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 introduces a general class of continuous multiobjective optimization test instances with arbitrary prescribed PS shapes, which could be used for studying the ability of MOEAs for dealing with complicated PS shapes. It also proposes a new version of MOEA/D, i.e., MOEA/D-DE and compares it with NSGA-II with the same reproduction operators on the test instances introduced in this paper. The experimental esults indicate that MOEA/D could significantly outperform NSGA-II on these test instances. It suggests that decomposition based multiobjective evolutionary algorithms are very promising in dealing with complicated PS shapes.
This paper has been accepted by IEEE Transactions on Evolutionary Computation.