Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II

TLDR

Partly due to a lack of test problems, the influence of Pareto set shapes on evolutionary algorithm performance has received limited attention. The study introduces a general class of continuous multiobjective test instances with arbitrary Pareto set shapes and proposes a differential‑evolution based MOEA/D (MOEA/D‑DE) to compare against NSGA‑II on these instances. The authors develop MOEA/D‑DE and evaluate it against NSGA‑II using the same reproduction operators on the newly defined test instances. Experiments show that MOEA/D‑DE significantly outperforms NSGA‑II on the proposed test instances, indicating that decomposition‑based algorithms are promising for complex Pareto set shapes.

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 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.