Genetic algorithm based on simplex method for solving linear-quadratic bilevel programming problem

被引：47

作者：

Wang, Guangmin ^{[1
]}

Wan, Zhongping ^{[2
]}

Wang, Xianjia ^{[3
]}

Lv, Yibing ^{[4
]}

机构：

[1] China Univ Geosci, Sch Econ & Management, Wuhan 430074, Peoples R China

[2] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[3] Wuhan Univ, Inst Syst Engn, Wuhan 430072, Peoples R China

[4] Yangtze Univ, Sch Informat & Math, Jinzhou 434102, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2008年 / 56卷 / 10期

基金：

中国国家自然科学基金;

关键词：

The linear-quadratic bilevel programming problem; Genetic algorithm; Simplex method; Fitness value;

D O I：

10.1016/j.camwa.2008.05.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The bilevel programming problems are useful tools for solving the hierarchy decision problems. In this paper, a genetic algorithm based on the simplex method is constructed to solve the linear-quadratic bilevel programming problem (LQBP). By use of Kuhn-Tucker conditions of the lower level programming, the LQBP is transformed into a single level programming which can be simplified to a linear programming by the chromosome according to the rule. Thus, in our proposed genetic algorithm, only the linear programming is solved by the simplex method to obtain the feasibility and Fitness value of the chromosome. Finally, the feasibility of the proposed approach is demonstrated by the example. Crown Copyright (C) 2008 Published by Elsevier Ltd. All rights reserved.

引用

页码：2550 / 2555

页数：6

共 50 条

[41] A neural network approach for solving linear bilevel programming problem
Hu, Tiesong
Guo, Xuning
Fu, Xiang
Lv, Yibing
[J]. KNOWLEDGE-BASED SYSTEMS, 2010, 23 (03) : 239 - 242
[42] A Neural Network Approach for Solving Linear Bilevel Programming Problem
Hu, Tiesong
Huang, Bing
Zhang, Xiang
[J]. SIXTH INTERNATIONAL SYMPOSIUM ON NEURAL NETWORKS (ISNN 2009), 2009, 56 : 649 - 658
[43] A Recurrent Neural Network for Solving Bilevel Linear Programming Problem
He, Xing
Li, Chuandong
Huang, Tingwen
Li, Chaojie
Huang, Junjian
[J]. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2014, 25 (04) : 824 - 830
[44] THE WATERMELON ALGORITHM FOR THE BILEVEL INTEGER LINEAR PROGRAMMING PROBLEM
Wang, Lizhi
Xu, Pan
[J]. SIAM JOURNAL ON OPTIMIZATION, 2017, 27 (03) : 1403 - 1430
[45] A genetic algorithm for solving linear fractional bilevel problems
Herminia I. Calvete
Carmen Galé
Pedro M. Mateo
[J]. Annals of Operations Research, 2009, 166
[46] A LINEAR BILEVEL PROGRAMMING ALGORITHM BASED ON BICRITERIA PROGRAMMING
UNLU, G
[J]. COMPUTERS & OPERATIONS RESEARCH, 1987, 14 (02) : 173 - 179
[47] A genetic algorithm for solving linear fractional bilevel problems
Calvete, Herminia I.
Gale, Carmen
Mateo, Pedro M.
[J]. ANNALS OF OPERATIONS RESEARCH, 2009, 166 (01) : 39 - 56
[48] A GENERALIZED SIMPLEX TECHNIQUE FOR SOLVING QUADRATIC-PROGRAMMING PROBLEM
GUPTA, AK
SHARMA, JK
[J]. INDIAN JOURNAL OF TECHNOLOGY, 1983, 21 (05): : 198 - 201
[49] A PRINCIPAL PIVOTING SIMPLEX ALGORITHM FOR LINEAR AND QUADRATIC PROGRAMMING
GRAVES, RL
[J]. OPERATIONS RESEARCH, 1967, 15 (03) : 482 - &
[50] A genetic algorithm for solving a class of multiobjective bilevel programming problems
Han, Junjie
Li, Hecheng
[J]. INFORMATION SCIENCE AND MANAGEMENT ENGINEERING, VOLS 1-3, 2014, 46 : 1107 - 1114

← 1 2 3 4 5 →