层次分析法中用于确定权重的最小-最大优化方法(英文)

被引：14

作者：

孙璐

机构：

[1] 东南大学交通学院

[2] Department of Civil Engineering

[3] Catholic University of America

[4] Washington DC

[5] USA

来源：

Journal of Southeast University(English Edition) | 2012年 / 28卷 / 02期

关键词：

层次分析法; 最小-最大优化; 权重; 线性优化;

D O I：

暂无

中图分类号：

O224 [最优化的数学理论];

学科分类号：

070105 ; 1201 ;

摘要：

提出了层次分析法中一种用于确定权重的最小-最大优化方法. 其思路为通过最小化由两两比较矩阵中每列所得到的优先权和理想的权重向量之间的最大绝对差异来实现权重确定. 通过适当的变换,问题转化为可以采用单纯形或内点法求解的线性优化问题. 推导建立了解析的 Karush-Kuhn-Tucker 条件. 所建立的临界阀值提供了关于两两比较矩阵不一致特性的一种直接的表征. 给出了几种实例的数值算法,并比较了所提方法和3 种现有的权重确定方法的性能,观察结果发现最小-最大优化方法对于非主导因素有较多考虑.

引用

页码：245 / 250

页数：6

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