Constrained Variable Genetic Algorithm

Hello,

Need help on solving a problem with the GA toolbox (have a variant soln that works but am not sure of the soln). I have a function say 'piqe' that I am looking for the global minimum. The inputs to this function are (x1 ... xn). These inputs variables can only take values 1:5 (upper and lower bound).

However the variables serve as indexes (1 say leftmost, 5 rightmost) to a matrix function say

P = [30 20 10 5 0; 27 17 7 2 0; 20 14 4 0 0; 14 12 7 4 0; ..................];

I need to constrain the inputs to 'piqe' so that P(1,x1) + P(2,x2) + ...... + P(n,xn)<Constant.

I am having some problem on implementing the last part (relational constraint) into the toolbox. thanks

[Walter Roberson]

When you say 1:5 do you mean the list 1, 2, 3, 4, 5? Or do you mean the range 1 to 5 ?

[Natialol]

Range 1 to 5. As in x(i) can only take values 1 to 5. Thanks

Answer 1

[Alan Weiss]

It seems from your description that you want all the variables x1,...,xn to have integer values. If this is the case, and if you have MATLAB R2011b or later, then you can use integer programming. See the documentation of integer programming and also see this extensive example.

Setting nonlinear inequality constraints means programming a function in the proper syntax. For your case, of you have P defined in your workspace, then you can use something like

 function [c,ceq] = pconstraint(x,P)
 ceq = [];
 c = -Constant; % put in the value of Constant here
 for ii = 1:numel(x)
    c = c + P(ii,x(ii));
 end

Pass @(x)pconstraint(x,P) as your nonlinear constraint function. Also, I would advise you to give both an initial range of 1 to 5 on all componenets, and set a large population size.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation