On Benchmark Problems for Constrained Multi-Objective Optimization Problems

Abstract

Recently, many efficient Multi-Objective Evolutionary Algorithms (MOEAs) for Constrained Multi-Objective Optimization Problems (CMOPs) have been proposed. For evaluating their performance, the C-DTLZ functions and Real-World-Like Problems (RWLPs) are frequently used in the previous work. In this paper, however, we point out that almost all of them have some critical problems. A part of the C-DTLZ functions has only one constraint, and the experimental results in this paper show that an MOEA without constraint handling techniques can obtain well-approximated nondominated feasible solutions on them. We also show that MOEAs can easily find feasible solutions on widely used RWLPs which are considered as “MOEA-hard” problems, and it is seldom that an infeasible solution violates multiple constraints simultaneously. Thus, benchmark problems for CMOPs and the performance of MOEAs reported in the previous work need a careful reconsideration.