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

摘要： 摘 要: 针对包含复杂约束条件的约束多目标优化问题（CMOP），在确保算法满足严格约束的同时，有效平衡算法的收敛性与多样性是一大挑战。因此，提出了一种双种群双阶段的进化算法（DPDSEA）。该算法引入了两个独立进化种群：主种群和副种群，分别利用可行性规则和改进的epsilon约束处理方法更新。在第一阶段，主种群和副种群分别探索约束Pareto前沿（CPF）与无约束Pareto前沿（UPF），获取UPF和CPF的位置信息。在第二阶段，设计了一种分类方法，根据UPF与CPF的位置对CMOP进行分类，对不同类型的CMOP执行特定的进化策略。此外，提出了一种随机扰动策略，在副种群进化到CPF的附近时，对其进行随机扰动产生一些位于CPF上的个体，促进主种群在CPF上的收敛与分布。最后，与六个具有代表性的算法CMOES（Constrained Multi-Objective Optimization based on Even Search）、dp-ACS（Dual-Population Evolutionary Algorithm based on Adaptive Constraint Strength）、c-DPEA（Dual-Population Based Evolutionary Algorithm）、CAEAD（Constrained Evolutionary Algorithm based on Alternative Evolution and Degeneration）、BiCo（Evolutionary Algorithm with Bidirectional Coevolution）和DDCMOEA（Dual-Stage Dual-Population Evolutionary Algorithm for Constrained Multiobjective Optimization）在LIRCMOP和DASCMOP两个测试集上进行实验。DPDSEA在23个问题中取得15个最优反转世代距离（IGD）值和12个最优超体积（HV）值，显著展现了其在处理复杂CMOP时的性能优势。

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