灰色多随从二层线性规划问题及其解法

J4 ›› 2011, Vol. 49 ›› Issue (04): 625-632.

灰色多随从二层线性规划问题及其解法

刘兵兵¹, 郭亚君²

1. 安庆师范学院数学与计算科学学院, 安徽安庆 246133；2. 河北科技师范学院 |数学与信息科技学院, 河北秦皇岛 066004

收稿日期:2010-08-27 出版日期:2011-07-26 发布日期:2011-08-16
通讯作者: 刘兵兵 E-mail:lbb122400@gmail.com

A Grey Linear Bilevel Programming Problem withMultiple Independent Followers and Its Algorithm

LIU Bingbing¹, GUO Yajun²

1. School of Mathematics and Computing Science, Anqing Teachers College, |Anqing 246133, Anhui Province, China|2. School of Mathematics &|Information Technology, |Hebei Normal University of Science &|Technology, Qinhuangdao 066004, Hebei Province, China

Received:2010-08-27 Online:2011-07-26 Published:2011-08-16
Contact: LIU Bingbing E-mail:lbb122400@gmail.com

摘要/Abstract

摘要：

针对多随从二层线性规划问题, 结合灰色特征, 提出了灰色独立多随从二层线性规划问题. 建立了该问题的数学模型, 并证明了漂移型灰色独立多随从二层线性规划问题等价于漂移型灰色二层线性规划问题. 对于漂移型灰色独立多随从二层线性规划问题, 基于单纯形法设计了一种求解算法. 数值算例表明该算法是可行有效的.

关键词: 二层线性规划, 灰色理论, 独立多随从, 单纯形方法

Abstract:

Based on the linear bilevel programming problem with multiple independent followers and the characteristic of grey system, a grey linear bilevel programming problem with multiple independent followers (GLBMIF) was put forward, and its model was given. We showed that the drifting grey linear bilevel programming problem with multiple independent followers (GLBMIF(θ)) is
equivalent to the drifting grey linear bilevel programming problem. An algorithm based on simplex method was developed to solve the GLBMIF (θ). A numerical example shows that the proposed algorithm is feasible and effective.

Key words: linear bilevel programming, grey system, multiple independent followers; , simplex method

中图分类号:

O221.1

刘兵兵, 郭亚君. 灰色多随从二层线性规划问题及其解法[J]. J4, 2011, 49(04): 625-632.

LIU Bing-Bing, GUO E-Jun. A Grey Linear Bilevel Programming Problem withMultiple Independent Followers and Its Algorithm[J]. J4, 2011, 49(04): 625-632.

[1]	孙金岭, 庞娟. 基于残差修正的灰色神经网络在数据挖掘中的应用[J]. 吉林大学学报(理学版), 2015, 53(06): 1263-1268.
[2]	黄庆道, 吕显瑞, 王国明. 变量有上界的线性规划的对偶单纯形方法[J]. J4, 2002, 40(01): 44-47.