Genetic Algorithm Tool Question.

I'm going to oversimplify my problem so that you know exactly what I am trying to figure out. So say you have an array of a few numbers and you have an extremely long code that does a bunch of operations on this array and returns three values. So I want ga to change the values in the array to minimize the three output values. How do I go about doing this? Changing the array values at the beginning of the code to minimize three outputs at the end of the code. Thanks!

Answer 1

[Alan Weiss]

This is known as multiobjective optimization, because you have three numbers that you are trying to minimize. Obviously, you cannot in general find one set of inputs that simultaneously minimizes all of the outputs.

The gamultiobj function is designed to find the Pareto set, meaning the set of nondominated points. Each point on the Pareto set can have one function value lowered only by raising some other ones.

See What Is Multiobjective Optimization and an example or even a different example.

Alan Weiss

MATLAB mathematical toolbox documentation

[Scott Lowrie]

Thanks for your reply Alan, this helps me understand how I'll go about minimizing these three things. But the real issue it seems is how gamultiobj will know to change the values of this array from the beginning of the program to minimize these three outputs. Such as below, in this basic form, the program changes x to minimize y(1) and y(2). How do I tell the program to change each of the values in an array to minimize y(1) and y(2)? This may be something simple that I am just missing. Thanks for the help!

        function y = simple_multiobjective(x)
           y(1) = (x+2)^2 - 10;
           y(2) = (x-2)^2 + 20;

        FitnessFunction = @simple_multiobjective;
        numberOfVariables = 1;
        [x,fval] = gamultiobj(FitnessFunction,numberOfVariables);

[Alan Weiss]

You have to write a fitness function that accepts a row vector x containing all the variables that you want to move, and that gives a row vector output f containing the function values at the point x. In other words,

 f = yourfunction(x)

where yourfunction is your function.

gamultiobj then tries to move all the values in x to find the Pareto points. Really, you should look at the examples that I linked to.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation