一类非线性两层规划问题的递阶优化解法  

Hierarchical optimization method for a class of nonlinear bilevel programming problems

作　　者：郑丕谔[1] 赵玉超[1] 刘国宏[1] 李瑞波[1] 

机构地区：[1]天津大学系统工程研究所,天津300072

出　　处：《控制与决策》2004年第10期1194-1196,1200,共4页Control and Decision

摘　　要：提出一种求解一类非线性两层规划问题的新方法.通过引入解耦向量将非线性两层规划问题分解为独立且易于求解的子问题,利用两级递阶结构第1级求解若干优化的子问题,而在第2级利用第1级求解的结果调整解耦向量.所提出的方法借助于分解-协调原理并按迭代方式最终求得问题的最优解.对于含整数的规划问题,通过连续化处理后也可按该方法方便地求解.算例表明所提出的算法是简便而有效的.A novel method for a class of nonlinear bilevel programming problems is proposed. By introducing a decoupling vector, a bilevel programming problem is decomposed into independent optimization sub-problems, which are easily solved at level 1 of a two-level hierarchical structure. At level 2 the decoupling vector is then updated using solutions from level 1. Based on decomposition-coordination principle, the proposed method can finally solve the optimal solution of the bilevel programming problem in an iterative fashion. For programming problems with integers, continualization technique is employed and continualized problems can be easily solved using the proposed method. Numerical examples are used to demonstrate simplicity and effectiveness of the proposed method.

关 键 词：非线性两层规划 连续化方法 分解-协调 递阶优化 

分 类 号：C934[经济管理—管理学]