heuristic approaches to problem solving

Heuristic is an adjective for experience-based techniques that help in problem solving, learning and discovery. A heuristic method is used to rapidly come to a solution that is hoped to be close to the best possible answer, or 'optimal solution'. Heuristics are "rules of thumb", educated guesses, intuitive judgments or simply common sense. A heuristic is a general way of solving a problem. Heuristics as a noun is another name for heuristic methods. In more precise terms, heuristics stand for strategies using readily accessible, though loosely applicable, information to control problem solving in human beings and machines.

While an algorithm is a method containing finite set of instructions used to solving a problem. The method has been proven mathematically or scientifically to work for the problem. There are formal methods and proofs.

Heuristic algorithm is an algorithm that is able to produce an acceptable solution to a problem in many practical scenarios, in the fashion of a general heuristic, but for which there is no formal proof of its correctness.

An algorithm is a self-contained step-by-step set of operations to be performed 4 , typically interpreted as a finite sequence of (computer or human) instructions to determine a solution to a problem such as: is there a path from A to B, or what is the smallest path between A and B. In the latter case, you could also be satisfied with a 'reasonably close' alternative solution.

There are certain categories of algorithms, of which the heuristic algorithm is one. Depending on the (proven) properties of the algorithm in this case, it falls into one of these three categories (note 1):

Notice that an approximation algorithm is also a heuristic, but with the stronger property that there is a proven bound to the solution (value) it outputs.

For some problems, noone has ever found an 'efficient' algorithm to compute the optimal solutions (note 2). One of those problems is the well-known Traveling Salesman Problem. Christophides' algorithm for the Traveling Salesman Problem, for example, used to be called a heuristic , as it was not proven that it was within 50% of the optimal solution. Since it has been proven, however, Christophides' algorithm is more accurately referred to as an approximation algorithm.

Due to restrictions on what computers can do, it is not always possible to efficiently find the best solution possible. If there is enough structure in a problem, there may be an efficient way to traverse the solution space, even though the solution space is huge (i.e. in the shortest path problem).

Heuristics are typically applied to improve the running time of algorithms, by adding 'expert information' or 'educated guesses' to guide the search direction. In practice, a heuristic may also be a sub-routine for an optimal algorithm, to determine where to look first .

(note 1) : Additionally, algorithms are characterised by whether they include random or non-deterministic elements. An algorithm that always executes the same way and produces the same answer, is called deterministic.

(note 2) : This is called the P vs NP problem, and problems that are classified as NP-complete and NP-hard are unlikely to have an 'efficient' algorithm. Note; as @Kriss mentioned in the comments, there are even 'worse' types of problems, which may need exponential time or space to compute.

There are several answers that answer part of the question. I deemed them less complete and not accurate enough, and decided not to edit the accepted answer made by @Kriss

Actually I don't think that there is a lot in common between them. Some algorithm use heuristics in their logic (often to make fewer calculations or get faster results). Usually heuristics are used in the so called greedy algorithms.

Heuristics is some "knowledge" that we assume is good to use in order to get the best choice in our algorithm (when a choice should be taken). For example ... a heuristics in chess could be (always take the opponents' queen if you can, since you know this is the stronger figure). Heuristics do not guarantee you that will lead you to the correct answer, but (if the assumptions is correct) often get answer which are close to the best in much shorter time.

An Algorithm is a clearly defined set of instructions to solve a problem, Heuristics involve utilising an approach of learning and discovery to reach a solution.

So, if you know how to solve a problem then use an algorithm. If you need to develop a solution then it's heuristics.

This should be the accepted answer. Should be stressed that both the programmer and the (complex) algorithm can use the heuristics approach. – G M Apr 27, 2022 at 7:12

Heuristics are algorithms, so in that sense there is none, however, heuristics take a 'guess' approach to problem solving, yielding a 'good enough' answer, rather than finding a 'best possible' solution.

A good example is where you have a very hard (read NP-complete) problem you want a solution for but don't have the time to arrive to it, so have to use a good enough solution based on a heuristic algorithm, such as finding a solution to a travelling salesman problem using a genetic algorithm.

Algorithm is a sequence of some operations that given an input computes something (a function) and outputs a result.

Algorithm may yield an exact or approximate values.

It also may compute a random value that is with high probability close to the exact value.

A heuristic algorithm uses some insight on input values and computes not exact value (but may be close to optimal). In some special cases, heuristic can find exact solution.

A heuristic is usually an optimization or a strategy that usually provides a good enough answer, but not always and rarely the best answer. For example, if you were to solve the traveling salesman problem with brute force, discarding a partial solution once its cost exceeds that of the current best solution is a heuristic: sometimes it helps, other times it doesn't, and it definitely doesn't improve the theoretical (big-oh notation) run time of the algorithm

I think Heuristic is more of a constraint used in Learning Based Model in Artificial Intelligent since the future solution states are difficult to predict.

But then my doubt after reading above answers is "How would Heuristic can be successfully applied using Stochastic Optimization Techniques? or can they function as full fledged algorithms when used with Stochastic Optimization?"

http://en.wikipedia.org/wiki/Stochastic_optimization

oops!! spelling mistake it should be "Artificial Intelligence" – A_tanA Jan 26, 2011 at 18:06

One of the best explanations I have read comes from the great book Code Complete , which I now quote:

A heuristic is a technique that helps you look for an answer. Its results are subject to chance because a heuristic tells you only how to look, not what to find. It doesn’t tell you how to get directly from point A to point B; it might not even know where point A and point B are. In effect, a heuristic is an algorithm in a clown suit. It’s less predict- able, it’s more fun, and it comes without a 30-day, money-back guarantee. Here is an algorithm for driving to someone’s house: Take Highway 167 south to Puy-allup. Take the South Hill Mall exit and drive 4.5 miles up the hill. Turn right at the light by the grocery store, and then take the first left. Turn into the driveway of the large tan house on the left, at 714 North Cedar. Here’s a heuristic for getting to someone’s house: Find the last letter we mailed you. Drive to the town in the return address. When you get to town, ask someone where our house is. Everyone knows us—someone will be glad to help you. If you can’t find anyone, call us from a public phone, and we’ll come get you. The difference between an algorithm and a heuristic is subtle, and the two terms over-lap somewhat. For the purposes of this book, the main difference between the two is the level of indirection from the solution. An algorithm gives you the instructions directly. A heuristic tells you how to discover the instructions for yourself, or at least where to look for them.

