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From: rhh@matilda.vut.edu.au (Robert Hinterding)
Subject: Re: Crossover vs Mutation
Message-ID: <Do7GL7.8p@matilda.vut.edu.au>
Organization: Victoria University of Technology
References: <4gfvv5$d7r@soleil.uvsq.fr> <DnBHuv.4r7@matilda.vut.edu.au> <4h3os4$hkb@soleil.uvsq.fr> <DnpwAo.2w7@matilda.vut.edu.au> <4i1jpl$d8o@soleil.uvsq.fr>
Date: Wed, 13 Mar 1996 12:12:43 GMT
Lines: 82

Olivier Chocron <chocron> writes:
>-- rhh@matilda.vut.edu.au (Robert Hinterding) wrote:

>>In Evolutionary Computation
>>we are currenlty only looking at problems which are trivial compared to living
>>organsims, and we are free to choose representations, operators and algorithms
>>which all have some effect on the problems we are trying to solve.

>I do not agree with "trivial", even compared to living organisms.
>As you know, EAs have been designed to solve some very complex optimization
>problems (as design) because for such problems, classic optimization algorithms
>did not work well, even did not work at all.

I think that says more about the limitations of classical optimisation 
algorithms.  They seem capable of only solving regular and well behaved
probems.  I agree that ESs can solve more complex and less well behaved
problems, or at least get good approximations to the solutions. But these 
problems are still trivial compared to the problem of designing, sequencing
the development and programming the maintenance of living organisms.

>>My own feeling is that Evolutionary Computation algorithms are simple (in terms
>>of complexity), but that their behaviour is complex.

>Nevertheless, I agree with that.So my feeling is that interest of EC is that it
>uses simples algorithms to solve complex problems...in a complex way.

>he then wrote:
>> By getting emperical
>>evidence of which operators and representations are effective for different
>>problems types, we should be able a gain a better understanding of these
>>operators and representations.  This should help us to able to predict which
>>algorithms, representation and operators to use for different problems and
>>give us a better understanding of how Evolutionary Computation works.

>Here, I do not believe it is a consistant approach, as for me, there is nothing
>such as an empirical evidence (but rather empirical verifications).An evidence
>needs to be mathematically proved to be used in a more general way than for one
>single case.As even for the same type of problems, there exist a multitude of
>ways to represent, encode, apply genetic operators and so on.
>If you can't mathematically prove the superiority of a genetic operator on a
>type of problems, you must at least find out what mecanisms are involved and
>you might then suppose what consequences it have on the search.

I am a computer scientist not a mathematician, and I think that we use 
mathematics to model observed behaviour, and then if our models results
are close enough to the observed behaviour (empirical evidence) and 
we can use it to produce results in a resonable time, we can use the model
to make definite predictions.  But if the system we are trying to model
is too complex and/or stocastic in nature we tend to be able to predict
results within a range of probabilities, or be able to say a certain result
will happen but not be able to say when it will happen. Hardly a proof.
I think that ESs fall into the latter category.  

>Of course, an empirical approach is not useless and all mathematical proof must
>be explain empirical results.But this kind of approach will not allow to have
>any real understanding of the search mecanisms, but only ideas about it.
>Finally, using mathematical representation of the problem is the best way to
>have insights (as you can explicitly see the consequences) the mecanisms of the
>search and so to improve your algorithm by new encoding or operators.

>Hoping you understand my point of view,

I am not sure that I do.

What I am saying is:
You can use empirical evidence to validate/invalidate a proof.
But you cannot use a proof to invalidate empirical evidence.

I think mathematics is a useful tool, but it does have limitations.
I also think we use mathematics more to explain what we find, and understand
what is happening, than to prove what will happen, especially for systems
with such complex behavior as ESs.


Greetings from the land downunder
Robert

-- 
Robert Hinterding                       Email: rhh@matilda.vut.edu.au 
VICTORIA UNIVERSITY OF TECHNOLOGY       Fax:   +61 3 9688 4050
P.O. Box 14428, Melb Mail Centre        Phone: +61 3 9688 4686              
AUSTRALIA 3000                          Home Page: http://dingo.vut.edu.au/~rhh
