摘要
基于分解的多目标进化算法(Multiobjective evolutionary algorithm based on decomposition, MOEA/D)将一个多目标优化问题(multiobjective optimization problem, MOP)分解成一系列的单目标优化子问题,然后利用相互协作的进化方式优化这些子问题. MOEA/D利用独特的分解机制促进种群逼近Pareto最优前端(Pareto optimal front, POF),同时利用均匀分布的权重向量维护种群的多样性,在解决MOPs时具有较大的优势.但是,在实际工程中,大多数MOPs的POF具有复杂的特性.比如说POF可能具有长尾和顶点,这极大地降低了MOEA/D算法的性能.基于惩罚的边界交集法(penalty-based boundary intersection, PBI)是MOEA/D常用的分解方法之一.在PBI法中,惩罚因子起着平衡算法收敛性和多样性的关键作用.本文提出了一种自适应惩罚策略(adaptive penalty strategy, APS),能够在进化过程中自适应调整每个权重向量对应的惩罚因子值,有效地增强了近似Pareto前端的多样性.最后,利用六个具有复杂POF的基准MOPs和空间桁架结构多目标优化实验验证了所提MOEA/D-APS算法的有效性.
Multiobjective evolutionary algorithm based on decomposition(MOEA/D) decomposes a multiobjective optimization problem(MOP) into a number of scalar optimization subproblems and optimizes them in a collaborative manner. In MOEA/D, decomposition mechanisms are used to push the population to approach the Pareto optimal front(POF), whilst a set of uniformly distributed weight vectors are applied to maintain the diversity of the population. MOEA/D has been shown to be very efficient in solving MOPs. However, the POF of many MOPs has complex characteristics, which significantly degrades the performance of MOEA/D. Penalty-based boundary intersection(PBI) is one of the frequently used decomposition approaches. In PBI approach, penalty factor plays a crucial role in balancing convergence and diversity. This paper proposes an adaptive penalty strategy(APS) which can dynamically adjust the value of the penalty factor for each weight vector during the evolutionary process. The diversity of approximated Pareto front can be enhanced by using this APS approach. The performance of the proposed MOEA/D-APS algorithm is investigated on six newly designed benchmark MOPs with complex POF shapes and the multiobjective optimization of space truss structure.
作者
柯永斌
周红标
KE Yong-bin;ZHOU Hong-biao(Faculty of Electronic Information Engineering,Huaiyin Institute of Technology,Huai'an 223001,China;Faculty of Automation,Huaiyin Institute of Technology,Huai'an 223001,China)
出处
《微电子学与计算机》
北大核心
2020年第7期59-65,共7页
Microelectronics & Computer
基金
江苏省产学研前瞻性项目(BY2016061-02)。
关键词
多目标优化
分解
基于惩罚的边界交集法
自适应惩罚策略
复杂Pareto最优前沿
空间桁架结构优化
multiobjective optimization
decomposition
penalty-based boundary intersection
adaptive penalty strategy
complex Pareto optimal front
space truss structure optimization