ).

Heuristics are considered economical because they are easy to execute, seek limited data, and do not include many calculations. Contrary to most traditional decision-making models followed in the social and behavioural sciences, models of fast-and-frugal heuristics portray not just the result of the process but also the process itself. They comprise three simple building blocks: the search rule that specifies how information is searched for, the stopping rule that specifies when the information search will be stopped, and finally, the decision rule that specifies how the processed information is integrated into a decision (Goldstein and Gigerenzer, 2002 ).

Rather than characterizing heuristics as rules of thumb or mental shortcuts that can cause biases and must therefore be regarded as irrational, Gigerenzer and his co-workers emphasize that fast-and-frugal heuristics are often ecologically rational, even if the conjunction of them may not even be logically consistent (Gigerenzer and Todd, 1999 ).

According to Goldstein and Gigerenzer ( 2002 ), a decision maker’s pool of mental techniques may contain logic and probability theory, but it also embraces a set of simple heuristics. It is compared to a toolbox because just as a wood saw is perfect for cutting wood but useless for cutting glass or hammering a nail into a wall, the ingredients of the adaptive toolbox are intended to tackle specific scenarios.

For instance, there are specific heuristics for choice tasks, estimation tasks, and categorization tasks. In what follows, we will discuss two well-known examples of fast-and-frugal heuristics: the recognition heuristic (RH), which utilizes the absence of data, and the take-the-best heuristic (TTB), which purposely disregards the data.

Both examples of heuristics can be connected to decision assignments and to circumstances in which a decision-maker needs to decide which of two options has a higher reward on a quantitative scale.

Ideal scenarios would be deducing which one of two stock shares will have a better income in the next month, which of two cars is more convenient for a family, or who is a better candidate for a particular job (Goldstein and Gigerenzer, 2002 ).

The recognition heuristic

The recognition heuristic has been examined broadly with the famous experiment to determine which of the two cities has a higher population. This experiment was conducted in 2002, and the participants were undergraduate students: one group in the USA and one in Germany. The question was as follows: which has more occupants—San Diego or San Antonio? Given the cultural difference between the student groups and the level of information regarding American cities, it could be expected that American students would have a higher accuracy rate than their German peers. However, most German students did not even know that San Antonio is an American city (Goldstein and Gigerenzer, 2002 ). Surprisingly, the examiners, Goldstein and Gigerenzer, found the opposite of what was expected. 100% of the German students got the correct answer, while the American students achieved an accuracy rate of around 66%. Remarkably, the German students who had never known about San Antonio had more correct answers. Their lack of knowledge empowered them to utilize the recognition heuristic, which states that if one of two objects is recognized and the other is not, then infer that the recognized object has the higher value concerning the relevant criterion. The American students could not use the recognition heuristic because they were familiar with both cities. Ironically, they knew too much.

The recognition heuristic is an incredible asset. In many cases, it is used for swift decisions since recognition is usually systematic and not arbitrary. Useful applications may be cities’ populations, players’ performance in major leagues, or writers’ level of productivity. However, this heuristic will be less efficient in more difficult scenarios than a city’s population, such as the age of the city’s mayor or its sea-level altitude (Gigerenzer and Todd, 1999 ).

Take-the-best heuristic

When the recognition heuristic is not efficient because the decision-maker has enough information about both options, another important heuristic can be used that relies on hints or cues to arrive at a decision. The take-the-best (TTB) heuristic is a heuristic that relies only on specific cues or signals and does not require any complex calculations. In practice, it often boils down to a one-reason decision rule, a type of heuristic where judgements are based on a single good reason only, ignoring other cues (Gigerenzer and Gaissmaier, 2011 ). According to the TTB heuristic, a decision-maker evaluates the case by selecting the attributes which are important to him and sorts these cues by importance to create a hierarchy for the decision to be taken. Then alternatives are compared according to the first, i.e., the most important, cue; if an alternative is the best according to the first cue, the decision is taken. Otherwise, the decision-maker moves to the next layer and checks that level of cues. In other words, the decision is based on the most important attribute that allows one to discriminate between the alternatives (Gigerenzer and Goldstein, 1996 ). Although this lexicographic preference ordering is well known from traditional economic theory, it appears there mainly to provide a counterexample to the existence of a real-valued utility function (Debreu, 1959 ). Surprisingly, however, it seems to be used in many critical situations. For example, in many airports, the customs officials may decide if a traveller is chosen for a further check by looking only at the most important attributes, such as the city of departure, nationality, or luggage weight (Pachur and Marinello, 2013 ). Moreover, in 2012, a study explored voters’ views of how US presidential competitors would deal with the single issue that voters viewed as most significant, for example, the state of the economy or foreign policy. A model dependent on this attribute picked the winner in most cases (Graefe and Armstrong, 2012 ).

