Adaptive Constraint-Boundary Learning-Based Two-Stage Dual-Population Evolutionary Algorithm

In recent years, numerous constrained multi-objective evolutionary algorithms (CMOEAs) have been proposed to tackle constrained multi-objective optimization problems (CMOPs). However, most of them still struggle to achieve a good balance among convergence, diversity, and feasibility. To address this issue, we develop an adaptive constraint-boundary learning-based two-stage dual-population evolutionary algorithm for CMOPs, referred to as CL-TDEA. The evolutionary process of CL-TDEA is divided into two stages. In the first stage, two populations cooperate weakly through environmental selection to enhance the exploration ability of CL-TDEA under constraints. In particular, the auxiliary population employs an adaptive constraint-boundary learning mechanism to learn the constraint boundary, which in turn enables the main population to more effectively explore the constrained search space and cross infeasible regions. In the second stage, the cooperation between the two populations drives the search toward the complete constrained Pareto front (CPF) through mating selection. Here, the auxiliary population provides additional guidance to the main population, helping it escape locally feasible but suboptimal regions by means of the proposed cascaded multi-criteria hierarchical ranking strategy. Extensive experiments on 54 test problems from four benchmark suites and three real-world applications demonstrate that the proposed CL-TDEA exhibits superior performance and stronger competitiveness compared with several state-of-the-art methods.