Stating that there exists a difference between an algorithm and a heuristic is like stating that there is a difference between a bird and a chicken. Heuristics are a type of algorithm. – Joost Jan 21, 2016 at 8:08

They find a solution suboptimally without any guarantee as to the quality of solution found, it is obvious that it makes sense to the development of heuristics only polynomial. The application of these methods is suitable to solve real world problems or large problems so awkward from the computational point of view that for them there is not even an algorithm capable of finding an approximate solution in polynomial time.

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Algorithms and heuristics

Obstacles to effective thinking.

Other means of solving problems incorporate procedures associated with mathematics, such as algorithms and heuristics , for both well- and ill-structured problems. Research in problem solving commonly distinguishes between algorithms and heuristics, because each approach solves problems in different ways and with different assurances of success.

A problem-solving algorithm is a procedure that is guaranteed to produce a solution if it is followed strictly. In a well-known example, the “ British Museum technique,” a person wishes to find an object on display among the vast collections of the British Museum but does not know where the object is located. By pursuing a sequential examination of every object displayed in every room of the museum, the person will eventually find the object, but the approach is likely to consume a considerable amount of time. Thus, the algorithmic approach, though certain to succeed, is often slow.

A problem-solving heuristic is an informal, intuitive, speculative procedure that leads to a solution in some cases but not in others. The fact that the outcome of applying a heuristic is unpredictable means that the strategy can be either more or less effective than using an algorithm . Thus, if one had an idea of where to look for the sought-after object in the British Museum, a great deal of time could be saved by searching heuristically rather than algorithmically. But if one happened to be wrong about the location of the object, one would have to try another heuristic or resort to an algorithm.

Although there are several problem-solving heuristics, a small number tend to be used frequently. They are known as means-ends analysis, working forward, working backward, and generate-and-test.

In means-ends analysis, the problem solver begins by envisioning the end, or ultimate goal, and then determines the best strategy for attaining the goal in his current situation. If, for example, one wished to drive from New York to Boston in the minimum time possible, then, at any given point during the drive, one would choose the route that minimized the time it would take to cover the remaining distance, given traffic conditions, weather conditions, and so on.

In the working-forward approach, as the name implies, the problem solver tries to solve the problem from beginning to end. A trip from New York City to Boston might be planned simply by consulting a map and establishing the shortest route that originates in New York City and ends in Boston. In the working-backward approach, the problem solver starts at the end and works toward the beginning. For example, suppose one is planning a trip from New York City to Paris. One wishes to arrive at one’s Parisian hotel. To arrive, one needs to take a taxi from Orly Airport. To arrive at the airport, one needs to fly on an airplane; and so on, back to one’s point of origin.

Often the least systematic of the problem-solving heuristics, the generate-and-test method involves generating alternative courses of action, often in a random fashion, and then determining for each course whether it will solve the problem. In plotting the route from New York City to Boston, one might generate a possible route and see whether it can get one expeditiously from New York to Boston; if so, one sticks with that route. If not, one generates another route and evaluates it. Eventually, one chooses the route that seems to work best, or at least a route that works. As this example suggests, it is possible to distinguish between an optimizing strategy, which gives one the best path to a solution, and a satisficing strategy, which is the first acceptable solution one generates. The advantage of optimizing is that it yields the best possible strategy; the advantage of satisficing is that it reduces the amount of time and energy involved in planning.

A better understanding of the processes of thought and problem solving can be gained by identifying factors that tend to prevent effective thinking. Some of the more common obstacles, or blocks, are mental set, functional fixedness, stereotypes , and negative transfer.

A mental set, or “entrenchment,” is a frame of mind involving a model that represents a problem, a problem context , or a procedure for problem solving. When problem solvers have an entrenched mental set, they fixate on a strategy that normally works well but does not provide an effective solution to the particular problem at hand. A person can become so used to doing things in a certain way that, when the approach stops working, it is difficult for him to switch to a more effective way of doing things.

Functional fixedness is the inability to realize that something known to have a particular use may also be used to perform other functions. When one is faced with a new problem, functional fixedness blocks one’s ability to use old tools in novel ways. Overcoming functional fixedness first allowed people to use reshaped coat hangers to get into locked cars, and it is what first allowed thieves to pick simple spring door locks with credit cards.

Another block involves stereotypes . The most common kinds of stereotypes are rationally unsupported generalizations about the putative characteristics of all, or nearly all, members of a given social group . Most people learn many stereotypes during childhood. Once they become accustomed to stereotypical thinking, they may not be able to see individuals or situations for what they are.

Negative transfer occurs when the process of solving an earlier problem makes later problems harder to solve. It is contrasted with positive transfer, which occurs when solving an earlier problem makes it easier to solve a later problem. Learning a foreign language, for example, can either hinder or help the subsequent learning of another language.

For a variety of reasons, the finding of an optimal solution is impractical for many O.R. problems. A common way of overcoming this unhappy state of affairs is the development of heuristic (approximate) methods. The purpose of this paper is to discuss some of the issues that arise with such an approach-that is, the use of a method which, on the basis of experience of judgement, seems likely to yield good solutions but which cannot guarantee optimality. The use of such methods is motivated by the emergence of the theory of NP-completeness, i.e. the study of the complexity of algorithms, which is briefly introduced. A number of heuristic methods are presented in order to illustrate some of the ideas discussed. Heuristic procedures are classified according to design. Some of the problems of both how to design effective heuristics and how to use heuristics in the real world are discussed.

