基于帕累托前沿关系求解约束多目标优化问题

Handling Constrained Multi-objective Optimization Problems Based on Relationship Between Pareto Fronts

为解决约束多目标优化问题中的平衡约束满足与目标函数优化以及可行域复杂等挑战,提出了基于不同帕累托前沿关系的分类搜索方法。提出一种双种群双阶段框架:进化一个辅助种群Pa和一个主种群Pm,并将进化过程分为学习阶段和搜索阶段。学习阶段,种群Pa向UPF(unconstrained Pareto front)进行搜索,而种群Pm向CPF(constrained Pareto front)进行搜索,旨在探索UPF与CPF之间的关系;完成学习后,对不同问题的UPF与CPF关系进行分类,以指导后续搜索策略;在搜索阶段,根据不同的分类关系,调整种群Pa的搜索策略,旨在使种群Pa为种群Pm提供更有效的辅助信息。基于此算法框架,对不同类型约束多目标优化问题的帕累托前沿关系进行了分类,实现了对CPF更有效的搜索。实验结果表明:所提算法与其他7种先进的约束多目标优化算法相比具有更显著的性能优势。通过学习与利用UPF与CPF的关系,能够选择更合适的搜索策略去应对具有不同特性的约束多目标优化问题,以获得更具优势的最终解集。

To address the challenges of balancing the constraint satisfaction and objective function optimization,and dealing with the complex feasible regions in constrained multi-objective optimization problems(CMOPs),a classification-based search approach is proposed based on different Pareto front relationships.A dual-population dual-phase framework is proposed in which an auxiliary population Pa and a main population Pm are evolved and the evolution process is divided into a learning phase and a search phase.During the learning phase,Pa explores unconstrained Pareto front(UPF)and Pm explores constrained Pareto front(CPF),through which the relationship between UPF and CPF is determined.After completing the learning phase,the different classified relationships guide the subsequent search strategies.In the search phase,the algorithm adaptively adjusts the search strategy of Pa to provide effective assistance for Pm according to the different classification relationships between UPF and CPF.Based on this framework,Pareto front relationships for different CMOPs are classified to achieve the more effective searching for CPF.Experimental results show that the proposed algorithm has a better performance compared with the seven state-of-the-art constrained multi-objective evolutionary algorithms(CMOEAs).Through learning and utilizing the relationship between UPF and CPF,the more appropriate search strategies can be selected to handle CMOPs with different characteristics and a more advantageous final solution set can be got.