## "Metaheuristic" or "Stochastic Local Search"?

Par nojhan le vendredi 7 novembre 2008, 10:38 - Anecdotique - Lien permanent

During their excellent tutorials at META 2008, both Thomas and Dick talked about "stochastic local search" and seems to be rather uncomfortable with the "metaheuristic" term. They seems to reserve it for very high level well known algorithms.

I'm not sure that using the term "stochastic" along with "local" is a good idea. In all the algorithms, the use of probabilistic processes aims at avoiding local optima. Thus, stochastic algorithms are not "local search" anymore, but "global search". While I agree that it is a very good approach to start with local search techniques, I would say that when you introduce stochastic processes, then you enter the field of metaheuristics. On the other hand, the paradoxal use of "stochastic" along with "local" may be interesting from a marketing point of vue... but I like paradoxes.

Anyway, despite the fact that there would be a lot more to say about the problem of nomenclature in our field (who says "everything is evolutionary"?), this is not very important, I tink I will continue using "metaheuristics", until a common term establish itself in the litterature.

## Commentaires

Hi Johann!

I would like to present here an idea that will take the "stochastic" and "local" idea even more further than Thomas and Dirk. In that view, even GAs are local search techniques! Why?

It has a lot to do with the definition of neighborhood of the current state of the algorithm. The state may be the position of an algorithm in the search space. In classical local search, the state is given by mere 1 point. In population-based techniques, the state is the whole population. New solutions are usually generated only by local modifications of the state, i.e. the search takes place only in the local neighborhood of the algorithm state.

Yes, of course, the local neighborhood of the population as a whole is very broad and such a local search is much less prone to premature convergence and exhibits a kind of global behaviour. But, IMHO, it is still a local search...

I completely understand your view: if there is a non-zero probability of generating any solution in the search space, then the search must eventually find the global optimum, and thus performs a global search. This is the case for many stochastic local search algorithm in continuous domain which use e.g. normal distribution. But if you set the variance too high, you will get very slow convergence to that global optimum which is in practice not desirable. If you set variance too low, you will quickly find local optimum, but you will have to wait for the global one virtually infinitely long - again undesirable. Or, put it in another way, would you call a "global optimization" technique still "global" if it takes zilions of years to find that global solution?

In practice, I think, for continuous spaces we have to resort to algorithms that exhibit local behavior since we always have some hard constraints on the length of the optimization run. In my eyes, this perfectly justifies the name "stochastic local search".

Thanks for you blog! I read it regularly!

Regards,

Petr