The Editorial Policy of the Journal of the Operational Research Society is: The Journal is a peer-refereed journal published 12 times a year on behalf of the Operational Research Society. It is the aim of the Journal to publish papers, including those from non-members of the Society, which are relevant to practitioners, researchers, teachers, students and consumers of operational research, and which cover the theory, practice, history or methodology of operational research. However, since operational research is primarily an applied science, it is a major objective of the Journal to attract and publish accounts of good, practical case studies. Consequently, papers illustrating applications of OR to real problems are especially welcome.

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Heuristic problem solving example

This Heuristic problem solving example supplies step-by-step instructions for solving all math troubles.

For example, an instant message about winning the latest automobile in exchange for a particular sum of money seems intriguing. People, however, pay just to be

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You can learn anything you want if you're willing to put in the time and effort. Just find a good tutorial and follow the instructions.

Math can be challenging, but with a little practice, it can be easy to clear up math tasks.

Using Heuristic Problem

We encounter heuristic examples daily when we discover our own solutions to a problem. See how many types you've done with examples of heuristics.

Heuristic Techniques for Problem Solving

Explanation. When you see a person with their hood up in a dark alley and you decide to subtly walk past a bit faster, your brain has probably used a heuristic to evaluate the situation instead of a full thought-out deliberation process.

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Examples of Heuristics in Everyday Life

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7.3 Problem-Solving

Learning objectives.

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

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.

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 :

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:

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.

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.

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 ________.

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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Problem-solving techniques that result in a quick and practical solution

What are Heuristics?

Heuristics are problem-solving techniques that result in a quick and practical solution. In contrast to business decisions that involve extensive analysis, heuristics are used in situations where a short-term solution is required.

Although heuristics may not result in the most optimal and ideal solution, it allows companies to speed up their decision-making process and achieve an adequate solution for the short term.

In situations where perfect solutions may be improbable, heuristics can be used to achieve imperfect but satisfactory decisions. Heuristics can also include mental shortcuts that help speed up the decision-making process.

Understanding Heuristics

When facing complex situations with limited time and resources, heuristics can help companies make quick decisions by using shortcuts and approximated calculations. Most heuristic methods involve using mental shortcuts to make decisions based on prior experiences.

Some of the most common fundamental heuristic methods include trial and error, historical data analysis, guesswork, and the process of elimination. Such methods typically involve easily accessible information that is not specific to the problem but is broadly applicable. It provides an opportunity to make imperfect decisions that can adequately address the problem in the short term.

Depending on the context, there may be several different heuristic methods, which correlate to the scope of the problem. They can include affect, representative, and availability heuristics.

Types of Heuristics

Affect Heuristics

Affect heuristics are based on positive and negative feelings that are associated with a certain stimulus. It typically involves quick, reactionary feelings that are based on prior beliefs. The theory of affect heuristics is that one’s emotional response to a stimulus can affect an individual’s decisions.

When people face little time to reflect and evaluate a situation carefully, they may base their decision on their immediate emotional reactions. Rather than conducting a cost-benefit analysis, affect heuristics focus on eliciting an automatic, reactionary response.

For example, it’s been shown that advertisements can influence consumers’ emotions and therefore affect their purchasing decisions. One of the most common examples is advertisements for products such as fast food. When fast-food companies run ads, they hope to elicit a positive emotional response that encourages you to view their products positively.

If individuals were to analyze the risks and benefits of consuming fast food carefully, they might decide that it is an unhealthy option. However, people rarely take the time to evaluate everything they see and often base their decisions on their automatic, emotional response. Fast-food ads rely on such a type of affect heuristic to generate a positive emotional response, which results in sales.

Availability Heuristics

Availability heuristics are judgments people make regarding the likelihood of an event based on information that comes to mind quickly. When people make decisions, they typically rely on prior knowledge of an event. As a result, we tend to overestimate the likelihood of an event occurring simply because it comes to mind quickly. Such mental shortcuts allow us to make decisions quickly, but they can also be inaccurate.

One example of the availability heuristic is stock prices, especially for newly public companies. Many investors tend to invest in new IPOs in the hopes that the stock price will increase significantly in the next few years. Rather than analyzing the company’s fundamentals, the investors remember IPOs that have become tremendously successful, such as Amazon or Apple.

Although it has been shown that most IPOs underperform, investors tend to overestimate the chances of landing a successful IPO based on prior examples that come to mind. It demonstrates a clear example of availability heuristics.

Representative Heuristics

Representative heuristics occur when we evaluate the probability of an event based on its similarity to another event. In general, people tend to overestimate the likelihood of an event occurring based on their perceived similarity with another event. When it happens, we tend to ignore the base rate, which is the actual probability of an event occurring, independent of its similarity to other events.

An example of the representative heuristic is product packaging, as consumers tend to associate quality products with their external packaging. If a generic brand packages its products in a way that resembles a well-known, high-quality product, then consumers will associate the generic product as having the same quality as the branded product.

Instead of evaluating the quality of the products, consumers are correlating the quality of the products based on the similarity in packaging.

More Resources

CFI is the official provider of the global Business Intelligence & Data Analyst (BIDA)® certification program, designed to help anyone become a world-class financial analyst. To keep advancing your career, the additional CFI resources below will be useful:

An Introduction to Problem-Solving using Search Algorithms for Beginners

This article was published as a part of the Data Science Blogathon

In computer science, problem-solving refers to artificial intelligence techniques, including various techniques such as forming efficient algorithms, heuristics, and performing root cause analysis to find desirable solutions.

The basic crux of artificial intelligence is to solve problems just like humans.

Examples of Problems in Artificial Intelligence

In today’s fast-paced digitized world, artificial intelligence techniques are used widely to automate systems that can use the resource and time efficiently. Some of the well-known problems experienced in everyday life are games and puzzles. Using AI techniques, we can solve these problems efficiently. In this sense, some of the most common problems resolved by AI are

Problem solving techniques.

