Newsgroups: comp.ai.genetic
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From: monty@watson.open.ac.uk (Tony Hirst)
Subject: Re: Fitness Landscapes
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Message-ID: <monty-221096111501@uu-igor-mac.open.ac.uk>
Date: Tue, 22 Oct 1996 11:15:01 GMT
References: <325e691a.0@news.iea.net> <32675DF0.41C67EA6@robot.uvsq.fr>
Organization: HCRL, The Open University, UK
Followup-To: comp.ai.genetic
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>> Steve McGrew wrote:

> >   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:
> > 

For what it's worth, I think that people are starting to think about this
more and more - witness the work of stadler, culberson, t.jones, wagner,
mayley, etc who all emphasize the structuring role of operators. (also my
own http://watson.open.ac.uk/~monty/wsc1-ssn.html)

Distance may be sensibly defined in terms of the number of times a genetic
operator has to be applied to an individual or pair of individuals to reach
another point in the genotypic representation space. In addition, the
ruggedness of the fitness landscape depends on the space over which it is
visualised - this space is usually the nearest neighbour/single bit
mutation space for convenience but it doesn't have to be so. 

Given that fitness of an individaul may depend on other members of the
population, I prefer to think of the fitness landscape over the current
population. This makes visualisation easier becasue a) there are less
points to consider and b) we can calculate all the other points in
principle reachable from the current population under the appliaction of
the genetic operators. Short termism for sure, but when you try and get
your head round looking into the far future evolution of the system you
realise anything's possible and it all becomes a nonsense. Remember, the
evolution of a pop is history dependent, individual lives do actually
matter (especially in small pops and under certain selective conditions).

On the subject of selection - it's all very well talking about the fitness
surface over a pop and using it to guide how you think the population will
evolve under proprtional selection, but when you start using other
selection regimes, such as truncation selection for an extreme example, the
fitness surface is transformed into a "surface of selective value" (after
wright) where many distinctions (on the basis of fitness) between
individuals may be lost. As a consequence, I would argue against thinking
about the fitness surface over the genotyopic space, structured by whatever
operator, and in favour of thinking about the selective value over the
current population.

Now, this raises the obvious question of how do I know what the pop will
look like even at the 2nd generation if i start off with an initial
diverged population and a huge possible number of next gen
populations...and the answer to this is don't start with a diverged pop,
start with a converged one (fewer possible next gen pops) and let neutral
evolution take the converged pop on a stroll through the fitness landscape
(you may want to find a reasonably fit region of the fitness landscape to
begin with by sending out a scouting party by evolving a small initially
divergent pop for a few tens of gens). To avoid getting stuck all the time,
neutrality must be supported by the *selective landscape* as it is with
truncation; adding a bit of plasticity so that the genotype to fitness
assessed phenotype mapping is one-many also allows for neutral evolution.

Enough...

monty
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 All opinions etc etc...
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      | Tony Hirst ("Monty")          | e-mail:  A.J.Hirst@open.ac.uk
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