A fuzzy constraint handling technique for decomposition-based constrained multi- and many-objective optimization

Abstract

The challenge in solving constrained multi-objective optimization problems (CMOPs) is how to balance minimizing objectives and satisfying constraints, especially when the infeasible region is very large. To address this issue, this work proposes a fuzzy constraint handling technique, which uses the fuzzy set theory to accurately characterize the difference between solutions on objective function values and constraint violation degrees. On this basis, a new concept, called “fuzzy advantage”, is introduced to comprehensively quantify the degree to which one solution is better than others, allowing the infeasible solutions with promising fitness to survive. The proposed method is integrated with a decomposition-based multi-objective evolutionary algorithm to verify its effectiveness. Compared with nine state-of-the-art MOEAs on a number of test problems and a real-world optimization problem, the proposed algorithm shows high competitiveness in solving a variety of CMOPs.