Monday, June 06, 2005

The Michalewicz Test Function


Going on with the Test Function Suit, today I have one function that is very interesting: The Michalewicz Test Function.

That function is writen by this way:

F(x1,x2) = -(sin(x1)*(sin(2*x1^2/pi))^(2*10))-(sin(x2)*(sin(2*x2^2/pi))^(2*10))
x1 = [0:pi]
x2 = [0:pi]

I don't know where the global minimum is located, but I think that it is as the graphs points: (x1,x2) = (pi/2, pi/2) what gives us F(x1,x2) = -2.

I used again an ES with the same configuration fo those ES below.

Population = 60
Offspring = 60 (I used the (mu+mu)ES )
Generation = 5000
Simulation Time = 12.82799 s

Below we have some graphs.

The function:

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Another view:

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Here you have a map of the function:

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The search graph:

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I began with the best values of:
F(x1,x2) = -1.9467647907315375
x1 = 1.553340240456647
x2 = 1.6026577871222381

After 5000 generations I got:

F(x1,x2) = -1.9999999999954916
x1 = 1.5707950628346909
x2 = 1.5707936022511222

I have to try the search with a GA.

See You!!



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