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From: "James Albert Larson" <larso171@maroon.tc.umn.edu>
Subject: Re: Very large search spaces
To: hslopes@gralha.cpgei.cefetpr.br
Message-ID: <32630.larso171@maroon.tc.umn.edu>
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Date: Fri, 25 Aug 1995 10:52:04 GMT
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Heitor,

>   Currently I am starting a project using GA's for searching a very 
>large space, something about 2^500. Available knowledge about the
>problem leads me to belive that the search space has lots of local
>maxima. 

Me too, the unit commitment electric utility generation scheduling problem.
The goal is to find an optimal hourly schedule (on/off) for NU generators 
over a period of NH hours.  With NU being say 20 and NH being say 100 (a 
medium-small problem) the search space is 2^(20*100) = 2^2000.  And 
gigatons of local minima.

The two papers that I've seen published on solving this problem with GA 
rely heavily on problem-specific special genetic operators (crossover, 
mutation, even hillclimbing).

Michalewicz ("Genetic Algorithms in Search, Optimization, and Machine 
Learning") illustrates solving difficult problems by designing 
problem-specific genetic operators.  The best example is his Genocop for 
solving constrained nonlinear problems (with linear constraints).  Since 
the problem has linear constraints, it is convex and there are other things 
that can be exploited to reformulate the problem in a way that is more GA - 
friendly.  And then lots of problem - specific genetic operators.  But the 
Genocop program works only on problems with continuous variables.

The Traveling Salesman problem in his book or Goldberg's 1989 book also 
involve specialized genetic operators for working with permutations, and 
crossover and mutation operators that don't completely scramble up the 
parent tours.

Best of luck.

Jim Larson

