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Tag - evolutionary computation

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jeudi 11 septembre 2008

The ultimate metaheuristic?

There exists a lot of different algorithms families that can be called "metaheuristics", stricly speaking, there are a very, very, very large number of metaheuristics instances.

Defining what is a metaheuristic "family" is a difficult problem: when may I called this or this algorithm an evolutionary one? Is estimation of distribution a sub-family of genetic algorithms? What is the difference between ant colony optimization and stochastic gradient ascent? Etc.

Despite the difficulty of classifying metaheuristics, there is some interesting characteristics shared by stochastic metaheuristics. Indeed, they are all iteratively manipulating a sample of the objective function[1]

For example, simulated annealing is often depicted as a probabilistic descent algorithm, but it is more than that. Indeed, simulated annealing is based on the Metropolis-Hastings algorithm, which is a way of sampling any probability distributionn, as long as you can calculate its density at any point. Thus, simulated annealing use an approximation of the objective function as a probability density function to generate a sampling. It is even more obvious if you consider a step by step decrease of the temperature. Estimation of distribution are another obvious example: they are explicitly manipulating samplings, but one can also have the same thoughts about evolutionary algorithms, even if they are manipulating the sampling rather implicitely.

The diagram tries to illustrate this idea: (a) a descent algorithm can have the same sampling behaviour than an iteration of a (b) "population" method.

Given these common processes, is it possible to design a kind of "universal" metaheuristic ? Theoretically, the answer is yes. For example, in the continuous domain, consider an estimation of distribution algorithm, using a mixture of gaussian kernel: it can learn any probability density function (possibly needing an infinite number of kernels). Thus, carefully choosing the function to use at each iteration and the selection operator, one can reproduce the behaviour of any stochastic metaheuristic.

Of course, choosing the correct mixture (and the other parameters) is a very difficult problem in practice. But I find interesting the idea that the problem of designing a metaheuristic can be reduced to a configuration problem.

Notes

[1] Johann Dréo, Patrick Siarry, "Stochastic metaheuristics as sampling techniques using swarm intelligence. ", in "Swarm Intelligence: Focus on Ant and Particle Swarm Optimization", Felix T. S. Chan, Manoj Kumar Tiwari (Eds.), Advanced Robotic Systems International, I-Tech Education and Publishing, Vienna, Austria , ISBN 978-3-902613-09-7 - December 2008

lundi 3 mars 2008

The problem with spreading new metaheuristics

Marcelo De Brito had interesting thoughts about what he call New Wave Of Genetic Algorithms. He is surprised that when "evolutionary computation" is applied to a new problem, the first algorithm used is the good old canonic genetic algorithm, despite that there exist active researchs on Estimation of Distribution Algorithms. Julian Togelius write that it may be because people does not understand other algorithms, or even know that anything else exists.

I think that is definitely true. This subject is a kind of hobby for me. Indeed, as I have came from ecology to applied mathematics, I feel like a kind of generalist researcher, not being able to be the best somewhere, but trying to be as good as possible on several fields. Concerning the field of what Marcelo called NWOGA, I would like to emphasize some other things.

As David E. Goldberg say in its courses, genetic algorithm is the term everybody use. For specialist, a GA is just a kind of "evolutionary algorithm", with specific rules, that are more defined by history than by anything else.

The litterature on evolutionary computation is quite big, the first algorithm being designed in 1965 (evolutionary strategies, followed by evolutionary programming in 1966), making it difficult to spread deep changes on basic concepts.

There exist a lot more stochastic algorithms for global optimization than just evolutionary ones. I prefer to call the stochastic metaheuristics, or simply metaheuristics, because this lead to far less bias than a metaphoric naming (cf. the previous post on classification of metaheuristics).

For example, during my PhD thesis, I was convinced that some Ant Colony Optimization algorithms were just equivalent to Estimation of Distribution Algorithms, when talking about continuous problems. Moreover, I'm now convinced that a lot of metaheuristics just shares some common stochastic sampling processes, that are not specifiquely related to evolution. For example, mathematically, Simulated Annealing is just a kind of EDA using an approximation of the objective function as a model (or inversely, of course).

As Julian says: I know roughly what an EDA does, but I couldn't sit down an implement one on the spot. This is, in my humble opinion, one of the more important thing to keep in mind. Indeed, there exist more and more papers claming that a correct parameter setting of a metaheuristic can lead to the performances of any competing metaheuristic.

