A simple two-stage evolutionary algorithm for constrained multi-objective optimization

Abstract The widespread existence of constrained multi-objective optimization problems (CMOPs) in practical applications encourages researchers to devote more efforts to the development of constrained multi-objective evolutionary algorithms (CMOEAs). An efficient way of handling CMOPs is to balance the satisfaction of constrains and the optimization of objective functions. Although many approaches have been designed to this end, most of them are still unable to handle CMOPs with diverse characteristics effectively. To remedy this issue, a simple and generic two-stage framework is proposed in this paper to achieve better efficiency and versatility for CMOPs. Specifically, the whole search process is simply divided into two stages with different purposes: (i) Stage 1 focuses on approaching the unconstrained Pareto front (PF) and storing the obtained feasible solutions in the archive. During stage 1, the archive is updated to promote convergence and diversity; (ii) Stage 2 is mainly designed to obtain the constrained PF of CMOPs. First, the solutions in the archive are used to form the initial population. Afterwards, the constrained Pareto front (CPF) is extensively explored. Based on this framework, a CMOEA, referred to as C-TSEA, is presented. Fifty-seven instances in five benchmark test suites are chosen to evaluate the performance of our approach. Compared with seven advanced CMOEAs, the results demonstrate the superiority or at least competitiveness of C-TSEA. The generality of the proposed framework is also verified by integrating other methods in the proposed framework.