However, the TTB heuristic has a stopping rule applied when the search reaches a discriminating cue. So, if the most important signal discriminates, there is no need to continue searching for other cues, and only one signal is considered. Otherwise, the next most important signal will be considered. If no discriminating signal is found, the heuristic will need to make a random guess (Gigerenzer and Gaissmaier, 2011 ).

Empirical evidence on fast-and-frugal heuristics

More studies have been conducted on fast-and-frugal heuristics using analytical methods and simulations to investigate when and why heuristics yield accurate results on the one hand, and on the other hand, using experiments and observational methods to find out whether and when people use fast-and-frugal heuristics (Luan et al., 2019 ). Structured examinations and benchmarking with standard models, for example, regression or Bayesian models, have shown that the accuracy of fast-and-frugal heuristics relies upon the structure of the information environment (e.g., the distribution of signal validities, the interrelation between signals, etc.). In numerous situations, fast-and-frugal heuristics can perform well, particularly in generalized contexts, when making predictions for new cases that have not been previously experienced. Empirical examinations show that people utilize fast-and-frugal heuristics under a time constraint when data is hard to obtain or must be retrieved from memory. Remarkably, some studies have inspected how individuals adjust to various situations by learning. Rieskamp and Otto ( 2006 ) found that individuals seemingly learn to choose the heuristic that has the best performance in a specific domain. Nevertheless, Reimer and Katsikopoulos ( 2004 ) found that individuals apply fast-and-frugal heuristics when making inferences in groups.

While interest in heuristics has been increasing, some of the literature has been mostly critical. In particular, the heuristics and biases programme introduced by Kahneman and Tversky has been the target of more than one critique (Reisberg, 2013 ).

The arguments are mainly in two directions. The first is that the main focus is on the coherence standards such as rationality and that the detection of biases ignores the context-environmental factors where the judgements occur (B.R. Newell, 2013 ). The second is that notions such as availability or representativeness are vague and undefined, and state little regarding the procedures’ hidden judgements (Gigerenzer, 1996 ). For example, it has been argued that the replies in the acclaimed Linda-the-bank-teller experiment could be considered sensible instead of biased if one uses conversational or colloquial standards instead of formal probability theory (Hilton, 1995 ).

The argument of having a vague explanation for certain phenomena can be illustrated when considering the following two scenarios. People tend to believe that an opposite outcome will be achieved after having a stream of the same outcome (e.g., people tend to believe that ‘heads’ should be the next outcome in a coin-flipping game with many consecutive ‘tails’). This is called the gambler fallacy (Barron and Leider, 2010 ). By contrast, the hot-hand fallacy (Gilovich et al., 1985 ) argues that people tend to believe that a stream of the same outcome will continue when there is a lucky day (e.g., a player is taking a shot in a sport such as a basketball after a series of successful attempts). Ayton and Fisher ( 2004 ) argued that, although these two practices are quite opposite, they have both been classified under the heuristic of representativeness. In the two cases, a flawed idea of random events drives observers to anticipate that a certain stream of results is representative of the whole procedure. In the first scenario of coin flipping, people tend to believe that a long stream of tails should not occur; hence the head is predicted. While in the case of the sports player, the stream of the same outcome is expected to continue (Gilovich et al., 1985 ). Therefore, representativeness cannot be diagnosed without considering in advance the expected results. Also, the heuristic does not clarify why people have the urge to believe that a stream of random events should have a representative, while in real life, it does not (Ayton and Fischer, 2004 ).

Nevertheless, the most common critique of Kahneman and Tversky is the idea that ‘we cannot be that dumb’. It states that the heuristics and biases programme is overly pessimistic when assessing the average human decision-making. Also, humans collectively have accumulated many achievements and discoveries throughout human history that would not have been possible if their ability to adequate decision-making had been so limited (Gilovich and Griffin, 2002 ).

Similarly, the probabilistic mental models (PMM) theory of human inference inspired by Simon and pioneered by Gigerenzer has also been exposed to criticism (B.R. Newell et al., 2003 ). Indeed, the enticing character of heuristics that they are both easy to apply and efficient has made them famous within different domains. However, it has also made them vulnerable to replications or variations of the experiments that challenge the original results. For example, Daniel Oppenheimer ( 2003 ) argues that the recognition heuristic (RH) could not yield satisfactory results after replicating the experiment of city populations. He claims that the participants’ judgements failed to obey the RH not just when there were cues other and stronger than mere recognition but also in circumstances where recognition would have been the best cue available. In any case, one could claim that there are numerous methods in the adaptive toolbox and that under certain conditions, people may prefer to use heuristics other than the RH. However, this statement is also questionable since many heuristics that are thought to exist in the adaptive toolbox acknowledge the RH as an initial step (Gigerenzer and Todd, 1999 ). Hence, if individuals are not using the RH, they cannot use many of the other heuristics in the adaptive toolbox (Oppenheimer, 2003 ). Likewise, Newell et al. ( 2003 ) question whether the fast-and-frugal heuristics accurately explain actual human behaviour. In two experiments, they challenged the take-the-best (TTB) heuristic, as it is considered a building block in the PMM framework. The outcomes of these experiments, together with others, such as those of Jones et al. ( 2000 ) and Bröder ( 2000 ), show that the TTB heuristic is not a reliable approach even within circumstances favouring its use. In a somewhat heated debate published in the Psychological Review 1996, Gigerenzer’s criticism of Kahneman and Tversky that many of the so-called biases ‘disappear’ if frequencies rather than probabilities are assumed, was countered by Kahneman and Tversky ( 1996 ) by means of a detailed re-examination of the conjunction fallacy (or Linda Problem). Gigerenzer ( 1996 ) remained unconvinced, and was in turn, blamed by Kahneman and Tversky ( 1996 , p. 591) for just reiterating ‘his objections … without answering our main arguments’.

