无比值检验的亏基原始Ⅰ阶段算法  

A Phase-I Algorithm Primal Simplex Method Based on the Deficient Basis and Ratioless Rule

作　　者：马艳琴[1] 张亚芳 杨红艳[3] 卜春霞[4] 

机构地区：[1]黄河科技学院电子系,河南郑州450063 [2]郑州外国语中学数学教研室,河南郑州450001 [3]中原工学院数理学院,河南郑州450007 [4]郑州大学数学系,河南郑州450001

出　　处：《数学的实践与认识》2014年第3期142-147,共6页Mathematics in Practice and Theory

基　　金：河南省科技厅基础与前沿技术研究资助项目(132300410217);郑州市科技局科技攻关项目(20130786)

摘　　要：首次将亏基和无比值检验列主元规则相结合,执行亏基对偶单纯形算法得到一个原始可行基,以充分发挥这两种算法的优势,从而为亏基原始单纯形算法提供一个新的I阶段算法,以使其进一步克服退化所带来的困扰.数值试验表明,亏基和无比值主元规则的结合,能有效地减少总迭代次数和运行时间,其效率远远优于传统两阶段单纯形算法.This article first combines deficient basis and ratioless column rule,then carries out deficient dual simplex algorithm to get a primal feasible basis and give full play to the advantages of these two kinds of algorithms.The new algorithm provides a new phase-1 algorithm for deficient basis algorithm and overcome the degradation.Numerical results show that the deficient basis can effectively reduce the total iterations and operation time,its efficiency is far superior to the traditional two stage simplex algorithm.

关 键 词：线性规划 单纯形法 亏基 退化 无比值主元规则 

分 类 号：O221.1[理学—运筹学与控制论]