Properties of searching algorithms

Types of search algorithms

Uninformed search algorithms, comparison of various uninformed search algorithms, informed search algorithms, comparison of uninformed and informed search algorithms.

In artificial intelligence, problems can be solved by using searching algorithms, evolutionary computations, knowledge representations, etc.

In this article, I am going to discuss the various searching techniques that are used to solve a problem.

In general, searching is referred to as finding information one needs.

The process of problem-solving using searching consists of the following steps.

Let’s discuss some of the essential properties of search algorithms.

Properties of search algorithms

Completeness.

A search algorithm is said to be complete when it gives a solution or returns any solution for a given random input.

If a solution found is best (lowest path cost) among all the solutions identified, then that solution is said to be an optimal one.

Time complexity

The time taken by an algorithm to complete its task is called time complexity. If the algorithm completes a task in a lesser amount of time, then it is an efficient one.

Space complexity

It is the maximum storage or memory taken by the algorithm at any time while searching.

These properties are also used to compare the efficiency of the different types of searching algorithms.

Now let’s see the types of the search algorithm.

Based on the search problems, we can classify the search algorithm as

The uninformed search algorithm does not have any domain knowledge such as closeness, location of the goal state, etc. it behaves in a brute-force way. It only knows the information about how to traverse the given tree and how to find the goal state. This algorithm is also known as the Blind search algorithm or Brute -Force algorithm.

The uninformed search strategies are of six types.

Let’s discuss these six strategies one by one.

1. Breadth-first search

It is of the most common search strategies. It generally starts from the root node and examines the neighbor nodes and then moves to the next level. It uses First-in First-out (FIFO) strategy as it gives the shortest path to achieving the solution.

BFS is used where the given problem is very small and space complexity is not considered.

Now, consider the following tree.

Breadth-First search | Problem-Solving using AI

Source: Author

Here, let’s take node A as the start state and node F as the goal state.

The BFS algorithm starts with the start state and then goes to the next level and visits the node until it reaches the goal state.

In this example, it starts from A and then travel to the next level and visits B and C and then travel to the next level and visits D, E, F and G. Here, the goal state is defined as F. So, the traversal will stop at F.

The path of traversal is:

A —-> B —-> C —-> D —-> E —-> F

Let’s implement the same in python programming.

Python Code:

Advantages of BFS

Disadvantages of BFS

2. Depth-first search

The depth-first search uses Last-in, First-out (LIFO) strategy and hence it can be implemented by using stack. DFS uses backtracking. That is, it starts from the initial state and explores each path to its greatest depth before it moves to the next path.

DFS will follow

Root node —-> Left node —-> Right node

Now, consider the same example tree mentioned above.

Here, it starts from the start state A and then travels to B and then it goes to D. After reaching D, it backtracks to B. B is already visited, hence it goes to the next depth E and then backtracks to B. as it is already visited, it goes back to A. A is already visited. So, it goes to C and then to F. F is our goal state and it stops there.

A —-> B —-> D —-> E —-> C —-> F

The output path is as follows.

Advantages of DFS

Disadvantages of DFS

3. Depth-limited search

Depth-limited works similarly to depth-first search. The difference here is that depth-limited search has a pre-defined limit up to which it can traverse the nodes. Depth-limited search solves one of the drawbacks of DFS as it does not go to an infinite path.

DLS ends its traversal if any of the following conditions exits.

Standard Failure

It denotes that the given problem does not have any solutions.

Cut off Failure Value

It indicates that there is no solution for the problem within the given limit.

Now, consider the same example.

Let’s take A as the start node and C as the goal state and limit as 1.

The traversal first starts with node A and then goes to the next level 1 and the goal state C is there. It stops the traversal.

Depth-limited search example | Problem-Solving using AI

A —-> C

If we give C as the goal node and the limit as 0, the algorithm will not return any path as the goal node is not available within the given limit.

If we give the goal node as F and limit as 2, the path will be A, C, F.

Let’s implement DLS.

When we give C as goal node and 1 as limit the path will be as follows.

Advantages of DLS

It takes lesser memory when compared to other search techniques.

Disadvantages of DLS

4. Iterative deepening depth-first search

Iterative deepening depth-first search is a combination of depth-first search and breadth-first search. IDDFS find the best depth limit by gradually adding the limit until the defined goal state is reached.

Let me try to explain this with the same example tree.

Consider, A as the start node and E as the goal node. Let the maximum depth be 2.

The algorithm starts with A and goes to the next level and searches for E. If not found, it goes to the next level and finds E.

Iterative deepening depth-first search example

The path of traversal is

A —-> B —-> E

Let’s try to implement this.

The path generated is as follows.

Advantages of IDDFS

Disadvantages of IDDFS

It does all the works of the previous stage again and again.

5. Bidirectional search

The bidirectional search algorithm is completely different from all other search strategies. It executes two simultaneous searches called forward-search and backwards-search and reaches the goal state. Here, the graph is divided into two smaller sub-graphs. In one graph, the search is started from the initial start state and in the other graph, the search is started from the goal state. When these two nodes intersect each other, the search will be terminated.

Bidirectional search requires both start and goal start to be well defined and the branching factor to be the same in the two directions.

Consider the below graph.

Bidirectional Search Example | Problem-Solving using AI

Here, the start state is E and the goal state is G. In one sub-graph, the search starts from E and in the other, the search starts from G. E will go to B and then A. G will go to C and then A. Here, both the traversal meets at A and hence the traversal ends.

E —-> B —-> A —-> C —-> G

Let’s implement the same in Python.

The path is generated as follows.

Advantages of bidirectional search

Disadvantages of bidirectional search

6. Uniform cost search

Uniform cost search is considered the best search algorithm for a weighted graph or graph with costs. It searches the graph by giving maximum priority to the lowest cumulative cost. Uniform cost search can be implemented using a priority queue.

Consider the below graph where each node has a pre-defined cost.

Uniform Cost Search example | Problem-Solving using AI

Here, S is the start node and G is the goal node.

From S, G can be reached in the following ways.

