A multi-recombinative active matrix adaptation evolution strategy for constrained optimization

Abstract

This paper presents the multi-recombinative constraint active matrix adaptation evolution strategy (Constraint Active-MA-ES). It extends the MA-ES recently introduced by Beyer and Sendhoff in order to handle constrained black-box optimization problems. The active covariance matrix adaptation approach for constraint handling similar to the method proposed by Arnold and Hansen for the $$(1+1)$$ covariance matrix adaptation evolution strategy is used. As a first step toward constraint handling, active covariance matrix adaptation is incorporated into the MA-ES and evaluated on unconstrained problems (Active-MA-ES). As the second step, constraint handling based on active covariance matrix adaptation for the MA-ES is proposed (Constraint Active-MA-ES). The algorithm has been tested on different test functions and it has been compared to other methods. The experiments show that for cases where directional sampling of the offspring mutations is beneficial, the Active-MA-ES can reach the target faster than the MA-ES. In particular, the Active-MA-ES reaches the final target precision on average by a factor of 1.4 generations (Ellipsoid), a factor of 1.6 generations (Different Powers), and a factor of 2.0 generations (Tablet) faster than the MA-ES. The experiments for the Constraint Active-MA-ES reveal that it achieves 80% of the considered targets with about $$N \times 10^5$$ function and constraint evaluations. With this result, it is the best method among the compared approaches.