Thus, the true discriminatory criterion is not the fantasised intrinsic capability, but the ease of implementation and parameter setting on a specific problem. In other words, choose the algorithm you like, but be aware that there exists a lot of other ones.

dimanche 7 janvier 2007

Evolving Objects 1.0 is out

The EO framework has just reached the 1.0 version. This is one of the most interesting library for metaheuristics.

It is a templatized C++ framework, with a component based architecture. EO is focused on "evolutionary computing" (a synonym of metaheuristics, imho) and can be used for any population-base metaheuristics. There exists versions for local searches, multi-objective optimization or parallel architectures... a real good piece of software :-)

mardi 19 décembre 2006

Metaheuristics and machine-learning

Metaheuristics and machine-learning algorithms shares a large number of characteristics, like stochastic processes, manipulaton of probability density functions, etc.

One of the interesting evolution of the research on metaheuristics these years is the increasing bridge-building with machine-learning. I see at least two interesting pathways: the use of metaheuristics in machine-learning and the use of machine-learning in metaheuristics.

The first point is not really new, machine-learning heavily use optimization, and it was natural to try stochastic algorithms where local search or exact algorithms failed. Nevertheless, there is now a sufficient litterature to organize some special sessions in some symposium. For 2007, there will be a special session on Genetics-Based Machine Learning at CEC, and a track on Genetics-Based Machine Learning and Learning Classifier Systems at GECCO. These events are centered around "genetic" algortihm (see the posts on the IlliGAL blog : 1, 2), despite the fact that there are several papers using other metaheuritics, like simulated annealing, but this is a common drawback, and does not affect the interest of the subject.

The second point is less exploited, but I find it of great interest. A simple example of what can be done with machine-learning inside metaheuristic can be shown with estimation of distribution algorithms. In these metaheuristics, a probability density function is used to explicitely build a new sample of the objective function (a "population", in the evolutionary computation terminology) at each iteration. It is then crucial to build a probability density function that is related to the structure of the objective function (the "fitness landscape"). There, it should be really interesting to build the model of the pdf itself from a selected sample, using a machine-learning algorithm. There is some interesting papers talking about that.

If you mix these approaches with the problem of estimating a Boltzmann distribution (the basis of simulated annealing), you should have an awesome research field...

dimanche 10 décembre 2006

Metaheuristics and experimental research

Springer has just published a book on "Experimental Research in Evolutionary Computation", written by Thomas Bartz-Beielstein.

Thomas Bartz-Beielstein is working on the statistical analysis of the behaviour of metaheuristics (see its tutorials at GECCO and CEC), and the publication of its book is a really great thing. I haven't read it yet, but the table of content seems really promising. There is a true need for such work in the metaheuristics community, and in stochastic optimization in general.

A friend said to me that the lack of experimental culture in the computer science community was a form of consensus, perhaps because theoretical aspects of mathematics was the "only way to make true science". This is a true problem when you deal with stochastic algorithm, applied to real world problem. Despite the fact that several papers early call for more rigourous experimental studies of metaheuristcs (E.D. Taillard has written papers on this problem several years ago, for example), the community does not seems to quickly react.

Yet, things are changing, after the series of CEC special sessions on benchmark for metaheuristics, there is more and more papers on how to test stochastic optimization algorithms and outline the results. I think this book is coming timely... the next step will be to promote the dissemination of the results data (and code!), in an open format, along with the papers.

mercredi 23 août 2006

What are metaheuristics ?

Despite the title of this blog, the term metaheuristic is not really well defined.

One of the first occurence of the term can (of course) be found in a paper by Fred Glover[1]: Future Paths for Integer Programming and Links to Artificial Intelligence[2]. In the section concerning tabu search, he talks about meta-heuristic:

Tabu search may be viewed as a "meta-heuristic" superimposed on another heuristic. The approach undertakes to transcend local optimality by a strategy of forbidding (or, more broadly, penalizing) certain moves.

In the AI field, a heuristic is a specific method that help solving a problem (from the greek for to find), but how must we understand the meta word ? Well, in greek, it means "after", "beyond" (like in metaphysic) or "about" (like in metadata). Reading Glover, metaheuristics seems to be heuristics beyond heuristics, which seems to be a good old definition, but what is the definition nowadays ? The litterature is really prolific on this subject, and the definitions are numerous.

