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I would like to know what 'heuristics' actually means in artificial intelligence. For example, I am reading a paper by Engelbrecht on the convergence analysis of the particles of the algorithm. The section where the author discusses the mathematical reasons why the particles behave the way they do was entitled 'heuristics'. Does it, in any way, mean ... the mathematical rigour, methodology, convergence, etc?

Your insights would be helpful.

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  • $\begingroup$ Heuristic generally is an approximate approach to solve any problem. In this case it could be the approximate model of particle behaviour. $\endgroup$
    – iLoveCamelCase
    Commented May 29, 2015 at 6:06
  • $\begingroup$ Thanks for your responses. A related question is ... what do 'hyperheuristics', 'meta-heuristics' mean? Why are they 'beyond' the normal heuristics? $\endgroup$
    – cgo
    Commented May 29, 2015 at 6:59
  • $\begingroup$ You can find answers to your questions on Wikipedia, see e.g. metaheuristics and hyperheuristic. $\endgroup$
    – Juho
    Commented May 29, 2015 at 7:36
  • $\begingroup$ Still, heuristics can be studies in a rigorous way. If the author calls model assumptions "heuristics", they may not solve the problem they want/claim to be solving. $\endgroup$
    – Raphael
    Commented May 29, 2015 at 7:57
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    $\begingroup$ The concept of a heuristic is to be understood with respect to a given purpose. For example, given a problem, you may have an algorithmic solution providing precisely the answer(s) you desire, but that is expressed as a non-deterministic algorithm, hence leaving room for different computation strategies which may results in computations that have different costs for achieving the same result. In such a case, you may want to use heuristics to make non-deterministic choices that may hopefully lead to lower computation costs. $\endgroup$
    – babou
    Commented May 29, 2015 at 10:46

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Heuristics typically have very little to do with rigor. (But you can surely study them in a rigorous way). They are rule of a thumb methods for solving (usually computationally difficult) problems, and typically they perform quite well in practice. In other words, there might not be any formal guarantees on the solution quality you get by running a heuristic, but experience and empirical analysis shows they can be quite effective. Arguably, it is rarely the case we understand their behaviour well.

Sometimes, when heuristics are analyzed formally, they turn out be to approximation algorithms. That is, methods for solving a problem with a formal guarantee on the solution quality. For example, one might have observed a heuristic usually works well, and an analysis proves it will always give a solution which is at most twice the optimum.

Perhaps in your particular case, the section "Heuristics" contains explanations (more or less formal) as to why the heuristic behaves or is expected to behave in certain ways when run.

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Heuristics or Heuristic value(s) are the approximations for your problem to reach the answer(goal). Let's say you have an algorithm that finds the shortest path from point A to Z. Now, if you go by predictions you may get lost as there're several other points in between your start & final position.

For an analogy, let's say you are traveling in a city, you don't know anything about the routes. To reach a certain place in that city, what you will do, you keep going on & on by taking advice from the people around you. Now, the time in which you reach the place depends on the quality of advice that the person gives to you.

Now, let's relate it. In the analogy, you is your algorithm that is trying to reach a certain place (goal) & the heuristic value is the advice of the person. Same as in the case of your AI algorithm, the better approximation (heuristic value) you have the less in time you reach your problem goal.

Hope it helped!

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