A (1+1)-CMA-ES for constrained optimisation

This paper introduces a novel constraint handling approach for covariance matrix adaptation evolution strategies (CMA-ES). The key idea is to approximate the directions of the local normal vectors of the constraint boundaries by accumulating steps that violate the respective constraints, and to then reduce variances of the mutation distribution in those directions. The resulting strategy is able to approach the boundary of the feasible region without being impeded in its ability to search in directions tangential to the boundaries. The approach is implemented in the (1+1)-CMA-ES and evaluated numerically on several test problems. The results compare very favourably with data for other constraint handling approaches applied to unimodal test problems that can be found in the literature.