Our historical review has revealed a number of issues that have received little attention in the literature.

Deliberate vs. automatic heuristics

We have differentiated between deliberate and automatic heuristics, which often seem to be confused in the literature. While it is a widely shared view today that the human brain often relies heavily on the fast and effortless ‘System 1’ in decision-making, but can also use the more demanding tools of ‘System 2’, and it has been acknowledged, e.g. by Kahneman ( 2011 , p. 98), that some heuristics belong to System 1 and others to System 2, the two systems are not as clearly distinct as it may seem. In fact, the very wide range of what one may call ‘heuristics’ shows that there is a whole spectrum of fallible decision-making procedures—ranging from the probably innate problem-solving strategy of the baby that cries whenever it is hungry or has some other problem, to the most elaborate and sophisticated procedures of, e.g., Polya, Bolzano, or contemporary chess-engines. One may be tempted to characterize instinctive procedures as subconscious and sophisticated ones as conscious, but a deliberate heuristic can very well become a subconsciously applied ‘habit of the mind’ or learnt routine with experience and repetition. Vice versa, automatic, subconscious heuristics can well be raised to consciousness and be applied deliberately. E.g., the ‘inductive inference’ from tasty strawberries to the assumption that all red berries are sweet and edible may be quite automatic and subconscious in little children, but the philosophical literature on induction shows that it can be elaborated into something quite conscious. However, while the notion of consciousness may be crucial for an adequate understanding of heuristics in human cognition, for the time being, it seems to remain a philosophical mystery (Harley, 2021 ; Searle, 1997 ), and once programmed, sophisticated heuristic algorithms can be executed by automata.

The deliberate heuristics that we reviewed also illustrate that some of them can hardly be called ‘simple’, ‘shortcuts’, or ‘rules of thumb’. E.g., the heuristics of Descartes, Bolzano, or Polya each consist of a structured set of suggestions, and, e.g., ‘to devise a plan’ for a mathematical proof is certainly not a shortcut. Llull ( 1308 , p. 329), to take another example, wrote of his ‘ars magna’ that ‘the best kind of intellect can learn it in two months: one month for theory and another month for practice’.

Heuristics vs. algorithms

Our review of heuristics also allowed us to clarify the distinction between heuristics and algorithms. As evidenced by our glimpse at computer science, there are procedures that are quite obviously both an algorithm and a heuristic. Within computer science, they are in fact quite common. Algorithms of the heuristic type may be required for certain problems even though an algorithm that finds the optimal solution exists ‘in principle’—as in the case of determining the optimal strategy in chess, where the brute-force-method to enumerate all possible plays of chess is just not practically feasible. In other cases, heuristic algorithms are used because an exhaustive search, while practically feasible, would be too costly or time-consuming. Clearly, for many problems, there are also problem-solving algorithms which always do produce the optimal solution in a reasonable time frame. Given our definition of a heuristic as a fallible method, algorithms of this kind are counterexamples to the complaint that the notion has become so wide that ‘any procedure can be called a heuristic’. However, as we have seen, there are also heuristic procedures that are non-algorithmic. These may be necessary either because the problem to be solved is not sufficiently well-defined to allow for an algorithm, or because an algorithm that would solve the problem at hand, is not known or does not exist. Kleining’s qualitative heuristics is an example of non-algorithmic heuristics necessitated by the ill-defined problems of research in the social sciences, while Polya’s heuristic for solving mathematical problems is an example of the latter: an algorithm that would allow one to decide if a given mathematical conjecture is a theorem or not does not exist (cf. Davis, 1965 ).

