Active covariance matrix adaptation for multi-objective CMA-ES

This paper proposes a novel approach for a derandomized covariance matrix adaptation for multi-objective optimization. Common derandomized multi-objective algorithms only utilize the information gained from successful mutations. However in case of optimization problems with a limited budget for fitness evaluations inferior mutations provide additional information to adjust the search. The proposed algorithm, called active-(μ+λ)-MO-CMA-ES, extends previous approaches as it reduces the covariance along directions of unsuccessful mutations. In experiments on a set of commonly accepted multi-objective test problems the presented algorithm outperforms other derandomized evolution strategies.