A Two-stage Single Population Evolutionary Algorithm for Constrained Multi-objective Optimization Problems

In recent years, there has been a growing interest in solving constrained multi-objective optimization problems (CMOPs) using simple helper problems. These constrained multi-objective evolutionary algorithms (CMOEAs) tackle the original CMOP by addressing a series of derived helper problems. However, a significant challenge remains: it is often difficult to maintain the relatedness among these helper problems. To address this issue, we develop a single-population constrained multi-objective optimization evolutionary algorithm (SPCMOEA) that does not require a focus on the relatedness of helper problems. To efficiently balance the convergence and constrained satisfaction, SPCMOEA adopts a two-stage strategy to solve CMOPs. In the first phase, the algorithm performs accelerated boundary-spanning searches targeting the unconstrained Pareto front (UPF), primarily focusing on the objective information. In the second phase, an adaptive ϵ - constraint relaxation method is introduced to steer population dynamics toward feasible Pareto-optimal regions systematically. Empirical evaluations on three standardized benchmark suites demonstrate that SPCMOEA achieves superior performance compared to four contemporary constrained multi-objective evolutionary algorithms.