Here, the path with the least cost is S, B, E, F, G.

Let’s implement UCS in Python.

The optimal output path is generated.

Advantages of UCS

This algorithm is optimal as the selection of paths is based on the lowest cost.

Disadvantages of UCS

The algorithm does not consider how many steps it goes to reach the lowest path. This may result in an infinite loop also.

Now, let me compare the six different uninformed search strategies based on the time complexity.

This is all about uninformed search algorithms.

Let’s take a look at informed search algorithms.

The informed search algorithm is also called heuristic search or directed search. In contrast to uninformed search algorithms, informed search algorithms require details such as distance to reach the goal, steps to reach the goal, cost of the paths which makes this algorithm more efficient.

Here, the goal state can be achieved by using the heuristic function.

The heuristic function is used to achieve the goal state with the lowest cost possible. This function estimates how close a state is to the goal.

Let’s discuss some of the informed search strategies.

1. Greedy best-first search algorithm

Greedy best-first search uses the properties of both depth-first search and breadth-first search. Greedy best-first search traverses the node by selecting the path which appears best at the moment. The closest path is selected by using the heuristic function.

Consider the below graph with the heuristic values.

Greedy best-first search algorithm example | Problem-Solving using AI

Here, A is the start node and H is the goal node.

Greedy best-first search first starts with A and then examines the next neighbour B and C. Here, the heuristics of B is 12 and C is 4. The best path at the moment is C and hence it goes to C. From C, it explores the neighbours F and G. the heuristics of F is 8 and G is 2. Hence it goes to G. From G, it goes to H whose heuristic is 0 which is also our goal state.

Path of traversal in Greedy best-first search algorithm | Problem-Solving using AI

A —-> C —-> G —-> H

Let’s try this with Python.

The output path with the lowest cost is generated.

The time complexity of Greedy best-first search is O(b m ) in worst cases.

Advantages of Greedy best-first search

Greedy best-first search is more efficient compared with breadth-first search and depth-first search.

Disadvantages of Greedy best-first search

Next, let’s discuss the other informed search algorithm called the A* search algorithm.

2. A* search algorithm

A* search algorithm is a combination of both uniform cost search and greedy best-first search algorithms. It uses the advantages of both with better memory usage. It uses a heuristic function to find the shortest path. A* search algorithm uses the sum of both the cost and heuristic of the node to find the best path.

Consider the following graph with the heuristics values as follows.

A* search example | Problem-Solving using AI

Let A be the start node and H be the goal node.

First, the algorithm will start with A. From A, it can go to B, C, H.

Note the point that A* search uses the sum of path cost and heuristics value to determine the path.

Here, from A to B, the sum of cost and heuristics is 1 + 3 = 4.

From A to C, it is 2 + 4 = 6.

From A to H, it is 7 + 0 = 7.

Here, the lowest cost is 4 and the path A to B is chosen. The other paths will be on hold.

Now, from B, it can go to D or E.

From A to B to D, the cost is 1 + 4 + 2 = 7.

From A to B to E, it is 1 + 6 + 6 = 13.

The lowest cost is 7. Path A to B to D is chosen and compared with other paths which are on hold.

Here, path A to C is of less cost. That is 6.

Hence, A to C is chosen and other paths are kept on hold.

From C, it can now go to F or G.

From A to C to F, the cost is 2 + 3 + 3 = 8.

From A to C to G, the cost is 2 + 2 + 1 = 5.

The lowest cost is 5 which is also lesser than other paths which are on hold. Hence, path A to G is chosen.

From G, it can go to H whose cost is 2 + 2 + 2 + 0 = 6.

Here, 6 is lesser than other paths cost which is on hold.

Also, H is our goal state. The algorithm will terminate here.

Path of traversal in A* | Problem-Solving using AI

Let’s try this in Python.

The output is given as

The time complexity of the A* search is O(b^d) where b is the branching factor.

Advantages of A* search algorithm

Disadvantages of A* search algorithm

Now, let’s compare uninformed and informed search strategies.

Uninformed search is also known as blind search whereas informed search is also called heuristics search. Uniformed search does not require much information. Informed search requires domain-specific details. Compared to uninformed search, informed search strategies are more efficient and the time complexity of uninformed search strategies is more. Informed search handles the problem better than blind search.

Search algorithms are used in games, stored databases, virtual search spaces, quantum computers, and so on. In this article, we have discussed some of the important search strategies and how to use them to solve the problems in AI and this is not the end. There are several algorithms to solve any problem. Nowadays, AI is growing rapidly and applies to many real-life problems. Keep learning! Keep practicing!

About the Author

Dhanya thailappan.

Data Science and AI enthusiast

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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.

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Heuristic method: Four principles

Pólya describes the following four principles in his book:

Heuristic Method Principles George Ploya - toolshero

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.

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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.

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How to Use Heuristics in Problem Solving and Minimise Errors

Posted by: Si Conroy in Strategy & Plans Leave a comment

Intuition is closely related to heuristics because intuition can be interpreted as layers of experience and knowledge in an area. The greater your experience of various aspects of the area, and the more niche the area – enabling a concentration of experience – the stronger your intuition can be argued to be.

So in fact we all use heuristics all the time in making judgements, problem solving and decision making.

The problem with heuristics and intuition could be seen as incomplete information in the face of complex problems. Experience and loosely applicable information as the basis from which to solve problems immediately sounds potentially flawed. This is even more of a problem when we recognise that emotions play a substantial role in heuristics and intuition. The errors we make because of the use of heuristics and intuition are called cognitive biases .

We immediately recognise the heuristics of trial & error and rules of thumb, and we have a sense of how they are flawed – arguably because less emotion is used in this type of shortcut. We need to be far more self aware to spot our cognitive biases when we use other heuristics. In fact, we often don’t recognise that we’re using heuristics, so to maintain awareness of the potential cognitive biases inherent in them is very challenging.

The following are the top 4 tips to use heuristics in problem solving and minimise errors:

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What Are Heuristics?

