Options for ga() with only integer variables

Hello to everyone,

I want to run a ga() with just integer variables.

The boundary conditions that I set for myself are: number of variables is 5, lb is 1 and the ub is 4. So there are 1024 possible combinations. My number of generations will be 7 with a Population of 30.

I am using gacreationuniform, crossoverlaplace and mutationpower. Also, I will try several Crossover fractions.

When I run with this set of parameters and with an crossover fraction of 0.2, I will "only" get 132 unique individuals.

Does any one have an idea to set better parameters for the ga()?

Thank you very much and greetings,

Jonas

[John D'Errico]

With that few possible options, why not just evaluate the objective at every valid combination, and take the best?

[Jonas]

My simulation time is several hours. Also I want to have an methodical approach.

Answer 1

[Walter Roberson]

Suppose you had a surface that had a large bowl, but also had a narrow deeper pit. Any given initial population might happen to all be in the catch-basin for the large bowl. Optimization on that bowl might only require examining 1/8th or so of the possibilities to find the minima of the bowl.

Is cross-over and mutation guaranteed to find the narrow deep pit? No -- at least not unless you run a large population for a lot of iterations. The catch-basin for the narrow deep pit might only cover (for example) 1/256 th of the possibilities.

[Sam Chak]

Hi @Jonas,

I think this is scenario of a large bowl with a narrow pit. The deepest pit lies at .

x = linspace(1, 7, 60001);
y = exp(-(exp(- abs((x - 4)/0.8))/0.04).^2) - exp(-(x.^4 - 16*x.^2 + 5*x).^2);
plot(x, y), grid on, xlabel('x'), ylabel('y')

fun = @(x) exp(-(exp(- abs((x - 4)/0.8))/0.04).^2) - exp(-(x.^4 - 16*x.^2 + 5*x).^2);
lb  = 1;
ub  = 7;
options = optimoptions('ga', 'PopulationSize', 30, 'MaxGenerations', 7);
x   = ga(fun, 1, [], [], [], [], lb, ub, [], options)

Optimization terminated: maximum number of generations exceeded.

x = 3.8839

[Walter Roberson]

Imagine something like

A                       B    C

*                       *    *
 **                   ** *  *
   ******** **********   * *
           *             **
                         +
                         
           D             E

if you start anywhere in the range A to B, you are going to end up either at D or in the shallow bowl.

If you start in B to C you may end up at the true minima at E (but in some cases you would end up near D anyhow even if you started in B to C range.)