利用重叠关系分类的自适应双种群框架求解约束多目标优化问题

An Adaptive Dual-Population Framework Based on Overlapping Relationship Classification for Solving Constrained Multi-Objective Optimization Problems

摘要: 在约束多目标优化问题(CMOPs)中，现有的约束多目标进化算法往往难以有效平衡多个冲突目标与复杂约束之间的关系，导致收敛性和多样性不足。本文提出一种自适应双种群进化算法(DPSCEA)，通过对约束Pareto前沿(CPF)与无约束Pareto前沿(UPF)的重叠位置关系进行分类，分类后根据不同位置关系采取针对性演化策略。DPSCEA采用双种群框架：P_C种群逼近CPF，P_U种群逼近UPF。演化过程分为学习阶段(分类关系)和演化阶段(基于重叠类型自适应调整参数和进化算子策略)。并通过增强转移机制，将P_C种群的非支配及精英个体迁移至P_U种群，提升优秀目标种群的利用效率。试验结果表明，与目前六种先进算法比较，DPSCEA在IGD和HV指标上表现出显著优势，结果验证了DPSCEA在处理约束多目标优化方面的有效性和先进性。

Abstract: In constrained multi-objective optimization problems (CMOPs), existing constrained multi-objective evolutionary algorithms often struggle to effectively balance multiple conflicting objectives with complex constraints, resulting in insufficient convergence and diversity. This paper proposes an adaptive dual-population evolutionary algorithm (DPSCEA), which classifies the overlapping positional relationships between the constrained Pareto front (CPF) and the unconstrained Pareto front (UPF), and then adopts targeted evolutionary strategies based on different positional relationships. DPSCEA uses a dual-population framework: the P_C population approximates the CPF, while the P_U population approximates the UPF. The evolutionary process is divided into a learning phase (classifying relationships) and an evolution phase (adaptively adjusting parameters and evolutionary operator strategies based on overlap type). Through an enhanced transfer mechanism, nondominated and elite individuals from the P_C population are migrated to the P_U population, improving the utilization efficiency of high-quality objective populations. Experimental results show that, compared with six state-of-the-art algorithms, DPSCEA exhibits significant advantages in IGD and HV metrics, and the results validate the effectiveness and superiority of DPSCEA in handling constrained multi-objective optimization.