Mentales habitudes - Tag - stochastic local search2015-10-19T19:25:25+02:00nojhanurn:md5:12147DotclearMore on "stochastic local search" definitionurn:md5:705773068ef68f0ce04b9d2bda4244322008-11-17T11:24:00+01:00nojhanAnecdotiquedefinitionmetaheuristicstochastic local search <p>Petr Pošík let an interesting comment on a previous post : <a href="http://metah.nojhan.net/post/2008/11/07/Metaheuristic-or-Stochastic-Local-Search#comments">"Metaheuristic"
or "Stochastic Local Search"?</a>. As bloggers always love worthwhile comments
from insightful readers, I copy it here, as an article, along with my
answer.</p>
<blockquote>
<p>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?</p>
<p>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.</p>
<p>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...</p>
<p>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.</p>
<p>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?</p>
<p>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".</p>
</blockquote>
<p>In fact, as far as I comprehend them, both Dick Thierens and Thomas Stützle
shares your point of view. For them, GA are a kind of stochastic local
search.</p>
<p>I find the classification in "descent" algorithm and "population" ones
<a href="http://metah.nojhan.net/post/2007/10/12/Classification-of-metaheuristics">quite
artificial</a>. For example, simulated annealing is implemented as a descent
algorithm, but <a href="http://metah.nojhan.net/post/2008/09/11/What-is-the-ultimate-metaheuristic">does actually perform a
sampling of the objective function</a>, which is commonly seen as a population
algorithm characteristic.</p>
<p>More rigourously, I think that every <em>stochastic</em> metaheuristic does
try to avoid local optima. Stochastic processes are always here to do
so<sup>[<a href="http://metah.nojhan.net/post/2008/11/14/#pnote-298520-1" id="rev-pnote-298520-1" name="rev-pnote-298520-1">1</a>]</sup>.</p>
<p>Maybe the problem is the definition of <em>local</em> search. In my humble
opinion, a local search is a method that search for a <em>local</em> optimum.
This can be opposed to <em>global</em> search, where one want to find a
<em>global</em> optimum.</p>
<p>You are right when you point out that this is related to ergodicity, as only
an ergodic<sup>[<a href="http://metah.nojhan.net/post/2008/11/14/#pnote-298520-2" id="rev-pnote-298520-2" name="rev-pnote-298520-2">2</a>]</sup> algorithm may converge<sup>[<a href="http://metah.nojhan.net/post/2008/11/14/#pnote-298520-3" id="rev-pnote-298520-3" name="rev-pnote-298520-3">3</a>]</sup>, and thus be able to reliably find a global
optimum. Thus, yes, I will say that a true and rigorous optimization method is
global if, and only if, it is at least quasi-ergodic<sup>[<a href="http://metah.nojhan.net/post/2008/11/14/#pnote-298520-4" id="rev-pnote-298520-4" name="rev-pnote-298520-4">4</a>]</sup>. A pure random search is the basic global
optimization method, that a good metaheuristic should at least outperforms.</p>
<p>Here, it is the stochastic operators that manipulates the solutions that
permits the global behaviour. This is not related to the encoding of the
solutions/the neighbourhood structure, even if it is a really <em>crucial</em>
part of the algorithm.</p>
<p>Thus, a "stochastic local search" may be defined as a local search seeking a
global optimum, which is a paradoxical definition. I'd rather prefer that we
keep the implementation and the mathematical bases separated, and thus talk of
"stochastic search", or "stochastic metaheuristic".</p>
<p>Or else, one may want to use a paradoxical definition, as a matter of fun,
which is also a good reason to do so :-)</p>
<div class="footnotes">
<h4>Notes</h4>
<p>[<a href="http://metah.nojhan.net/post/2008/11/14/#rev-pnote-298520-1" id="pnote-298520-1" name="pnote-298520-1">1</a>] There may be probabilistic choices that are not related
to such tasks, but they are not linked to the iterative aspects of the search
algorithms, thus not being <em>stochastics</em></p>
<p>[<a href="http://metah.nojhan.net/post/2008/11/14/#rev-pnote-298520-2" id="pnote-298520-2" name="pnote-298520-2">2</a>] i.e. that can evaluate any solution</p>
<p>[<a href="http://metah.nojhan.net/post/2008/11/14/#rev-pnote-298520-3" id="pnote-298520-3" name="pnote-298520-3">3</a>] i.e. that have a non-null probability of finding the
global optimum in a finite time, or to say it differently, that can find the
global optimum after a time that may tends towards infinity (for continuous
problems, for discrete ones it is bounded by the size of the instance)</p>
<p>[<a href="http://metah.nojhan.net/post/2008/11/14/#rev-pnote-298520-4" id="pnote-298520-4" name="pnote-298520-4">4</a>] i.e. that can reach any solution in a <em>finite</em>
number of iterations</p>
</div>"Metaheuristic" or "Stochastic Local Search"?urn:md5:fa05f907c5ed0dfb9c71b2ae3e7664312008-11-07T10:38:00+01:00nojhanAnecdotiqueconferencesdefinitionmetaheuristicstochastic local search <p>During <a href="http://metah.nojhan.net/post/2008/11/06/2nd-International-Conference-on-Metaheuristics-and-Nature-Inspired-Computing">
their excellent tutorials at META 2008</a>, 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.</p>
<p>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.</p>
<p>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.</p>