关键词: 约束多目标优化, 双种群, 双阶段, 进化算法, 约束处理方法, 分类方法, 随机扰动

Abstract: For constrained multi-objective optimization problems (CMOPs) with complex constraints, effectively balancing the algorithm's convergence and diversity while ensuring strict constraint satisfaction is a significant challenge. Therefore, a Dual-Population Dual-Stage Evolutionary Algorithm (DPDSEA) was proposed. This algorithm introduced two independently evolving populations: the main and secondary populations, updated using feasibility rules and an improved epsilon constraint handling method, respectively. In the first stage, the main and secondary populations were directed to explore the Constrained Pareto Front (CPF) and the Unconstrained Pareto Front (UPF) to obtain positional information about the UPF and CPF. In the second stage, a classification method was designed to classify CMOPs based on the positions of the UPF and CPF, executing specific evolutionary strategies for different types of CMOPs. Additionally, a random perturbation strategy was proposed, which randomly perturbed the secondary population near the CPF to generate individuals on the CPF, promoting convergence and distribution of the main population on the CPF. Finally, experiments were conducted on the LIRCMOP and DASCMOP test suites, comparing the proposed algorithm with six representative algorithms: Constrained Multi-Objective Optimization based on Even Search (CMOES), Dual Population Evolutionary Algorithm based on Adaptive Constraint Strength (dp-ACS), Dual-Population Based Evolutionary Algorithm (c-DPEA), Constrained Evolutionary Algorithm based on Alternative Evolution and Degeneration (CAEAD), Constrained Multi-objective Evolutionary Algorithm with Bidirectional Coevolution (BiCo) and Dual-Stage Dual-Population Evolutionary Algorithm for Constrained Multiobjective Optimization (DDCMOEA). DPDSEA achieved 15 best Inverted Generational Distance (IGD) values and 12 best HyperVolume (HV) values in 23 problems, significantly demonstrating its performance advantages in handling complex CMOPs.

Key words: constrained multi-objective optimization, dual-population, dual-stage, evolutionary algorithm, constraint handling method, classification method, random perturbation