Injecting CMA-ES into MOEA/D

MOEA/D is an aggregation-based evolutionary algorithm which has been proved extremely efficient and effective for solving multiobjective optimization problems. It is based on the idea of decomposing the original multi-objective problem into several singleobjective subproblems by means of well-defined scalarizing functions. Those single-objective subproblems are solved in a cooperative manner by defining a neighborhood relation between them. This makes MOEA/D particularly interesting when attempting to plug and to leverage single-objective optimizers in a multi-objective setting. In this context, we investigate the benefits that MOEA/D can achieve when coupled with CMA-ES, which is believed to be a powerful single-objective optimizer. We rely on the ability of CMA-ES to deal with injected solutions in order to update different covariance matrices with respect to each subproblem defined in MOEA/D. We show that by cooperatively evolving neighboring CMA-ES components, we are able to obtain competitive results for different multi-objective benchmark functions.