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。
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 prob- lem 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.
出处
《山东大学学报（理学版）》
CAS
CSCD
北大核心
2012年第5期122-126,共5页
Journal of Shandong University(Natural Science)
基金
安徽省高校优秀青年人才基金资助项目(2009SQRZ121)
关键词
二层线性多目标规划
灰色系统
约束域
极点
bilevel linear multi-objective programming
grey system
constraint region
extreme point
