Multiobjective optimization problems with complicated pareto sets

Abstract—Partly due to lack of test problems, the impact of the Pareto set (PS) shapes on the performance of evolutionary algorithms has not yet attracted much attention. This paper in-troduces a general class of continuous multiobjective optimization test instances with arbitrary prescribed PS shapes, which could be used for studying the ability of multiobjective evolutionary algorithms for dealing with complicated PS shapes. It also pro-poses a new version of MOEA/D based on differential evolution (DE), i.e., MOEA/D-DE, and compares the proposed algorithm with NSGA-II with the same reproduction operators on the test instances introduced in this paper. The experimental results indicate that MOEA/D could significantly outperform NSGA-II on these test instances. It suggests that decomposition based mul-tiobjective evolutionary algorithms are very promising in dealing with complicated PS shapes. Index Terms—Aggregation, decomposition, differential evolu-tion, evolutionary algorithms, multiobjective optimization, Pareto optimality, test problems. I