Constraining Dependent Variables in ga Optimization

Hi,

I am trying to constrain my optimization for min f(x) by restricting the range allowed for a dependent variable h(x). I am using a the ga optimizer from the Optimization Toolbox. Do I need to write a penalty or barrier function into by objective function, or is there another simpler way that I can apply the constraint? I tried using the nonlcon input in the ga function, however have been unable to get it to converge. The documentation suggests that nonlcon can only take x (independent variable vector) as an input and so I think that reading in dependent variables may be a misuse of the function.

Please help! Any guidance would be greatly appreciated.

Answer 1

[Matt J]

The documentation suggests that nonlcon can only take x (independent variable vector) as an input and so I think that reading in dependent variables may be a misuse of the function.

Well, nonlcon should be written to accept a vector in the space of x as input, not a vector in the space of h. However, since h is a function of x, that should be straightforward. Something like this,

     function [c,ceq] = nonlcon(x)

        ub=... %upper bounds
        lb=... %lower bounds          

        hx=h(x);

        c=[hx(:)-ub(:);  lb(:)-hx(:) ];
        ceq=[];

     end

Are you sure it's not converging, or might it just be converging to something you don't like? With nonlinear constraints, it can be difficult to find a good initial population, especially if the constraints define a set with several disconnected regions.

[dpud12]

Hey Matt thanks for the quick answer. Unfortunately yes, it is definitely not converging. Also, in each generation it says that my best penalty value is the same as my average penalty value for the population.

Your suggested code makes sense, except that I use ga to optimize a "black box" model (a large excel sheet that I read/write), and h(x) is produced by this model and then read in from it; and so I am unable to calculate it from the independent variables alone. I know in theory this shouldn't be a problem, however, when I run the optimization without the constraint it converges quickly, and so by process of elimination I think this is the error. Any ideas? I can attach my code if that would make it you'd like.

Thanks again for your help!

[Matt J]

and so I am unable to calculate it from the independent variables alone.

I assume that means that there are additional problem constants that the calculation of h(x) depends on. If so, that is covered in Passing Extra Parameters.

[dpud12]

Hey Matt,

Thanks for the help, turns out I was not properly passing the parameters as you noted. The specific problem was my assumption for when the constrain functions were evaluated. I was under the impression that the constraints were evaluated at the same time the objective function was evaluated for each member of the population. As a result I was only reading in from my excel sheet and not writing the x variables to the excel. This was resulting in the error I noted:

 Also, in each generation it says that my best penalty value is the same as my average penalty value for the population.

I changed it to write to my excel sheet for each variable vector x and the problem is now converging wonderfully! I now just need to figure out whether it evaluating the constraints for the entire population set before or after the objective function, so that I can reduce run time and eliminate unnecessary xlswrite1 commands, but should be able to figure that out easily enough on my own.

Thanks again for your help!