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From: "James Albert Larson" <larso171@maroon.tc.umn.edu>
Subject: Re: Using GA to optimize highly constrained problems
To: mcintyre@cis.csuohio.edu
Message-ID: <93484.larso171@maroon.tc.umn.edu>
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Date: Fri, 14 Apr 1995 05:26:09 GMT
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On Fri, 7 Apr 1995 07:03:34 GMT, 
Dave McIntyre  <mcintyre@grail.cba.csuohio.edu> wrote:

>I am somewhat familiar with the basics of GA as discussed in several chapters
>of GOLDBERG's book, and I have a fairly basic question on GA.
>
>THE PROBLEM
>Many problems are heavily constrained problems.  As a result the encoded
>chromosomes (binary) after crossover and after mutation for such problems
>*often* decode back into infeasible solutions to the problem.  

I'd recommend Zbigniew Michaelewicz's Genetic Algorithms + Data Structures 
= Evolution Programs, 2nd Edition, 1994.  First, I consider it an update 
to, and almost a superset of the Goldberg 1989 book (except classifier 
systems).  A lot has been learned in 5 years in GA.  Second, he 
concentrates on the more difficult problems such as highly constrained 
problems.  His main theme is that binary encodings, penalty functions to 
penalize constraint violations, and / or repair algorithms that turn 
infeasible individuals to feasible individuals is a poor approach to 
heavily constrained problems.  Rather, as suggested in some of the replies 
you've gotten, come up with a chromosome data structure that makes sense in 
the problem domain you are working in (e.g. a matrix of real numbers), and 
devise problem - specific genetic operators that produces feasible children 
from feasible adults.  He has many case studies, e.g. TSP, scheduling 
problems, graph problems, transportation problem with nonlinear objective 
function, and many more that illustrate this approach.

Jim Larson

