混合整数拟分离的向量值优化的可分化理论  

Decomposition Theory in the Vector-Valued Optimization with Mixed Integer Quasi-Separable Subsystems

作　　者：王磊 白富生[2] 

机构地区：[1]江西省九江市第三中学,江西九江332000 [2]重庆师范大学数学学院,重庆400047

出　　处：《重庆师范大学学报（自然科学版）》2011年第5期7-12,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.10171118)

摘　　要：在由相互作用的子系统构成的大规模系统的优化中,许多分层和不分层的分化方法已经提出来。除了一些例外,所有这些方法的性质基本上是启发式的。最近的研究考虑的是一系列称为拟分离的优化问题mins,lf(0)(s)+∑N i=1(s,l(i)),s.t.g(0)(s)≤0,g(i)(s,l(i))≤0,i=1,…,N,已经给出了严格的分解理论,一般足以涵盖许多大型工程的设计问题。与文献[1]中利用可分化方法求解实值的目标函数模型不同,本文将同样用可分化方法求解更一般的目标函数——向量值目标函数,给出了其局部弱Pareto解的必要条件以及全局弱Pareto解的充分必要条件。Numerous hierarchical and nonhierarchical decomposition strategies for the optimization of large scale systems,comprised of interacting subsystems,have been proposed.With a few exceptions,all of these strategies are essentially heuristic in nature.Recent work considered a class of optimization problems,called quasi-separable mins,l f(0)(s)+∑N i=1f(i)(s,l(i)),s.t.g(0)(s)≤0,g(i)(s,l(i))≤0,i=1,…,N,narrow enough for a rigorous decomposition theory,yet general enough to encompass many large scale engineering design problems.With the literature [1] in solving real-value of objective function is different,in this paper we solve more general objective function—vector-valued objective function using decomposition methods,and extend the necessary conditions for local weak Pareto solution and the necessary and sufficient conditions for global Pareto solution.

关 键 词：可分化 全局(局部)优化 向量值优化 混合整数规划 多目标设计 拟分离子系统 弱Pareto解 

分 类 号：N[自然科学总论]