Abstract:

For Constrained Multi-Objective Optimization Problem （CMOP） with complex constraints， balancing the algorithm's convergence and diversity effectively while ensuring strict constraint satisfaction is a significant challenge. Therefore， a Dual-Population Dual-Stage Evolutionary Algorithm （DPDSEA） was proposed. In this algorithm， two independently evolving populations were introduced： the main and secondary populations， and the feasibility rules and an improved epsilon constraint handling method were used for updating， respectively. In the first stage， the main and secondary populations were employed to explore the Constrained Pareto Front （CPF） and the Unconstrained Pareto Front （UPF）， respectively， to obtain positional information about the UPF and the CPF. In the second stage， a classification method was designed to classify CMOPs based on positions of the UPF and the CPF， thereby executing specific evolutionary strategies for different types of CMOPs. Additionally， a random perturbation strategy was proposed to perturb the secondary population evolved near the CPF randomly to generate some individuals on the CPF， thereby promoting convergence and distribution of the main population on the CPF. Finally， experiments were conducted on LIRCMOP and DASCMOP test sets to compare the proposed algorithm with six representative algorithms： 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 for constrained multi-objective optimization）， CAEAD （Constrained Evolutionary Algorithm based on Alternative Evolution and Degeneration）， BiCo （evolutionary algorithm with Bidirectional Coevolution）， and DDCMOEA （Dual-stage Dual-Population Evolutionary Algorithm for Constrained Multiobjective Optimization）. The results show that DPDSEA achieves 15 best Inverted Generational Distance （IGD） values and 12 best Hyper Volume （HV） values in 23 problems， demonstrating DPDSEA’s performance advantages in handling complex CMOPs significantly.

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

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重大挑战。因此，提出一种双种群双阶段的进化算法（DPDSEA）。该算法引入2个独立进化种群：主种群和副种群，并分别利用可行性规则和改进的epsilon约束处理方法进行更新。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），从而获取UPF和CPF的位置信息；在第二阶段，设计一种分类方法，根据UPF与CPF的位置对CMOP进行分类，从而对不同类型的CMOP执行特定的进化策略；此外，提出一种随机扰动策略，在副种群进化到CPF附近时，对它进行随机扰动以产生一些位于CPF上的个体，从而促进主种群在CPF上的收敛与分布。把所提算法与6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 for constrained multi-objective optimization）、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比较。实验结果表明，DPDSEA在23个问题中取得了15个最优反转世代距离（IGD）值和12个最优超体积（HV）值，展现了DPDSEA在处理复杂CMOP时显著的性能优势。

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