MATLAB: Constraining Dependent Variables in ga Optimization

constrained optimizationgenetic algorithmGlobal Optimization ToolboxMATLAB

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.

Best Answer

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.
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