一类线性半向量二层规划问题全局最优解的搜索算法  

A Search Algorithm for Global Optimal Solution of a Class of Linear Semivectorial Bilevel Programming Problems

作　　者：王媛 吕博慧 吕一兵[1] WANG Yuan;LYU Bohui;LYU Yibing(School of Information and Mathematics,Yangtze University,Jingzhou 434023;CCTV Financial Channel,Beijing 100020)

机构地区：[1]长江大学信息与数学学院,湖北荆州434023 [2]中央电视台财经频道,北京100020

出　　处：《湖北民族大学学报（自然科学版）》2020年第1期19-25,共7页Journal of Hubei Minzu University:Natural Science Edition

基　　金：国家自然科学基金项目(11771058);湖北省自然科学基金项目(2019CFA088).

摘　　要：本文研究了下层为正矢量优化的线性半向量二层规划问题的搜索算法.首先运用加权方法将原问题转化为一般的二层规划问题;然后以下层问题的最优条件代替下层问题,进而将原问题转化为单层规划问题;最后通过对单层规划问题的可行集的分析,设计了原半向量二层规划问题全局最优解的搜索算法,同时采用相关算例验证了所设计算法的可行性.In this paper,we propose a search algorithm for the global optimal solution of the linear semivectorial bilevel programming with positive vector optimization problem in the lower level.Firstly,we adopt the weights approach to transform the semivectorial bilevel programming problem into the bilevel single objective programming problem;then,the bilevel single objective programming problem is transformed into the usual single level programming problem.Through analyzing the characters of the feasible set of the single level programming problem,we propose the global search algorithm for the original semivectorial bilevel programming problem.To verify the feasibility of the proposed algorithm,we solve some semivectorial bilevel programming problems.

关 键 词：线性半向量二层规划 搜索算法 最优性条件 全局最优解 

分 类 号：O221[理学—运筹学与控制论]