Re: [asa] Parameterized Evolution

On Aug 24, 2008, at 3:39 PM, William Hamilton wrote:

>
>
> I find much that I agree with in this thread -- and some things that
> are puzzling. As Iain pointed out, when the input variables are
> coupled, changing a number of inputs (not necessarily all)
> simultaneously makes sense. If you can compute the gradient, then
> you can use steepest descent or the conjugate gradient method or
> Newton's method to determine how much to adjust each input variable.

The problem why GA and simulated annealing are used rather than
Newton's method is to avoid a local minima which your discussion below
alludes to. You change too many variables simultaneously and you get
too greedy. Maybe a clarifying note here will be helpful. When I am
talking about vary multiple variables I am talking about varying
multiple variables that all lower the cost function. (See my next
paragraph) If you dive too quickly to a local minima you might get
"stuck".

>
>
> I find this puzzling. I think the criterion for using a GA is the
> form of the fitness function. If it varies smoothly and (especially)
> if its gradient can be computed or approximated without undue
> computational effort then steepest descent, conjugate gradient or
> possibly Newton's method are appropriate. If it has a complex and/or
> nondifferentiable structure, then GA's are appropriate. For example
> if you were trying to maximize (1-x^2)*sin(1/x) on [-1,1] a gradient
> algorithm wouldn't be appropriate because the function is not
> differentiable at 0. Yet a GA would (I haven't tried it but I'm
> pretty sure this is so) find a point near zero. (The function isn't
> even defined at zero, but the peaks will increase in value as the
> search point tends toward zero. )
> In a multivariable optimization problem a GA will vary many, perhaps
> all, of the input variables, in possibly large steps. Chaos doesn't
> result because the unsuccessful variations are eliminated in the
> next generation.

As you stated unsuccessful states get pruned by GA. What the effect of
what was proposed by UcD was a set of large net changes which would
presumably be after pruning and that would be chaotic. What we are
illustrating is that a large number of simultaneous deliberate changes
is inferior to a large number of random changes subject to selection
as a design strategy. Selection keeps that rate under control. When I
am designing in a deliberate fashion rather than running a brute-force
computer model I better not be turning all the knobs simultaneously.
If something goes wrong I don't have a clue why.

>
> Agreed. Genetic algorithms work well in computers and in nature
> because they are brute force paralel algorithms. Use a large enough
> population and have available a rich enough set of variations, and
> eventually you will get an improvement in fitness. And as Iain
> pointed out, such a population can track a changing fitness
> function. (I don't understand Rich's comment about how static
> fitness function can lead to extinction. Shouldn't it just lead to a
> fairly stable population that wanders around the peak of the fitness
> function?)
>

If your cost is static then the diversity that is producing is small.
As you rightly say, it just wanders around the peak. If such an
environment gets "shocked" it cannot respond well to the shock and all
the selection does is to select everything away and thus mass
extinction. Take a modern example. If you have a stable climate and
have life that's adapted to it there is very little to select from
when you shock it with a large anthropogenic climate change. This is
why mass extinction rather than a burst of biodiversity is being
predicted given AGW.

Rich Blinne
Member ASA

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Received on Sun Aug 24 20:13:48 2008