Two-Stage Multi-Objective Evolution Strategy for Constrained Multi-Objective Optimization

For the past many years, several constrained multiobjective evolutionary algorithms (CMOEAs) have been designed for solving constrained multi-objective optimization problems (CMOPs). In these CMOEAs, some constraint-handling techniques (CHTs) were proposed to balance the convergence and constrained satisfaction, however, they still face some serious challenges, such as premature convergence to the local optimal region and labor-intensive tuning of parameters for a specific CMOP. Furthermore, most of the existing CHTs are derived by solving constrained single-objective optimization. The information hidden from the feasible non-dominated set (FNDS) has not been fully utilized. This study proposed a novel parameter-less constraint handling technique, which divides the entire population into three mutually exclusive subsets dynamically: FNDS, the subset dominated by FNDS, and the subset not dominated by FNDS. According to the proposed division of labor, it is not necessary to balance the convergence and constrained satisfaction in each subset. To avoid being entrapped in local optima, the proposed algorithm adopts a two-stage strategy to solve CMOPs. In the first stage, the proposed algorithm focuses solely on converging toward the unconstrained Pareto front without considering the constrained satisfaction. In the second stage, the FNDS constraint handling technique is adopted to guide the population converging toward constrained Pareto front effectively. The performance of the proposed algorithm was compared to that of nine state-of-the-art CMOEAs, and the comparison results show that the proposed algorithm performs significantly better on the CF, MW, and LIRCMOP test suites.