MATLAB: Constraints in Genetic Algorithm – Not Just Input Constraints

Question

Is it possible to specify constraints that are not just reliant on the input variable? I.e. a constrain that may be a function of the output or an intermediate variable.

NOTE: The output of this system is calculated from a "black box" (it's a PSS SINCAL simulation).

At this stage I've been using a workaround – making the result of the fitness function a very high value when the output is not within the constraints. Looking for a more elegant solution.

Thank you

Elvis

Answer 1

Nonlinear constraint functions allow you to express any constraint at all, as long as MATLAB can calculate what you need to decide if a point is feasible.

For nonlinear inequality constraints, the mechanism assumes that the constraint is of the form

 c(x) <= 0

where c(x) is a smooth function. So, for example, if you want to constrain x to be within the circle

 norm(x) <= 5

you would write the constraint

 c(x) = norm(x) - 5;

This way, when norm(x) is a bit greater than 5, the solver knows it is infeasible, but also knows that it is close to being feasible.

What I am saying is, don't just set the objective value to an arbitrary high value when the nonlinear constraint is not met, but use a nonlinear constraint function, and set it to a positive value when the constraint is not met, but one that goes smoothly to negative as the constraint becomes satisfied.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation