Newsgroups: comp.ai.genetic
From: stevem@comtch.iea.com (Steve McGrew)
Subject: Re: About GA theory
Organization: New Light Industries, Ltd.
References: <32F6A4A7.5357@comp.polyu.edu.hk> <32FA1A24.6F7C@santafe.edu>
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In article <32FA1A24.6F7C@santafe.edu>, Erik Van Nimwegen <erik@santafe.edu> wrote:

>It has been proven though that GA are NOT better in general than any
>other search technique. That is; averaged over ALL possible fitness
>functions GA's do as well as any other search method. This is called the 
>no free lunch theorem by David Wolpert and Bill MacReady.
>
>A GA would probably be better at some particular subset of fitness
>functions and there are speculations on what kind of functions that
>might be, but as far as I know nobody has come up with a suggestion for
>such a subset that seems to make sense. Let alone somebody proving on
>what kind of fitness functions GA would do well.

        The No Free Lunch theorem basically is equivalent to the theorem that 
says the number of rational numbers is of measure zero with respect to the 
number of irrational numbers.  GA's work on problems where the "fitness 
landscape" has some sort of order or organization; they are no better than 
random search on totally random "fitness landscapes".

        The important thing is that virtually every real-world problem *does* 
have some order or organization, so GA's or other evolutionary methods *do* 
have dramatic advantages over random search, *if* they are able to exploit 
that order or organization.

Steve

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