Adapting MOEA/D to CMA-ES for Dealing with Ill-conditioned Multiobjective Problems

Ill-conditioned problems are widely acknowledged as a major challenge in singleobjective optimization, yet they remain largely unexplored in evolutionary multiobjective optimization. In this paper, we introduce a decomposition-based multiobjective evolution strategy (MOES/D) for optimizing non-separable and ill-conditioned multiobjective problems. In contrast to most existing approaches that integrate evolution strategies while potentially compromising their essential features, we develop novel, tailored strategies to coordinate evolution strategies, maximizing their strengths. These strategies collectively contribute to the efficiency of MOES/D, which include an importance mixing algorithm that enhances sample efficiency in an unbiased manner, a collaborative ascent method that optimizes multiple subproblems simultaneously, and a principled resource allocation based on expectation-maximization that prioritizes the evolution strategy models. To bridge the gap in the field, we propose a novel benchmark suite in which all instances are non-separable and either moderate- or illconditioned. Extensive experiments on the suite demonstrate that MOES/D excels at solving moderate- or ill-conditioned multiobjective problems, outperforming most state-of-the-art algorithms by a significant margin.