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J4 ›› 2012, Vol. 47 ›› Issue (5): 122-126.

• 数学 • 上一篇    

一类灰色二层线性多目标规划问题及其算法

刘兵兵   

  1. 安庆师范学院数学与计算科学学院, 安徽 安庆 246133
  • 收稿日期:2011-03-16 出版日期:2012-05-20 发布日期:2012-06-01
  • 作者简介:刘兵兵(1980- ),男,讲师,硕士,研究方向为二层规划理论与灰色系统理论. Email:lbb122400@gmail.com
  • 基金资助:

    安徽省高校优秀青年人才基金资助项目(2009SQRZ121)

A grey bilevel linear multi-objective programming problem and its algorithm

LIU Bing-bing   

  1. School of Mathematics and Computing Science, Anqing Teachers College, Anqing 246133, Anhui, China
  • Received:2011-03-16 Online:2012-05-20 Published:2012-06-01

摘要:

 将下层带多目标函数的二层线性规划与灰色理论相结合, 提出了一类灰色二层线性多目标规划问题,给出了该问题的数学模型和相关概念。在约束域为非空紧集的条件下, 证明了漂移型灰色二层线性多目标规划问题的最优解一定可以在约束域的极点达到,并提出了一个基于k次最好法的求解算法, 证明了该算法具有全局收敛性, 算例分析验证了所提算法是有效的。

关键词: 二层线性多目标规划;灰色系统;约束域;极点

Abstract:

 Based on the bilevel linear multi-objective programming problem with multiple objectives at the lower level and the characteristic of the grey system, a grey bilevel linear multi-objective programming problem is put forward, and its model and theorem are given. Under the assumption of the constraint region of the proposed model nonempty and compactness, it is  shown that the optimal solution of the drifting grey bilevel linear multi-objective programming problem can be reached on the extreme point of the constraint region. Finally, an algorithm based on the k-th best method is developed and its global convergence is proven. Numerical examples show that the proposed algorithm is effective.

Key words:  bilevel linear multi-objective programming; grey system; constraint region; extreme point

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