Newsgroups: comp.ai.genetic
From: stevem@comtch.iea.com (Steve McGrew)
Subject: Fitness Landscapes
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In article <53ir9d$71u@ra.nrl.navy.mil>, shaffer@ccf.nrl.navy.mil wrote:
>[snip] As a practioner of GAs, I would really 
>like to see more research into determining what type of 
>landscape features allow the GA to outperform other algorithms 
>and conversely what landscape features to avoid. 

        Something that almost everybody seems to overlook is the fact that the 
landscape is itself determined by the representation, the mutation operators 
and the recombination operator, as much as by the fitness function.

        This is a very important point.  The whole concept of landscape in 
optimization problems depends on the "distance" between two points, vs their 
relative fitness.  However, "distance" only makes sense in this context as a 
measure of the difficulty of getting from one point to the other.  This 
implies that:

1) In a GA, "distance" is different depending on the direction in which you 
measure it.  Recombination is one of the ways to get from one point to 
another, and recombination is NOT a symmetrical operation.  Similarly, if 
mutation is not entirely random (for example, if it involves some form of 
hillclimbing or other bias),  the distance from point A to point B is 
different from the distance from point B to point A.

2) If a mutation operator allows large, entirely random mutations, all points 
in the fitness landscape are roughly equidistant from each other.  

3) Small mutations are like walking through solution space in small steps.

4) Recombination is like stepping through a wormhole to distant parts of 
solution space.  It makes solution space multiply connected.

5) The set of possible destinations depends both on the location of point A, 
but *also* on the locations of all the other members of the population and 
their fitnesses.  In other words,  the fitness landscape evolves along with 
the population.

6) In biological evolution, the representation (genotype -> phenotype mapping) 
is itself subject to evolution, along with the mutation operators and 
recombination operators.  

        The "No Free Lunch" theorem, and other models that have come out of 
the Santa Fe Institute, are limited by their a priori assumptions-- which I 
believe (based on my reading of Stuart Kauffman's books) exclude the multiple 
connectivity, the asymmetry, and the evolvable representation and operators 
that exist in both biogenetic systems and genetic algorithms.

Steve

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