北大中文核心期刊
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运筹学学报 ›› 2018, Vol. 22 ›› Issue (4): 141-147.doi: 10.15960/j.cnki.issn.1007-6093.2018.04.014

• 运筹学 • 上一篇    下一篇

鲁棒优化中的Pareto有效性

王峰1  刘三阳1,*   

  1. 1. 西安电子科技大学数学与统计学院, 西安 710071
  • 收稿日期:2017-07-31 出版日期:2018-12-15 发布日期:2018-12-15
  • 通讯作者: 刘三阳 E-mail: liusanyang@126.com
  • 基金资助:

    国家自然科学基金(No. 61373174)

Pareto efficiency in robust optimization

WANG Feng1  LIU Sanyang1,*   

  1. 1. School of Mathematics and Statistics, Xidian University, Xi'an 710017, China
  • Received:2017-07-31 Online:2018-12-15 Published:2018-12-15

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摘要：

对于一般的不确定优化问题, 研究了鲁棒解的~Pareto 有效性. 首先, 证明了Pareto 鲁棒解集即是鲁棒解集的Pareto 有效集, 因此求Pareto 鲁棒解等价于求鲁棒解集的Pareto 有效元. 其次, 基于推广的epsilon-约束方法, 得到了Pareto 鲁棒解的生成方法.

关键词: 鲁棒优化, Pareto 有效性, Pareto 鲁棒解, epsilon-约束方法

Abstract:

In this paper, we study the Pareto efficiency of robust solutions to general optimization problems under uncertainty. Firstly, we prove that the set of Pareto robust solutions is the Pareto efficient set of the robust solution set, by which to obtain Pareto robust solutions reduces to find Pareto efficient elements of the robust solution set. Then on the basis of an extension of epsilon-constraint method, we get two ways of generating Pareto robust solutions.

Key words: robust optimization, Pareto efficiency, Pareto robust solution, epsilon-constraint method