Pre-SEU vs. post-SEU heuristics

As we noted in the introduction, the emergence of the SEU theory can be regarded as a kind of watershed for the research on heuristics, as it came to be regarded as the standard definition of rational choice. Post-SEU, fallible methods of decision-making would have to face comparison with this standard. Gigerenzer’s almost belligerent criticism of SEU shows that even today it seems difficult to discuss the pros and cons of heuristics unless one relates them to the backdrop of SEU. However, his criticism of SEU is mostly en passant and seems to assume that the SEU model requires ‘known probabilities’ (e.g., Gigerenzer, 2021 ), ignoring the fact that it is, in general, subjective probabilities, as derived from the agent’s preferences among lotteries, that the model relies on (cf. e.g., Jeffrey, 1967 or Gilboa, 2011 ). In fact, when applied to an ill-defined decision problem in, e.g., management, the SEU theory may well be regarded as a heuristic—it asks you to consider the possible consequences of the relevant set of actions, your preferences among those consequences, and the likelihood of those consequences. To the extent that one may get all of these elements wrong, SEU is a fallible method of decision-making. To be sure, it is not a fast and effortless heuristic, but our historical review of pre-SEU heuristics has illustrated that heuristics may be quite elaborate and require considerable effort and attention.

It is quite true, of course, that the SEU heuristic will hardly be helpful in problem-solving that is not ‘just’ decision-making. If, e.g., the problem to be solved is to find a proof for a mathematical conjecture, the set of possible actions will in general be too vast to be practically contemplated, let alone evaluated according to preferences and probabilities.

Positive vs. negative heuristics

To the extent that the study of heuristics aims at understanding how decisions are actually made, it is not only positive heuristics that need to be considered. It will also be required to investigate the conditions that may prevent the agent from adopting certain courses of action. As we saw, Lakatos used the notion of negative heuristics quite explicitly to characterize research programmes, but we also briefly review Duncker’s notion of ‘functional fixedness’ as an example of a hindrance to adequate problem-solving. A systematic study of such negative heuristics seems to be missing in the literature and we believe that it may be a helpful complement to the study of positive heuristics which has dominated the literature that we reviewed.

To the extent that heuristics are studied with the normative aim of identifying effective heuristics, it may also be useful to consider approaches that should not be taken. ‘Do not try to optimize!’ might be a negative heuristic favoured by the fast-and-frugal school of thought.

Heuristics as the product of evolution

Clearly, heuristics have always existed throughout the development of human knowledge due to the ‘old mind’s’ evolutionary roots and the frequent necessity to apply fast and sufficiently reliable behaviour patterns. However, unlike the behaviour patterns in the other animals, the methods used by humans in problem-solving are sufficiently diverse that the dual-process theory was suggested to provide some structure to the rich ‘toolbox’ humans can and do apply. As all our human DNA is the product of evolution, it is not only the intuitive inclinations to react to certain stimuli in a particular way that must be seen as the product of evolution, but also our ability to abstain from following our gut feelings when there is reason to do so, to reflect and analyse the situation before we embark on a particular course of action. Quite frequently, we experience a tension between our intuitive inclinations and our analytic mind’s judgement, but both of them are somehow the product of evolution, our biography, and the environment. Thus, to point out that gut feelings are an evolved capacity of the brain does in no way provide an argument that would support their superiority over the reflective mind.

Moreover, compared to the speed of problem change in our human lifetimes, biological evolution is very slow. The evolved capacities of the human brain may have been well-adapted to the survival needs of our ancestors some 300,000 years ago, but there is little reason to believe that they are uniformly well-adapted to human problem-solving in the 21st century.

Resource-bounded and ecological rationality

Throughout our review, the reader will have noticed that many heuristics have been suggested for specific problem areas. The methods of the ancient Greeks were mainly centred around solving geometrical problems. Llull was primarily concerned with theological questions, Descartes and Leibniz pursued ‘mechanical’ solutions to philosophical issues, Polya suggested heuristics for Mathematics, Müller for engineering, and Kleining for social science research. This already suggests that heuristics suitable for one type of problem need not be suitable for a different type. Likewise, the automatic heuristics that both the Kahneman-Tversky and the Gigerenzer schools focused on, are triggered by particular tasks. Simon’s observation that the success of a given heuristic will depend on the environment in which it is employed, is undoubtedly an important one that has motivated Gigerenzer’s notion of ecological rationality and is strikingly absent from the SEU model. If ‘environment’ is taken in a broad sense that includes the available resources, the cost of time and effort, the notion seems to cover what has been called resource-rational behaviour (e.g., Bhui et al., 2021 ).

Avenues of further research

A comprehensive study describing the current status of the research on heuristics and their relation to SEU seems to be missing and is beyond the scope of our brief historical review. Insights into their interrelationship can be expected from recent attempts at formal modelling of human cognition that take the issues of limited computational resources and context-dependence of decision-making seriously. E.g., Lieder and Griffiths ( 2020 ) do this from a Bayesian perspective, while Busemeyer et al. ( 2011 ) and Pothos and Busemeyer ( 2022 ) use a generalization of standard Kolmogorov probability theory that is also the basis of quantum mechanics and quantum computation. While it may seem at first glance that such modelling assumes even more computational power than the standard SEU model of decision-making, the computational power is not assumed on the part of the human decision-maker. Rather, the claim is that the decision-maker behaves as if s/he would solve an optimization problem under additional constraints, e.g., on computational resources. The ‘as if’ methodology that is employed here is well-known to economists (Friedman, 1953 ; Mäki, 1998 ) and also to mathematical biologists who have used Bayesian models to explain animal behaviour (McNamara et al., 2006 ; Oaten, 1977 ; Pérez-Escudero and de Polavieja, 2011 ). Evolutionary arguments might be invoked to support this methodology if a survival disadvantage can be shown to result from behaviour patterns that are not Bayesian optimal, but we are not aware of research that would substantiate such arguments. However, attempting to do so by embedding formal models of cognition in models of evolutionary game theory may be a promising avenue for further research.

