A note on constrained multi-objective optimization benchmark problems

Abstract

We investigate the properties of widely used constrained multi-objective optimization benchmark problems. A number of Multi-Objective Evolutionary Algorithms (MOEAs) for Constrained Multi-Objective Optimization Problems (CMOPs) have been proposed in the past few years. The C-DTLZ functions and Real-World-Like Problems (RWLPs) have frequently been used for evaluating the performance of MOEAs on CMOPs. In this paper, however, we show that the C-DTLZ functions and widely-used RWLPs have some unnatural problem features. The experimental results show that an MOEA without any Constraint Handling Techniques (CHTs) can successfully find well-approximated nondominated feasible solutions on the C1-DTLZ1, C1-DTLZ3, and C2-DTLZ2 functions. It is widely believed that RWLPs are MOEA-hard problems, and finding the feasible solutions on them is a very hard task. However, we show that the MOEA without any CHTs can find feasible solutions on widely-used RWLPs such as the speed reducer design problem, the two-bar truss design problem, and the water problem. Also, it is seldom that the infeasible solution simultaneously violates multiple constraints in the RWLPs. Due to the above reasons, we conclude that constrained multi-objective optimization benchmark problems need a careful reconsideration.