基于最小二乘法的高维目标减少算法  

Objective-reduction using the least squares method

作　　者：郑金华[1] 周聪[1] 李珂[1] 吕卉[1] 

机构地区：[1]湘潭大学信息工程学院,湖南湘潭411105

出　　处：《控制理论与应用》2011年第7期947-955,共9页Control Theory & Applications

基　　金：国家自然科学基金资助项目(60773047);湖南省教育厅重点科研项目资助项目(06A074)

摘　　要：多目标进化算法在许多领域有广泛的应用,大部分文献都只针对二维与三维的测试问题,目标减少成为高维优化的热点之一.本文从决策者角度考虑冗余目标问题,提出了基于最小二乘法的目标减少算法(ORLSM),该方法将每个目标函数分段拟合为若干条直线段,然后比较各直线段之间的斜率来确定最冗余目标对,进而确定冗余目标.同时针对目标减少前后个体支配关系的变化情况,提出了支配关系改变率的评价方法.通过3个测试函数,分别用逆世代距离(IGD)、支配关系改变率(CDR)和时间效率3个方面,对同类的两个算法进行了性能测试.结果表明,ORLSM在总体上具有最好的性能:CDR和IGD具有基本一致的评价结果.Multi-objective evolutionary algorithms are widely applied to many real world problems; however, most of the papers merely focus on the problems with two or three objectives, in which objective-reduction has become a research focus for many multi-objective optimization. From the views of decision makers, this paper proposes a new objective-reduction using the least squares metbod（ORLSM）. This algorithm fits each objective into multi-straight lines and determines the most redundant objective couples between each two slope vectors for searching the most redundant objective. Moreover, in view of the variety of individual dominance relation after the number of objectives is decreased, a performance assessment metric based on the changed Pareto dominance ratio（CDR） is also proposed. From an extensive comparative study with two similar algorithms in terms of inverted generational distance（IGD）, CDR, and running time on 3 test problems, ORLSM indicates its superiority in overall performances; CDR and IGD almost have the evaluation in assessments.

关 键 词：高维目标进化 目标减少算法 最小二乘法 评价方法 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]