NP stands for ‘nondeterministic polynomial-time’, which indicates that the optimal solution can be found by a nondeterministic Turing-machine in a running time that is bounded by a polynomial function of the input size. In fact, the TSP is ‘NP-hard’ which means that it is ‘at least as hard as the hardest problems in the category of NP problems’.

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8.2 Problem-Solving: Heuristics and Algorithms

Learning objectives.

• Describe the differences between heuristics and algorithms in information processing.

When faced with a problem to solve, should you go with intuition or with more measured, logical reasoning? Obviously, we use both of these approaches. Some of the decisions we make are rapid, emotional, and automatic. Daniel Kahneman (2011) calls this “fast” thinking. By definition, fast thinking saves time. For example, you may quickly decide to buy something because it is on sale; your fast brain has perceived a bargain, and you go for it quickly. On the other hand, “slow” thinking requires more effort; applying this in the same scenario might cause us not to buy the item because we have reasoned that we don’t really need it, that it is still too expensive, and so on. Using slow and fast thinking does not guarantee good decision-making if they are employed at the wrong time. Sometimes it is not clear which is called for, because many decisions have a level of uncertainty built into them. In this section, we will explore some of the applications of these tendencies to think fast or slow.

We will look further into our thought processes, more specifically, into some of the problem-solving strategies that we use. Heuristics are information-processing strategies that are useful in many cases but may lead to errors when misapplied. A heuristic is a principle with broad application, essentially an educated guess about something. We use heuristics all the time, for example, when deciding what groceries to buy from the supermarket, when looking for a library book, when choosing the best route to drive through town to avoid traffic congestion, and so on. Heuristics can be thought of as aids to decision making; they allow us to reach a solution without a lot of cognitive effort or time.

The benefit of heuristics in helping us reach decisions fairly easily is also the potential downfall: the solution provided by the use of heuristics is not necessarily the best one. Let’s consider some of the most frequently applied, and misapplied, heuristics in the table below.

In many cases, we base our judgments on information that seems to represent, or match, what we expect will happen, while ignoring other potentially more relevant statistical information. When we do so, we are using the representativeness heuristic . Consider, for instance, the data presented in the table below. Let’s say that you went to a hospital, and you checked the records of the babies that were born on that given day. Which pattern of births do you think you are most likely to find?

Most people think that list B is more likely, probably because list B looks more random, and matches — or is “representative of” — our ideas about randomness, but statisticians know that any pattern of four girls and four boys is mathematically equally likely. Whether a boy or girl is born first has no bearing on what sex will be born second; these are independent events, each with a 50:50 chance of being a boy or a girl. The problem is that we have a schema of what randomness should be like, which does not always match what is mathematically the case. Similarly, people who see a flipped coin come up “heads” five times in a row will frequently predict, and perhaps even wager money, that “tails” will be next. This behaviour is known as the gambler’s fallacy . Mathematically, the gambler’s fallacy is an error: the likelihood of any single coin flip being “tails” is always 50%, regardless of how many times it has come up “heads” in the past.

The representativeness heuristic may explain why we judge people on the basis of appearance. Suppose you meet your new next-door neighbour, who drives a loud motorcycle, has many tattoos, wears leather, and has long hair. Later, you try to guess their occupation. What comes to mind most readily? Are they a teacher? Insurance salesman? IT specialist? Librarian? Drug dealer? The representativeness heuristic will lead you to compare your neighbour to the prototypes you have for these occupations and choose the one that they seem to represent the best. Thus, your judgment is affected by how much your neibour seems to resemble each of these groups. Sometimes these judgments are accurate, but they often fail because they do not account for base rates , which is the actual frequency with which these groups exist. In this case, the group with the lowest base rate is probably drug dealer.

Our judgments can also be influenced by how easy it is to retrieve a memory. The tendency to make judgments of the frequency or likelihood that an event occurs on the basis of the ease with which it can be retrieved from memory is known as the availability heuristic (MacLeod & Campbell, 1992; Tversky & Kahneman, 1973). Imagine, for instance, that I asked you to indicate whether there are more words in the English language that begin with the letter “R” or that have the letter “R” as the third letter. You would probably answer this question by trying to think of words that have each of the characteristics, thinking of all the words you know that begin with “R” and all that have “R” in the third position. Because it is much easier to retrieve words by their first letter than by their third, we may incorrectly guess that there are more words that begin with “R,” even though there are in fact more words that have “R” as the third letter.

