Competitive coevolutionary algorithm for robust multi-objective optimization: the worst case minimization

Abstract

Multi-Objective Optimization (MOO) problems might be subject to many modeling or manufacturing uncertainties that affect the performance of the solutions obtained by a multi-objective optimizer. The decision maker must perform an extra step of sensitivity analysis in which each solution should be verified for its robustness, but this post optimization procedure makes the optimization process expensive and inefficient. In order to avoid this situation, many researchers are developing Robust MOO, where uncertainties are incorporated in the optimization process, which seeks optimal robust solutions. We introduce a coevolutionary approach for robust MOO, without incorporating robustness measures neither in the objective function nor in the constraints. Two populations compete in the environment, one representing solutions and minimizing the objectives, another representing uncertainties and maximizing the objectives in a worst case scenario. The proposed coevolutionary method is a coevolutionary version of MOEA/D. The results clearly suggest that these competing co-evolving populations are able to identify robust solutions to multi-objective optimization problems.