Date: Mon, 1 Mar 93 09:43:37 -0500
From: Peter J Angeline <pja@cis.ohio-state.edu>
Message-Id: <9303011443.AA00409@neuron.cis.ohio-state.edu>
To: genetic-programming@cs.stanford.edu
In-Reply-To: Howard@quercus.demon.co.uk's message of Sat, 27 Feb 1993 23:06:39 +0000 <9302272257.aa02863@gate.demon.co.uk>
Subject: Fitness Adjustments
Reply-To: pja@cis.ohio-state.edu
Status: OR


Wow, great discussion about this stuff.  Here's my 2 pence.

Howard Oakly types:

> There emphatically *is* effective 'global knowledge' imposed on a
> population by the ecological niche and environment, as the members of the
> population are competing for the same food, reproductive partners, space,
> etc.  In nature, the 'fitness' of an individual as regards natural
> selection is normalised against the fitnesses of all the other individuals
> in that population which shares the same reproductive and feeding pool.  

I would have to argue, Howard, that you've successfully argued against yourself
on this one.  I agree that there are niches and competition for food and
resources but these are LOCAL competitions.  If there's a drought in Somalia,
the deer in North America are not affected by it.  The niches in Australia that
brought about the kangaroo don't alter the turtles on Galapagos. To be global,
the concequences must be available to ALL members of the population.  Natural
evolution and its method of "fitness calculation" is local.  Now if global
warming managaes to make the entire planet the same temperature, then we can
talk...


Sombody wrote:

> Then a NON-LINEAR transformation is done to get the adjusted
> fitness used in the roulette wheel. Do you realize, that when you scale the
> value returned by a factor 10 for instance, the normalized fitnesses CHANGE!?

Other's have already answered this one.  I just want to point out something
related. There are MANY ways to adjust fitness.  The Koza/Rice method of using
an exponential separation between the members of the population with better
fitness is only one method.  As Walter Tacket wrote, I am not fond of this
particular scaling function.  Here's why. The function is 1/(1+S) where S is
the standardized fitness measure. The problem is that there is a different
degree of scaling depending on the average fitness of the population.  In the
early stages, when average fitness is poor, making the values of S in the
population large, there is little separation and the function does nothing if S
is large enough. Towards the end of the run when S is small, then the
exponential kicks in and minute differences between population members are
blown up extremely large. I think this is at best exactly backwards. I'd rather
see better separation at the beginning of the run and less separation at the
end to allow more competition between nearly optimal solutions.

Goldberg's book decribes several scaling methods.  I have adopted linear
scaling, which scales by fitting a line through the fitnesses of the population
so that the best member will have a scaled fitness which is about M, the
average member will have a scaled fitness of about 1 and the worst member will
have a scaled fitness of about 1/M. This scaling method is consistent
throughout the run. When M=1.5 or 2, this is a really nice scaling function
and the one I prefer.  Not too elitist and not too non-elitist.

But, as others have said, competitive selection is the current favorite.

-pete angeline

+-------------------------+---------------------------------------------------+
| Peter J. Angeline       |  Laboratory for AI Research (LAIR)                |
| Graduate Research Asst. |  THE Ohio State University, Columbus, Ohio 43210  |
| pja@cis.ohio-state.edu  |  "Nature is more ingenious than we are."          |