The availability heuristic may explain why we tend to overestimate the likelihood of crimes or disasters; those that are reported widely in the news are more readily imaginable, and therefore, we tend to overestimate how often they occur. Things that we find easy to imagine, or to remember from watching the news, are estimated to occur frequently. Anything that gets a lot of news coverage is easy to imagine. Availability bias does not just affect our thinking. It can change behaviour. For example, homicides are usually widely reported in the news, leading people to make inaccurate assumptions about the frequency of murder. In Canada, the murder rate has dropped steadily since the 1970s (Statistics Canada, 2018), but this information tends not to be reported, leading people to overestimate the probability of being affected by violent crime. In another example, doctors who recently treated patients suffering from a particular condition were more likely to diagnose the condition in subsequent patients because they overestimated the prevalence of the condition (Poses & Anthony, 1991).

The anchoring and adjustment heuristic is another example of how fast thinking can lead to a decision that might not be optimal. Anchoring and adjustment is easily seen when we are faced with buying something that does not have a fixed price. For example, if you are interested in a used car, and the asking price is $10,000, what price do you think you might offer? Using $10,000 as an anchor, you are likely to adjust your offer from there, and perhaps offer $9000 or $9500. Never mind that $10,000 may not be a reasonable anchoring price. Anchoring and adjustment does not just happen when we’re buying something. It can also be used in any situation that calls for judgment under uncertainty, such as sentencing decisions in criminal cases (Bennett, 2014), and it applies to groups as well as individuals (Rutledge, 1993).

In contrast to heuristics, which can be thought of as problem-solving strategies based on educated guesses, algorithms are problem-solving strategies that use rules. Algorithms are generally a logical set of steps that, if applied correctly, should be accurate. For example, you could make a cake using heuristics — relying on your previous baking experience and guessing at the number and amount of ingredients, baking time, and so on — or using an algorithm. The latter would require a recipe which would provide step-by-step instructions; the recipe is the algorithm. Unless you are an extremely accomplished baker, the algorithm should provide you with a better cake than using heuristics would. While heuristics offer a solution that might be correct, a correctly applied algorithm is guaranteed to provide a correct solution. Of course, not all problems can be solved by algorithms.

As with heuristics, the use of algorithmic processing interacts with behaviour and emotion. Understanding what strategy might provide the best solution requires knowledge and experience. As we will see in the next section, we are prone to a number of cognitive biases that persist despite knowledge and experience.

Key Takeaways

• We use a variety of shortcuts in our information processing, such as the representativeness, availability, and anchoring and adjustment heuristics. These help us to make fast judgments but may lead to errors.
• Algorithms are problem-solving strategies that are based on rules rather than guesses. Algorithms, if applied correctly, are far less likely to result in errors or incorrect solutions than heuristics. Algorithms are based on logic.

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MacLeod, C., & Campbell, L. (1992). Memory accessibility and probability judgments: An experimental evaluation of the availability heuristic.  Journal of Personality and Social Psychology, 63 (6), 890–902.

Poses, R. M., & Anthony, M. (1991). Availability, wishful thinking, and physicians’ diagnostic judgments for patients with suspected bacteremia.  Medical Decision Making,  11 , 159-68.

Rutledge, R. W. (1993). The effects of group decisions and group-shifts on use of the anchoring and adjustment heuristic. Social Behavior and Personality, 21 (3), 215-226.

Statistics Canada. (2018). Ho micide in Canada, 2017 . Retrieved from https://www150.statcan.gc.ca/n1/en/daily-quotidien/181121/dq181121a-eng.pdf

Tversky, A., & Kahneman, D. (1973). Availability: A heuristic for judging frequency and probability.  Cognitive Psychology, 5 , 207–232.

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German heuristisch , from New Latin heuristicus , from Greek heuriskein to discover; akin to Old Irish fo- fúair he found

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1860, in the meaning defined at sense 1

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Heuristics in Mathematics Education

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In this entry we examine Polya’s contribution to the role of heuristics in problem solving, in attempting to propose a model for enhancing students’ problem-solving skills in mathematics and its implications in the mathematics education.

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Research studies in the area of problem solving, a central issue in mathematics education during the past four decades, have placed a major focus on the role of heuristics and its impact on students’ abilities in problem solving. The groundwork for explorations in heuristics was established by the Hungarian Jewish mathematician George Polya in his famous book “ How to Solve It ” (1945) and was given a much more extended treatment in his Mathematical Discovery books (1962, 1965). In “ How to Solve It ,” Polya ( 1945 ) initiated the discussion on heuristics by tracing their study back to Pappus, one of the commentators of Euclid, and other great mathematicians and philosophers like Descartes and Leibniz, who attempted to build a...

