Two-stage bidirectional coevolutionary algorithm for constrained multi-objective optimization

Abstract

Objective optimization and constraint satisfaction are two primary and conflicting tasks in solving constrained multi-objective optimization problems (CMOPs). To better trade off them, this paper proposes a two-stage bidirectional coevolutionary algorithm, termed C-TBCEA, for constrained multi-objective optimization. It consists of two stages, with each concentrating on specific targets, i.e., the first stage primarily focuses on objective optimization while the second stage focuses on constraint satisfaction by employing different evolutionary strategies at each stage. Via the synergy of the two stages, a dynamic trade-off between objective optimization and constraint satisfaction can be achieved, thus overcoming the distinctive challenges that may be encountered at different stages of evolution. In addition, to take advantage of both feasible and infeasible solutions, we employ two populations, i.e., the main population that stores the non-dominated feasible solutions and the archive population that maintains the informative infeasible solutions, to prompt the bidirectional coevolution of them. To validate the effectiveness of the proposed C-TBCEA, experiments are carried out on 6 CMOP test suites and 17 real-world CMOPs. The results demonstrate that the proposed algorithm is very competitive with 9 state-of-the-art constrained multi-objective optimization evolutionary algorithms (CMOEAs).