Sunday, July 31, 2005

Evolution Strategies Comparison

Hello, My Friends!! :D

NOTE: Correction made: before I had writen (5+5)-ES where now is (25+25)-ES.

Today I will show a little comparison that I made with the Evolution Strategies(ES). I tested three ES:

(60+60)-ES
(15,120)-ES
(25+25)-ES

In all I used the same kind of genetic operators: mutation and crossover. The (25+25)-ES I made some modifications and these seems to have worked very well, once that ES was the best in all tests. The (25+25)-ES used only 500 generations, the other two used 3000.

First Test: The Easom Function
Global Optimum: x1 = x2 = pi; f(x1,x2) = -1;
Minimization Problem.

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The "Red Line" is the (25+25)-ES, the "Blue Line" is the (60+60)-ES and the "Black Line" is the (15,120)-ES.

I think that the (15,120)-ES was so random, it remembers me a random walk.

Second Test: Schaffer Function
Global Optimum: x1=x2=0; f(x1,x2)=0;
Minimization Problem.


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The "Red Line" is the (25+25)-ES, the "Blue Line" is the (60+60)-ES and the "Black Line" is the (15,120)-ES.

Third Test: Michalewicz Function.
Global Optimum:x1=x2=pi/2; f(x1,x2)=-2;
Minimization Problem.

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The "Red Line" is the (25+25)-ES, the "Blue Line" is the (60+60)-ES and the "Green Line" is the (15,120)-ES.

A closer view:

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Well, as you see in all three cases the (25+25)-ES was superior in achieving the global optimum, even using a smaller population and using only 500 generations.

Até Mais!!!

[]´s

Nosophorus

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