A two-stage evolutionary algorithm based on three indicators for constrained multi-objective optimization

One of the key issues in solving constrained multi-objective optimization problems (CMOPs) is balancing the three indicators of convergence, diversity, and feasibility. We believe at different stages of the evolution, different indicators should be emphasized. This paper proposes a two-stage constrained multi-objective evolutionary algorithm (CMOEA) with different emphases on the three indicators. In Stage-I, the Pareto nondominated sorting and the unbiased two-objective model are used to evaluate the three indicators. The purpose of Stage-I is to obtain solutions with good distribution and to prevent the population from falling into local optima. After Stage-I, almost all of the individuals in the population are distributed in the vicinity of all feasible areas. The goal of Stage-II is to quickly converge the population to the Pareto front (PF). Thirty benchmark CMOPs and four real-world problems were used to evaluate the performance of our algorithm. Experimental results indicate that our approach achieved significantly better results or was at least competitive to the compared eight state-of-the-art CMOEAs on most of the benchmark problems.