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From: marcoj@ai.rl.af.mil (James D. Marco)
Subject: Re: [Q] negative fitness function?
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Date: Thu, 17 Aug 1995 11:03:12 GMT
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In article <40n415$4t1@lyra.csx.cam.ac.uk>, 93djh2@eng.cam.ac.uk (Dave
Holland) wrote:

> Hi,
> 
> Is there any reason why a fitness function for use with a genetic
> algorithm shouldn't have a negative value? Or should it be scaled to be
> always non-negative?
> 
>[snip...]

Dave,
   The data representation within GA's requires a ranking between genomes.
This can be accomplished in many ways, positive integer numerical values are
just easy to work with, in general terms.


Given two values A, B,  three possible relations occur: A>B, A<B, A=B
   If you apply negation to both sides of the relations, you get:
         -A<-B, -A>-B, -A=-B
Conclusion: Negative or Positive values can represent GA gene fitness.

The ranking within a gene pool can be represented several ways.
      Examples:
         1) Positionally - the genes are maintained in a sorted order,
                           represented in some data structure (usually an 
                           array, list or tree). 
         2) Lexographically - Some alphebetic value is supplied to represent
                           fitness values. (good for small populations) 
         3) Numerically -  The fitness value is represented as a number.
         4) Boolean     -  Some binary scheme for selecting the 'better' of
                           2 genes.
      
      (The last three are actually the same... just different numerical bases.
       The first can be represented by some numerical scheme.)      

   Analysis of these methodes gives us a logical identity, they are all
equally effective. Choose the representational methode that works best for 
your problem.

My thoughts are my own, as is my writing.      marcoj@venus.se.rl.af.mil
                                                         or
                                               marcoj.ai.rl.af.mil
                                          (I have some server problems.)
