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From: mjd4c@uvacs.cs.Virginia.EDU (Michael J. Daniel)
Subject: Re: Bloating the population size
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Date: Mon, 19 Jun 1995 16:23:30 GMT
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In article <3rqoe7$j10@pith.uoregon.edu>, ben@chinook.uoregon.edu (Ben Marcotte) writes:
> Simon Thompson (sgt@sis.port.ac.uk) wrote:
> 
> : Basically I think that GA's can be improved in two ways with regard to 
> : populations.
> 
> : 1) Increase the size for the whole shibang.
> 
> 	Not neccesarily.  And if my previous discussion wasn't confusing, 
> this one will be!
> 
> 	The quick way to put it is that two individuals with "good" 
> fitnesses have a harder time "finding" each other for mating in a larger
> population.  Imagine that we have two individuals, A and B that both have
> fitnesses of 0.2.  Also, these fitnesses are scaled such that the sum of
> all the fitnesses in the population is 1.0 (this makes it easier to do
> round-robin selection of parents for mating, but that's another
> discussion).  This means that A and B would have a 8% chance (0.2*0.2 * 2
> for AxB or BxA) of mating with each other.  Now, if the population were
> doubled (and the new individuals had similar fitnesses to the pre-existing
> members), the new scaled fitnesses for A and B would both be 0.1.  They
> would now have a 2% chance (0.1*0.1*2) of mating with each other. 
> 
> 	This difference can be seen in a graph showing the best individual
> fitness in the population over time in a population with a zero mutation
> rate.  With the zero mutation rate, the population will reach a plateau
> after some number of generations due to all of the combination space 
> being searched through crossover.

This last sentence is clearly wrong.
Most of the combination space is never searched.


I have trouble with a lot of this poster's explanations.
These are large (relatively anyway) dynamical systems whose emergent bahavior
can not be discovered from, infered by, or attributed to the behavior of 
a few individuals. (That's why it's so interesting!)


Larger populations take longer but find better answers because
intermediate solutions survive longer allowing them a greater
chance of contributing to better answers. 
(Which seems to be the opposite of explanation given by the poster)

You can often obtain a similar result by reducing the selective 
pressure, ie slowing down evolution, without increasing the population
size.


> : 2) Maintain greater diversity, without loosing the focus of the search.
> 
> 	This is the purpose of mutation and crossover!

Crossover has the quite regular result of eliminating diversity.


Michael


