English

运筹学学报 >

2015 , Vol. 19 >Issue 3: 42 - 47

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2015.03.006

运筹学

多目标数学规划有效集的参数表示

展开
  • 1. 美国南加州爱迪生电力公司

收稿日期: 2015-04-24

  网络出版日期: 2015-09-15

收起

On parametric representations of the efficient set of multiple objective mathematical programming problems

Expand
  • 1. Senior Energy Market Specialist,  Southern California Edison,  Rosemead,  CA 91770, USA

Received date: 2015-04-24

  Online published: 2015-09-15

Fold

摘要

研究了p-维多目标数学规划问题有效集的参数表示. 通过研究相关的单目标优化问题和相关的(p-1)-维多目标优化问题, 提出了几个新的关于p-维多目标规划有效集的表示定理.

关键词： 多目标数学规划; 有效集; 弱有效集; 参数表示

本文引用格式

孙尔江 . 多目标数学规划有效集的参数表示[J]. 运筹学学报, 2015 , 19(3) : 42 -47 . DOI: 10.15960/j.cnki.issn.1007-6093.2015.03.006

Abstract

In this paper we present some new results that characterize the efficient solutions of a p-dimensional multiple objective mathematical programming (MOMP). These characterizations are in terms of the optimal solutions of appropriate scalar optimization problems or in terms of efficient solutions of appropriate (p-1)-dimensional parametric MOMP.

Key words： multiple objective mathematical programming; efficient set; weakly efficient set; parametric representations

参考文献

Kuhn H W, Tucker A W. Nonlinear Programming [C]// Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, California, 1951, 481-492.


Haimes Y Y, Lasdon L S, Wismer D A. On a bicriterion formulation of the problems of integrated system identification and system optimization [J].  IEEE Transactions on Systems, Man, and Cybernetics, 1971, SMC-1: 296-297.

Chankong V, Haimes Y Y.  Multiobjective Decision Making  : Theory and Methodology [M].  New York: Elsevier Science Publishing, 1983.

Sun E J. New Closedness Results and Algorithms for Finding Efficient Sets in Multiple Objective Mathematical Programming [D]. University of Florida, 2000.

Sun E J. On the connectedness of the efficient set for strictly quasiconvex vector minimization problems [J].  Journal of Optimization Theory and Applications, 1996,  89: 475-481.

 
Options
文章导航

/

〈 〉