Surrogate Constraint Functions for CMA Evolution Strategies

Many practical optimization problems are constrained black boxes. Covariance Matrix Adaptation Evolution Strategies (CMA-ES) belong to the most successful black box optimization methods. Up to now no sophisticated constraint handling method for Covariance Matrix Adaptation optimizers has been proposed. In our novel approach we learn a meta-model of the constraint function and use this surrogate model to adapt the covariance matrix during the search at the vicinity of the constraint boundary. The meta-model can be used for various purposes, i.e. rotation of the mutation ellipsoid, checking the feasibility of candidate solutions or repairing infeasible mutations by projecting them onto the constraint surrogate function. Experimental results show the potentials of the proposed approach.