Genetic Algorithm for multiple variables

Hi everyone, I'm new to matlab and would like to use the GA function. I am having issues writing a proper fitness function I believe. I was wondering if anyone could help me. I am working on two GA problems one the function that I'm trying to optimize is:

    max f(x1, x2) = 2x(1)^2 + x(2)^2 + 3x(3)^2

When I've tried to put this function into matlab, it gives me errors for having two variables.

The second function that I'm trying to use with GA is:

    Min f(a,b,c,d) = 18abcd

Any information that anyone could provide would be greatly appreciated. Thanks.

Answer 1

[Alan Weiss]

There are at least two issues here.

1. All fitness functions must be a function of ONE VARIABLE. However, this variable, usually called x, can be a vector or matrix, so this is not a restriction. For example, your fitness function would be

 fun = @(x)-(2x(1)^2 + x(2)^2 + 3x(3)^2)

(Why do I have a negative sign? ga minimizes, so to get the maximum, minimize the negative.) And to me this seems to be a function of THREE variables, not two.

2. This is a smooth objective function. You should not use ga to minimize a smooth objective, you should use fmincon. I assume that you have some nonlinear constraints. If you have only linear constraints, you should use lsqlin.

3. By now you should realize that your second objective function should be coded as

 fun = @(x)18*x(1)*x(2)*x(3)*x(4)

or maybe the negative of that if you are trying to maximize.

Good luck,

Alan Weiss

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