Understanding heuristics, advantages of using heuristics, disadvantages of using heuristics, example of heuristics in behavioral economics, heuristics and psychology, the bottom line.

Investing Basics

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

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A heuristic is a mental shortcut 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

Watch Now: What Are Heuristics?

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."

The main advantage to using heuristics is that they allow us 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 us to go beyond our 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.

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 bias our understanding of the world. Such heuristics have been identified and catalogued by the field of behavioral economics.

Pros and Cons of Heuristics

Quick & easy

Allows decision-making that goes beyond our cognitive capacity

Allows for snap-judgements when time is limited

Often inaccurate

Can lead to systemic biases or errors in judgment

Representativeness

Although his 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 salesman begins 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 probabilities of events occurring.

Confirmation Bias

Confirmation bias is a well-documented heuristic whereby people give more weight to information that fits with our 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 towards 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. But 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.

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 catalogues 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 for people's irrational use of heuristics, in order to help them achieve more optimal outcomes. For instance, by having people opt out of a retirement savings plan by default, instead of having to opt-in.

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.

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 vs. emotional biases or errors in judgment vs. 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., save 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 with 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.

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Exact Algorithm or Heuristic?

A step-by-step guide to make the right choice for your mathematical optimization problem.

Are you struggling to find the best method for solving your optimization problem? When it comes to solving optimization problems, there are two main approaches: (meta-)heuristics and exact algorithms. Each approach has its own strengths and weaknesses, and the choice of method will depend on the specific characteristics of the problem. In this post, we will explore the differences between heuristics and exact algorithms, and help you decide which method is best suited for your problem.

Often used exact algorithms are linear programming , mixed integer programming and constraint programming . Famous heuristics are local search, genetic algorithms and particle swarm optimization. To improve an heuristic like local search it’s interesting to combine it with meta-heuristics like simulated annealing or tabu search.

In this post, we’ll start with an example to compare and explain different characteristics of exact algorithms and heuristics. The parts that follow will explain some considerations when choosing for an exact algorithm or heuristic, starting with a flowchart to make it even easier for you to make the right choice!

Besides the considerations of this post, other factors can play a part in your choice, like experience with different methods or maybe even gut feeling. This is a heads up that this post tries to generalize, but that every problem can have its own characteristics and circumstances that make you choose a certain approach, or let you deviate from the flowchart.

Comparison by Example

Let’s start with an example to explain the main differences between exact algorithms and heuristics: say you have a delivery company with a fleet of trucks that need to deliver packages to different locations. The goal of the problem is to determine the best routes for each truck to deliver the packages in the most efficient way, while taking into account factors such as distance, delivery time windows, and truck capacity. This problem is a variation of the capacitated vehicle routing problem.

An exact algorithm for this problem might be a MIP model that formulates the problem as a mathematical optimization problem. The MIP model would consider all the constraints and objective(s) of the problem, and find the optimal solution that minimizes the total delivery time and cost, while ensuring that all the packages are delivered on time and within the capacity of each truck.

However, solving the MIP model for large problems can be computationally expensive and time-consuming , even with powerful computers. This is where heuristics come into play. A heuristic for this problem might be a simple nearest neighbor algorithm that assigns each package to the closest truck, and then optimizes the route for each truck using local search. While this approach may not guarantee an optimal solution, it can quickly generate good-quality solutions that are close to the optimal solution , and may be sufficient for practical applications.

In summary, the main difference between an exact algorithm and a heuristic is the level of accuracy and efficiency . Exact algorithms aim to find the optimal solution, but may be computationally expensive and impractical for large-scale problems. Heuristics, on the other hand, aim to find a good solution quickly and efficiently , but may not guarantee an optimal solution . The choice between these approaches depends on the specific characteristics of the problem and the trade-off between accuracy and efficiency.

Exact or Heuristic?

A couple of things are important to keep in mind when choosing between an exact algorithm and heuristic. I have divided them into four main topics: solution quality, performance, flexibility and costs. If you are looking for a quick answer (heuristic or exact algorithm), this flowchart might help:

Let’s take a look at each of them in more depth.

Solution Quality

If your most important goal is to get solutions with the highest possible quality, because a slightly better solution brings a lot of value, you can stop here. In that case you should go for an exact algorithm. By using an exact algorithm, you know the gap between the optimal and current solution and you can continue the search until you have found the optimum.

But, an important note, if the problem is really large, an exact algorithm can take a lot of time to come to that optimal. Hours, days, or weeks are possible. Especially if you use an open source solver like CBC or glpk , you can’t expect an optimal solution fast. You’d rather use a commercial one like Gurobi or CPLEX . And even with state of the art solvers, finding the optimal solution can take a lot of time.

The difficulty with heuristics is that it’s hard to know the quality of the solution. You can compare it with a baseline, but you don’t know the gap between the optimal and the current solution.

Performance

Heuristics are generally faster than exact algorithms because they sacrifice accuracy for speed. Exact algorithms aim to find the optimal solution to a problem, but this can be computationally expensive and time-consuming, especially for large-scale problems. Exact algorithms typically explore the entire solution space, which can be very large for some problems, and require the use of complex mathematical techniques to find the optimal solution.

Heuristics use simple rules of thumb to guide the search for a solution. Often they focus on a subset of the most promising solutions. This reduces the computational effort required to find a solution and allows heuristics to generate good-quality solutions in a shorter amount of time.

It’s easier to implement problem-specific knowledge in a heuristic to guide the search for a solution, which can help to avoid exploring parts of the solution space that are unlikely to contain good solutions. This can further reduce the computational effort required to find a solution.

Flexibility

Heuristics are often more flexible than exact algorithms because they are not bound by the same restrictions as exact algorithms and can be adapted to address specific problem characteristics or constraints. Heuristics can often be implemented using simple algorithms and data structures, making them easier to develop and modify than exact algorithms. This allows heuristics to quickly adapt to new or changing problem instances, making them a good choice for problems where the solution needs to be found quickly or where the problem is likely to change over time.

