Re: Symbolic Integration with Genetic Algorithms?

You could have a look at this site:
http://www.gepsoft.com/gepsoft/
I am currently using one of their programs.
aprx


Binesh Bannerjee a écrit:

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> Hi!
>         I was struggling with trying to do a program that would
> numerically integrate this multivariate function (The function
> is complicated and isn't really important, I think), but, this
> thought occured to me, and I was wondering what everyone thought
> here:
>
>         Say you have a function f(X) where X is a vector of n
> dimensions (terminology? but, in c parlance, I mean to say an
> array of n doubles) anyway, you have a function f(X) which is
> defined in some way, and you can't find a closed form solution
> to Integrate[f(X),X1,X2,...Xn]
>
>         Would genetic algorithms be a good way of finding
> FUNCTIONS, that might approximate it on certain ranges, the
> way that for instance, I've seen an approximation to the Normal
> CDF where z > 0 as
>         CDF = 1 - 0.5 * ((1+c1 z + c2 z^2 + c3 z^3 + c4 z^4) ^ -4);
> where
>         c1 = 0.196854,
>         c2 = 0.115194,
>         c3 = 0.000344
>         c4 = 0.019527
>
> So, I could pass the GA my function and tell it that I expect
> to want to numerically integrate on ranges from -100,100 and it
> would generate a function that would _approximate_ the integration
> without actually doing the numerical integration. I could then
> look at the function, and decide what it's error characteristics
> were, before plugging it into the actual app, etc.
>
> I'm expecting that the GA would be of the "genetic programming" type
> where the functions would include exp and tan, and all the usual
> mathematical operators.
>
> Has this been done? Does that seem like a reasonable app for a
> GA? I'm not stuck on the idea of generating the function via GA,
> so if others have different means to generate an approximate
> function given f that computes the integral of f, I'd be open to that
> as well...
>
>
> Thanks!
> Binesh Bannerjee
>
> - -- 
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> 	-- Numerical Recipes in C
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