There is at least three tendencies :

  1. one that consider that the most important part of metaheuristcs is the gathering of several heuristics,
  2. one other that promotes the fact that metaheuristics are designed as generalistic methods, that can tackle several problems without major changes in their design,
  3. the last one that use the term only for evolutionnary algorithms when they are hybridicized with local searches (methods that are called memetic algorithms in the other points of vue).

The last one is quite minor in the generalistic litterature, it can mainly be found in the field of evolutionnary computation, separate out the two other tendencies is more difficult.

Here are some definitions gathered in more or less generalistic papers:

"iterative generation process which guides a subordinate heuristic by combining intelligently different concepts for exploring and exploiting the search space" (Osman and Laporte, 1996[3])

"(metaheuristics) combine basic heuristic methods in higher level frameworks aimed at efficiently and effectively exploring a search space" (Blum and Roli, 2003[4])

"a metaheuristic can be seen as a general-purpose heuristic method designed to guide an underlying problem-specific heuristic (...) A metaheuristic is therefore a general algorithmic framework which can be applied to different optimization problems with relative few modifications to make them adapted to a specific problem." (Dorigo and Stützle, 2004[5])

"(metaheuristics) apply to all kinds of problems (...) are, at least to some extent, stochastic (...) direct, i.e. they do not resort to the calculation of the gradients of the objective function (...) inspired by analogies: with physics, biology or ethology" (Dréo, Siarry, Petrowski and Taillard, 2006[6])

One can summarize by enumerating the expected characteristics:

  • optimization algorithms,
  • with an iterative design,
  • combining low level heuristics,
  • aiming to tackle a large scale of "hard" problems.

As it is pointed out by the last reference, a large majority of metaheuristics (well, not to say all) use at least one stochastic (probabilistic) process and does not use more information than the solution and the associated value(s) of the objective function.

Talking about combining heuristics seems to be appropriate for Ant Colony Optimization, that specifically needs one (following Dorigo's point of vue), it can be less obvious for Evolutionnary Algorithms. One can consider that mutation, or even the method's strategy itself, is a heuristic, but isn't it too generalistic to be called a heuristic ?

If we forget the difficulty to demarcate what can be called a heuristic and what is the scope of the term meta, one can simply look at the use of the term among specialists. Despite the fact that the definition can be used in several fields (data mining, machine learning, etc.), the term is used for optimization algorithms. This is perhaps the best reason among others: the term permits to separate a research field from others, thus adding a little bit of marketing...

I would thus use this definition:

Metaheuristics are algorithms designed to tackle "hard" optimization problems, with the help of iterative stochastic processes. These methods are manipulating direct samples of the objective function, and can be applied to several problems without major changes in their design.

Notes

[1] A recurrent joke says that whatever is your new idea, it has already be written down by Glover

[2] Comput. & Ops. Res.Vol. 13, No.5, pp. 533-549, 1986

[3] Metaheuristic: A bibliography, Annals of Operations Research, vol. 63, pp. 513-623, 1996

[4] Metaheuristics in combinatorial optimization: Overview and conceptual comparison, ACM Computing Surveys, vol. 35, issue 3, 2003

[5] Ant Colony Optimization, MIT Press, 2004

[6] Metaheuristics for Hard Optimization, Springer, 2006

mardi 1 août 2006

About this blog

This blog is an attempt to publish thoughts about metaheuristics and to share them with others. Indeed, blogs are fun, blogs are popular, ok... but most of all, blogs can be very usefull for researchers, that constently need to communicate, share ideas and informations.

Metaheuristics are (well, that's one definition among others, but in my opinion the better one) iterative (stochastic) algorithms for "hard" optimization. Well known metaheuristics are the so-called "genetic algorithms" (lets call them evolutionary ones), but these are not the only class: dont forget simulated annealing, tabu search, ant colony algorithms, estimation of distribution, etc.

This blog will try to focuse on the theory, the design, the understanding, the application, the implementation and the use of metaheuristics. I hope this blog will be profitable to other peoples (researchers as well as users), and will be a place to share thoughts.

Welcome aboard, and lets sleep with metaheuristics.