Exact algorithms are based on mathematical models that provide a formal, rigorous framework for solving problems. These models are based on a set of constraints and objective functions that define the problem to be solved. However, this rigidity can make it difficult to address specific problem characteristics or constraints that are not easily captured by the mathematical model.

Overall, the flexibility of heuristics is one of their key strengths, allowing them to be applied to a wide range of problems and to quickly adapt to changing problem characteristics.

When it comes to solving large problems, obtaining a high-quality solver can cost a lot of money. However, the investment is often worth it for those who require the highest level of accuracy and speed in their solutions. And a great addition: you usually get good support when getting a commercial solver license, people with a lot of experience can help you with the model formulation and improve performance.

In terms of time, hiring consultants to implement solutions for you can be an efficient way to get things done quickly. However, this approach can also be costly, and may not always yield the most optimal results. For those who don’t have the budget for consultants or want to maintain greater control over the problem-solving process, learning and implementing different heuristics can be a viable option. While it may take more time upfront, investing in the development of heuristics can pay off in the long run by providing a more customized and efficient solution process.

This post compares exact algorithms and heuristics for solving optimization problems. Exact algorithms aim for optimal solutions, but can be slow and computationally expensive. Heuristics sacrifice accuracy for speed, but can generate good solutions quickly. The choice depends on the specific problem and the trade-off between accuracy and efficiency. The flowchart provided aims to help choosing between the two methods. Considerations include solution quality, performance, flexibility, and costs.

And one final note: every problem is different and sometimes small nuances can make you choose another approach, which is perfectly fine. You can always reconsider your choice in a later stage, or try both approaches for comparison purposes.

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Problem-solving and decision making

Problem-solving refers to a way of reaching a goal from a present condition, where the present condition is either not directly moving toward the goal, is far from it, or needs more complex logic in order to find steps toward the goal.

Types of problem-solving

There are considered to be two major domains in problem-solving : mathematical problem solving, which involves problems capable of being represented by symbols, and personal problem solving, where some difficulty or barrier is encountered.

Within these domains of problem-solving, there are a number of approaches that can be taken. A person may decide to take a trial and error approach and try different approaches to see which one works the best. Or they may decide to use an algorithm approach following a set of rules and steps to find the correct approach. A heuristic approach can also be taken where a person uses previous experiences to inform their approach to problem-solving.

Barriers to effective problem solving

Barriers exist to problem-solving they can be categorized by their features and tasks required to overcome them.

The mental set is a barrier to problem-solving. The mental set is an unconscious tendency to approach a problem in a particular way. Our mental sets are shaped by our past experiences and habits. Functional fixedness is a special type of mindset that occurs when the intended purpose of an object hinders a person’s ability to see its potential other uses.

The unnecessary constraint is a barrier that shows up in problem-solving that causes people to unconsciously place boundaries on the task at hand.

Irrelevant information is a barrier when information is presented as part of a problem, but which is unrelated or unimportant to that problem and will not help solve it. Typically, it detracts from the problem-solving process, as it may seem pertinent and distract people from finding the most efficient solution.

Confirmation bias is a barrier to problem-solving. This exists when a person has a tendency to look for information that supports their idea or approach instead of looking at new information that may contradict their approach or ideas.

Strategies for problem-solving

There are many strategies that can make solving a problem easier and more efficient. Two of them, algorithms and heuristics, are of particularly great psychological importance.

A heuristic is a rule of thumb, a strategy, or a mental shortcut that generally works for solving a problem (particularly decision-making problems). It is a practical method, one that is not a hundred per cent guaranteed to be optimal or even successful, but is sufficient for the immediate goal. Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps.

An algorithm is a series of sets of steps for solving a problem. Unlike a heuristic, you are guaranteed to get the correct solution to the problem; however, an algorithm may not necessarily be the most efficient way of solving the problem. Additionally, you need to know the algorithm (i.e., the complete set of steps), which is not usually realistic for the problems of daily life.

Biases can affect problem-solving ability by directing a problem-solving heuristic or algorithm based on prior experience.

Anchoring bias -Tendency to focus on one particular piece of information when making decisions or problem-solving

Confirmation bias – Focuses on information that confirms existing beliefs

Hindsight bias – Belief that the event just experienced was predictable

Representative bias – Unintentional stereotyping of someone or something

Availability bias – Decision is based upon either an available precedent or an example that may be faulty

Belief bias – casting judgment on issues using what someone believes about their conclusion. A good example is belief perseverance which is the tendency to hold on to pre-existing beliefs, despite being presented with evidence that is contradictory.

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Sample Test P/S Section Passage 3 Question 12

Practice Exam 2 P/S Section Passage 8 Question 40

Practice Exam 2 P/S Section Passage 8 Question 42

Practice Exam 4 P/S Section Question 12

• Problem-solving can be considered when a person is presented with two types of problems – mathematical or personal

• Barriers exist to problem-solving maybe because of the mental set of the person, constraints on their thoughts or being presented with irrelevant information

• People can typically employ a number of strategies in problem-solving such as heuristics, where a general problem-solving method is applied to a problem or an algorithm can be applied which is a set of steps to solving a problem without a guaranteed result

• Biases can affect problem-solving ability by directing a problem-solving heuristic or algorithm based on prior experience.

