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### Re: Evolution in Action.

by kvale (Monsignor)
 on Feb 26, 2005 at 16:27 UTC ( #434789=note: print w/replies, xml ) Need Help??

in reply to Evolution in Action.

Cool program!

The evolution of the score you see is pretty typical of genetic algorithms and genetic programs: much progress is made in the initial iterations, but it takes a lot more to gain further improvement.

I just wanted to mention that the assertion by ff's professor that you only need 30 tries is patently false. If a problem has many degrees of freedon and a complex error surface, in general the amount of searching one must do is O(k^N), where N is the number of degrees of freedom and k is related to the complexity of the error surface.

To see this, consider a simple example. Suppose we one have degree of freedom and we know that a good solution lies either at x = -1 or x = 1. Then we only have to search twice. Now add a similar degree of freedon y that interacts with x in a complex way. Then we would need to search (+-1, +-1), or 4 attempts. Adding another would need 8 attempts, and so on, yielding O(2^N) behavior. An this is just looking for a good quadrant! This blowup of search space with degrees of freedom is called the 'curse of dimensionality' and along with a complex error surface, is the basic reason that some problems are NP-complete.

Some problems have some nice large scale structure of the error surface that admit heurisitic guesses that often do well, but others, like k-satisfiability for k > 2, don't seem to. So don't throw away your simulated annealing and genetic algorithms code yet!

-Mark

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