An adaptive penalty function with meta-modeling for constrained problems

Constraints can make a hard optimization problem even harder. We consider the blackbox scenario of unknown fitness and constraint functions. Evolution strategies with their self-adaptive step size control fail on simple problems like the sphere with one linear constraint (tangent problem). In this paper, we introduce an adaptive penalty function oriented to Rechenberg's 1/5th success rule: if less than 1/5th of the candidate population is feasible, the penalty is increased, otherwise, it is decreased. Experimental analyses on the tangent problem demonstrate that this simple strategy leads to very successful results for the high-dimensional constrained sphere function. We accelerate the approach with two regression meta-models, one for the constraint and one for the fitness function.