高维多目标电磁场逆问题计算的改进多重单目标Pareto采样算法  

An Improved Multiple Single Objective Pareto Sampling Algorithm Applied to Many-Objective Inverse Problems

作　　者：刘磊[1] 安斯光[1] Junwei Lu 杨仕友[1] 

机构地区：[1]浙江大学电气工程学院,杭州310027 [2]Griffith University ,Brisbane 4222

出　　处：《电工技术学报》2013年第6期9-15,共7页Transactions of China Electrotechnical Society

基　　金：国家自然科学基金资助项目(50777054、51077114)

摘　　要：电气工程中的优化设计(电磁场逆)问题一般为多极值点的非线性全局优化问题。当需要考虑不同性能指标时,又必须同时给出多个非控解以供决策。这进一步加剧了问题的复杂度。虽然进化算法在多目标优化设计中获得了广泛应用,但对于目标函数超过三维的高维多目标优化问题,目前基于非控关系的多目标进化算法很难获得满意的优化结果。为此,人们提出了高维多目标优化的多重单目标Pareto采样(MSOPS)算法。该算法具有结构简单,计算复杂度低等优点。然而,研究表明,MSOPS算法收敛速度慢,优化结果往往缺乏多样性。为此,本文对MSOPS算法进行了改进研究,提出了目标矢量的拥挤操作以增加解的多样性,借助非均匀的目标矢量更新以及附加外部档案等改进措施对搜索区域进行有效地搜索,加快算法收敛。直线阵列和Yagi-Uda天线阵的实例分析、计算证明了本文算法的优越性和可靠性。The optimal design （inverse） problems in electrical engineering are generally characterized as highly nonlinear mathematical programming ones. If more than one objectives are involved, a set of non-dominated solutions, rather than a single one, are required for decision making. The search of multiple solutions increases further the complexity of the problem. Although extensively and successfully applied in different engineering disciplines, the non-dominance based evolutionary algorithms will encounter difficulties in solving optimal problems with more than three objectives, termed many-objective optimization problems. To solve many-objective optimal problems, the multiple single objective pareto sampling （MSOPS and MSOPS-II） algorithm is proposed with exclusive features of simplicities of implementations and low computational complexities. However, it is observed that this algorithm is not satisfactory in views of convergence and diversity performances. In this regard, an improved MSOPS is proposed. In the proposed algorithm, a crowding operation of target vectors is incorporated to preserve the diversity of the solutions; a non-uniform target vector updating mechanism and an external archive are introduced to effectively explore the search space to speed up the convergence rate. The numerical results on the synthesis of a linear array and a Yagi-Uda array demonstrate the feasibility and merits of the proposed algorithm.

关 键 词：高维多目标优化算法 进化算法 多重单目标Pareto采样算法 多样性保持 

分 类 号：TM12[电气工程—电工理论与新技术]