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English L, Sriraman B (2010) Problem solving for the 21st century. In: Sriraman B, English L (eds) Theories of mathematics education: seeking new frontiers. Springer, Berlin, pp 263–290

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Heuristics Unleashed: A Comprehensive Guide to Heuristics in Computer Science and Programming

Heuristics are nothing new, they play an important role in our daily lives, in both problem-solving and data-driven decision-making (DDDM) . As nowadays, the world is full of information, and our brains are only capable of processing a certain amount of it, heuristics help us a lot in this sense. Because if you would try to analyze every single aspect of every situation or decision, you would never get anything done.

We take thousands of decisions every single day and most of them we don’t really think about, we “know” how to behave in certain situations based on our experience and that’s what heuristics are about. When we are trying to solve a problem or make a decision, we often turn to these mental shortcuts when we need a quick solution.

Introduction to Heuristics

In the world of computer science, heuristics play a vital role in tackling complex problems and providing efficient solutions. This introductory section will explore the concept of heuristics and highlight their significance in problem-solving.

Definition of Heuristics

Heuristics is practical problem-solving techniques or methods used to find quick and effective solutions when dealing with complex issues. They are only sometimes guaranteed to produce the best or optimal solution, but they often lead to satisfactory results within a reasonable time frame. Heuristics are particularly useful when dealing with problems that have incomplete, uncertain, or imprecise information or when the search space is too ample for a complete, exhaustive search.

Importance of Heuristics in Problem Solving

The importance of heuristics in problem-solving is evident in their versatility and adaptability across different computer science domains. Some of the reasons why heuristics are crucial for problem-solving include:

• Efficiency : Heuristics can significantly reduce the time and resources needed to solve problems, especially when the search space is enormous, or the problem is too complex.
• Simplicity : Heuristic methods are often easier to implement and understand than complicated algorithms, making them more accessible to a broader audience.
• Flexibility : Heuristics can be applied to various problem domains, often with minor modifications, making them versatile problem-solving tools.
• Robustness : In situations where the available data is incomplete, uncertain, or noisy, heuristics can still provide helpful solutions, making them applicable to real-world problems.

History of Heuristics in Computer Science

Heuristics have been crucial to the growth and advancement of computer science. Here's how the history of heuristics and how they have changed over time.

Early Beginnings

Ancient Greek mathematicians and philosophers used heuristic techniques to solve mathematical and logical issues, giving rise to heuristic usage. 

Yet, with the development of artificial intelligence (AI) research in the 1950s and 1960s, heuristics were formally introduced in computer science for the first time.

Alan Turing, one of the early AI pioneers, first suggested a heuristic search in his landmark article " Computing Machines and Intelligence ." The exploration of heuristics as a tool to solve challenging problems in AI and computer science was made possible thanks to Turing's work.

George Pólya, another important person, wrote the famous book " How to Solve It " in 1945. It offered a collection of heuristics for resolving mathematical issues. Many computer scientists and researchers were motivated by Pólya's efforts to

Evolution of Heuristic Techniques

Over the years, heuristic techniques have evolved and diversified to address various complex problems in computer science. Some of the most notable developments in the history of heuristics include:

• Game Theory : In the 1950s and 1960s, researchers like Claude Shannon and Arthur Samuel developed early heuristics to explore optimal game strategies like chess and checkers. Their work paved the way for more advanced heuristic techniques used in game theory today.
• Optimization : In the 1970s, researchers began developing metaheuristic optimization algorithms, such as genetic and simulated annealing, to find near-optimal solutions to complex optimization problems.
• Machine Learning : The 1980s and 1990s witnessed significant advancements in machine learning techniques, such as decision trees and neural networks, which rely on heuristic methods to learn from data and make predictions.
• Human-Computer Interaction : Heuristic evaluation, a method for identifying usability issues in user interfaces, was introduced by Jakob Nielsen in the 1990s, highlighting the application of heuristics in human-computer interaction.
• As computer science continues to evolve, so do heuristic techniques, with researchers constantly developing new and innovative ways to apply heuristics to tackle increasingly complex problems.

So, What is Heuristic Programming?

Heuristics are mental shortcuts that help us make decisions and judgments quickly without having to spend a lot of time researching and analyzing information. They usually involve focusing on one aspect of a complex problem and ignoring others. They work well under most circumstances, but they can lead to systematic deviations from logic, probability, or rational choice. Examples that employ heuristics include using a rule of thumb, an educated guess, an intuitive judgment, a guesstimate, stereotyping, profiling, or common sense.

Heuristics in Software Development

Heuristics have become indispensable to software engineering , helping developers create more efficient, maintainable, and user-friendly software. This section will explore various ways heuristics are employed in software development.

Design Patterns

Design patterns are reusable solutions to common problems that arise in software design. They are heuristics that software developers can apply when faced with specific design challenges. By leveraging these well-established patterns, developers can create more maintainable and scalable software while avoiding common pitfalls.