Mental set: an unconscious tendency to approach a problem in a particular way

Problem : the difference between the current situation and a goal

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 bias : 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

Problem-solving strategy : a method for solving problems

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

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

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The Heuristic Problem-Solving Approach

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COAL: a new heuristic approach for solving the fixed charge problem―computational results

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COMMENTS

Problem-Solving Strategies and Obstacles
Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.
Problem Solving
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.
Teachers' metacognitive and heuristic approaches to word problem
We conducted a 7-month video-based study in two sixth-grade classrooms focusing on teachers' metacognitive and heuristic approaches to problem solving. All problem-solving lessons were analysed regarding the extent to which teachers implemented a metacognitive model and addressed a set of eight heuristics. We observed clear differences between both teachers' instructional approaches ...
Heuristic Approaches to Problem Solving
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Heuristics are essentially problem-solving tools that can be used for solving non-routine and challenging problems. A heuristic method is a practical approach for a short-term goal, such as solving a problem. The approach might not be perfect but can help find a quick solution to help move towards a reasonable way to resolve a problem.
12 Approaches To Problem-Solving for Every Situation
The Simplex Process is an eight-step approach similar to the rational approach, but tailored for situations in which you are unsure of what the problem actually is. It begins with problem-finding and research, where users collect the information necessary for defining the problem.
The Algorithm Problem Solving Approach in Psychology
Algorithms vs. Heuristics. When solving a problem, choosing the right approach is often the key to arriving at the best solution. In psychology, one of these problem-solving approaches is known as an algorithm. While often thought of purely as a mathematical term, the same type of process can be followed in psychology to find the correct answer ...
What is the difference between a heuristic and an algorithm?
A heuristic is a general way of solving a problem. Heuristics as a noun is another name for heuristic methods. In more precise terms, heuristics stand for strategies using readily accessible, though loosely applicable, information to control problem solving in human beings and machines.
Heuristics Flashcards
Heuristics approach to problem solving, learning or discovery that employs a practical methodology not guaranteed to be optimal or perfect, but sufficient for immediate goals Pros quick, inexpensive feedback early feedback cons acquires knowledge and experience to apply effectively experts hard to find and expensive
Thought
A problem-solving heuristic is an informal, intuitive, speculative procedure that leads to a solution in some cases but not in others. The fact that the outcome of applying a heuristic is unpredictable means that the strategy can be either more or less effective than using an algorithm.
The Heuristic Problem-Solving Approach
The Heuristic Problem-Solving Approach L. R. FOULDS University of Florida For a variety of reasons, the finding of an optimal solution is impractical for many O.R. problems. A common way of overcoming this unhappy state of affairs is the development of heuristic (approximate) methods. The purpose of this paper is to discuss some of the issues ...
Heuristic problem solving example
Heuristic problem solving example - Explanation. When you see a person with their hood up in a dark alley and you decide to subtly walk past a bit faster, your. ... Heuristics decisions and mental thinking shortcut approach outline diagram. Clarify mathematic equations To solve a mathematical problem, you need to first understand what the ...
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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.
(PDF) Heuristics and Problem Solving
A Greek word meaning "serving to find out or discover", heuristics are experientially derived cognitive "rules of thumb" that serve as guides in problem-solving processes (Todd and Gigerenzer ...
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Some of the most common fundamental heuristic methods include trial and error, historical data analysis, guesswork, and the process of elimination. Such methods typically involve easily accessible information that is not specific to the problem but is broadly applicable.
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In psychology, heuristics are simple, efficient rules, either learned or inculcated by evolutionary processes. These psychological heuristics have been proposed to explain how people make decisions, come to judgements, and solve problems. These rules typically come into play when people face complex problems or incomplete information.
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The process of problem-solving using searching consists of the following steps. Define the problem Analyze the problem Identification of possible solutions Choosing the optimal solution Implementation Let's discuss some of the essential properties of search algorithms. Properties of search algorithms Completeness
ERIC
One of the major aims of STEM education is the development of mathematical thinking. The common misconception is that "doing mathematics" is the same as getting involved in "mathematical thinking". Rallying to such argument, many would agree that mathematics should be taught as a thinking activity. Thus, this study endeavours to review the effects of a problem-solving heuristic application ...
Heuristic Method definition, steps and principles
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.
How to Use Heuristics in Problem Solving and Minimise Errors
The word heuristics comes from the Greek "find" or "discover" and refers to experience-based techniques for problem solving, learning, and discovery - Wikipedia. Judea Pearl in 'Heuristics: Intelligent Search Strategies for Computer Problem Solving' defines heuristics as strategies using readily accessible, though loosely applicable, information to control problem solving in ...
Heuristics Definition
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...
Exact Algorithm or Heuristic?. A step-by-step guide to make the right
When it comes to solving optimization problems, there are two main approaches: (meta-)heuristics and exact algorithms. Each approach has its own strengths and weaknesses, and the choice of method will depend on the specific characteristics of the problem.
Heuristic problem solving example
To determine what the math problem is, you will need to take a close look at the information given and use your problem-solving skills. Once you have determined what the problem is, you can begin to work on finding the solution. ... Get quality lessons Heuristic Approach to problem-solving Intermediate Example 3.
Heuristic problem solving
A problem-solving heuristic is an informal, intuitive, speculative procedure that leads to a solution in some cases but not in others. The fact that the outcome of applying a heuristic is unpredictable means that the strategy can be either more or less effective than using an algorithm.
Problem Solving And Decision Making
A heuristic approach can also be taken where a person uses previous experiences to inform their approach to problem-solving. Barriers to effective problem solving Barriers exist to problem-solving they can be categorized by their features and tasks required to overcome them. The mental set is a barrier to problem-solving. The mental set is an ...
The Heuristic Problem-Solving Approach
The Heuristic Problem-Solving Approach. L. Foulds. Published 1 October 1983. Business. Journal of the Operational Research Society. For a variety of reasons, the finding of an optimal solution is impractical for many O.R. problems. A common way of overcoming this unhappy state of affairs is the development of heuristic (approximate) methods.
Heuristic problem solving example
Heuristics: Definition, Examples, and How. For example, an instant message about winning the latest automobile in exchange for a particular sum of money seems intriguing. People, however, pay just to be. Solve equation. Solving math problems can be a fun and rewarding experience. Get detailed step-by-step answers.
Review the legalistic approach and problem-solving approach during the
Apa format 1-2 paragraphs references Review the legalistic approach and problem-solving approach during the arbitration hearing process. Then, develop two approaches that an organization could use to make the typical arbitration procedure more effective than either of these approaches. Review good faith bargaining. Discuss the major advantages and major disadvantages of your approaches ...