How can i use ga optimization to generate bit solutions in a vector?

Hi.

I am trying to use optimization toolbox with ga solver or only with ga function to find a solution that contains only bit variables present in a vector with 9 positions. Each position contains 0 or 1, as a representation of the "on/off" of 9 branches in a distribution network.

I've set: Polpulation type as : bitString Creation funtion as : uniform Mutation function as: uniform Crossover funtion as: scaterred

As was said by toolbox warning that appears when bitString population is choosen.

I've defined an equality constraint to confine the solutions to 6 and only 6 bits. For that, I set:

Aeq=[1,1,1,1,1,1,1,1,1].

beq=6

The problem is that generated solutions are not only bits. Some solutions do not respect the population type specified, so they are not valid.

I mean, when it should generate solutions like [1,1,1,1,1,1,0,0,0].

In many cases it generates a solution like [1.6161, 0, 0, 0.7306, 0, 0.7306, 0.7306, 0.7306, 0].

So I do not understand what is happening, and I think that I am probably missing some parameter that is adulterating the solutions generated in each iteration.

So if anyone can help me I really appreciate.

Best regards, Vitor Ribeiro.

Answer 1

[Alan Weiss]

The bit string population type does not accept linear constraints, as the documentation states.

I suggest that you use mixed integer GA. This form does not take equality constraints, but, as documented, you can use two inequality constraints, possibly with a bit of slack.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[Vitor Ribeiro]

Firstly, I want you to know that I very appreciate your answer.

So, I tried to use your recommendation but I'm affraid that I may not be able to do that changes, cause I am not so conversant with toolbox as I probably should.

If I wanted to keep bit string population, could I create a nonlinear constraint function for having [9x1] vector solutions with all nine positions composed by bits and only 6 positions of a solution with bit 1? Limiting all inside a nonlcon funtion?

If yes, pls tell me how to learn creating nonlinear constraints.

Thanks by answering me. I really appreciate that.

Regards, Vitor Ribeiro.

[Alan Weiss]

The documentation link I gave states the following for the bit string population type:

You cannot use a Hybrid function, and ga ignores all constraints, including bounds, linear constraints, and nonlinear constraints.

It is very easy to use mixed integer GA, I suggest again that you look at it.

Alan Weiss

MATLAB mathematical toolbox documentation