[Qingfu Zhang's homepage]
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 multiobjective evolutionary algorithms for dealing with complicated PS shapes. It also proposes 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 multiobjective evolutionary algorithms are very promising in dealing with complicated PS shapes.
Test problems have played a fundamental role in understanding the strengths and weaknesses of the existing Evolutionary Multi-objective Optimization (EMO) algorithms. A range of test problems exist which have enabled the research community to understand how the performance of EMO algorithms is affected by the geometrical shape of the Pareto front (PF), i.e., PF being convex, concave or mixed. However, the shapes of the Pareto Set (PS) of most of these test problems are rather simple (linear or quadratic), even though the real-world engineering problems are expected to have complicated PS shapes. The state-of-the-art in many-objective optimization problems (those involving four or more objectives) is rather worse. There is a dearth of test problems (even those with simple PS shapes) and the algorithms that can handle such problems. This paper proposes a framework for continuous many-objective test problems with arbitrarily prescribed PS shapes. The behavior of two popular EMO algorithms namely NSGAII and MOEA/D has also been studied for a sample of the proposed test problems. It is hoped that this paper will promote an integrated investigation of EMO algorithms for their scalability with objectives and their ability to handle complicated PS shapes with varying nature of the PF.