Some widely used design patterns include:

• Singleton : Assures a class has just one instance and offers a universal access point to that instance.
• Factory Method : Establishes a framework for instantiating objects in a superclass, allowing subclasses to select the objects they want to use.
• Observer : Establishes a one-to-many relationship between objects so that all of its dependents are automatically informed and updated when one changes.

Agile Development

Agile development methodologies , such as Scrum and Kanban, have become famous for managing software projects more efficiently in recent years. These methodologies incorporate heuristics to streamline development, improve collaboration, and deliver high-quality software.

Some critical heuristics in agile development include:

• Iterative Development : Agile methodologies promote short development cycles, allowing teams to gather feedback continuously, identify issues, and adjust their plans accordingly.
• Time-boxing : Setting strict time limits for tasks helps teams maintain focus and prevents them from getting bogged down in unnecessary details.
• Daily Stand-ups : Regular short meetings enable team members to share updates, identify roadblocks, and ensure everyone is on the same page.
• Prioritization : Agile methodologies prioritize tasks based on their value to the end user, ensuring that the most critical features are delivered first.

Code Smells and Refactoring

Code smells indicate potential problems in the source code, often resulting from poor design choices or programming practices. Heuristics can be used to identify these code smells and guide developers in refactoring their code to improve its maintainability, readability, and overall quality.

Some examples of code smells, and corresponding refactoring techniques include:

• Long Method : A method that is too long and difficult to understand can be broken down into smaller, more manageable processes.
• Duplicate Code : Identical or similar code in multiple locations can be consolidated into a single reusable method or class.
• Feature Envy : When a method accesses data from another class more than its data, moving the technique to that class may be more appropriate.
• Software engineers can produce more effective, maintainable, and user-friendly software that satisfies the requirements of their customers and end users by utilizing heuristics in the development process.

Heuristics in Computer Sciences

In computer science, a heuristic is a problem-solving strategy or method that is not guaranteed to find the optimal solution, but is designed to find a satisfactory solution in a reasonable amount of time. Heuristics are often used in artificial intelligence, search algorithms, and optimization problems where it is not possible or impractical to use an algorithm that guarantees a correct solution.

Heuristics are often based on experience, intuition, or common sense and are used to guide the search for a solution in a way that is efficient and effective. They can be useful in situations where the problem is too complex or too large to be solved by an algorithm that guarantees a correct solution.

Examples of heuristics in computer science include:

• Best-first search
• Hill climbing
• Simulated annealing
• Genetic algorithms

Heuristics can be very useful in computer science, they can be faster and more efficient than other techniques, but they are also less reliable and might not provide optimal solutions.

In computer science, artificial intelligence , and mathematical optimization, a heuristic is a technique designed for solving a problem more quickly when classic methods are too slow or for finding an approximate solution when classic methods fail to find any exact solution. This is achieved by trading optimality, completeness, accuracy, or precision for speed. 

Heuristic programming employs a practical method, not guaranteed to be optimal, perfect, logical, or rational, but instead sufficient for reaching an immediate goal. It is important to highlight that Heuristics are the strategies derived from previous experiences with similar problems. These strategies rely on using readily accessible, though loosely applicable, information to control problem-solving in human beings, machines, and abstract issues.  And the objective of a heuristic is to produce a solution in a reasonable time frame that is good enough for solving the problem at hand. 

The trade-off criteria for deciding whether to use a heuristic for solving a given problem:

• Optimality: When several solutions exist for a given problem, does the heuristic guarantee that the best solution will be found? Is it actually necessary to find the best solution?
• Completeness: When several solutions exist for a given problem, can the heuristic find them all? Do we actually need all solutions? Many heuristics are only meant to find one solution.
• Accuracy and precision: Can the heuristic provide a confidence interval for the purported solution? Is the error bar on the solution unreasonably large?
• Execution time: Is this the best-known heuristic for solving this type of problem? Some heuristics converge faster than others. Some heuristics are only marginally quicker than classic methods.

And now, the main question is: why do we rely on heuristics?  Psychologists have suggested a few different theories:

• Effort reduction: According to this theory, people utilize heuristics as a type of cognitive laziness. Heuristics reduce the mental effort required to make choices and decisions.
• Attribute substitution: Other theories suggest people substitute simpler but related questions in place of more complex and difficult questions.
• Fast and frugal: Still other theories argue that heuristics are actually more accurate than they are biased. In other words, we use heuristics because they are fast and usually correct.

This is in contrast to algorithmic programming, which is based on mathematically provable procedures. But what is important to understand here is that Heuristic programming is characterized by programs that are self-learning; they get better with experience. Remember, heuristics don't guarantee the best or perfect solution, but they often lead to good solutions in a reasonable time frame, which is why they're so widely used in computer science.

Let us know about your thoughts and experience with heuristic programming, we would be happy to discuss it in the comments section below.