解线性整数规划的劣元消去搜索法

• 作 者: 郭卫东 庞娟珍
• 出 处: 抚顺石油学院学报
• 发表日期: 1987年01期
• 关键词: 整数规划 解线性 取整数 行阶 整数阶 消去法 搜索法 实数空间 目标函数值 有穷

纯线性整数规划的一般型为: IP—1 max CX s.t.AX≤B X≥0 取整数其中:C=[C_1,C_2……,C_n] X=[X_1,X_2……X_n]~T B=[b_1,b_2,……b_m]~T 记线性整数规划的可行域ΩE_n。令J=sum from i=1 to n X_1称为变量阶,若J∈Ω,则称J为可行阶。否则JΩ,J称为非可行阶。因X必取整数,阶J也必为整数阶。(整数之和仍为整数)若Ω是有穷的n维实数空间,即对所有的i有:a_i≤X_i≤b_i,则线性整数规划的可行阶J必有上界和下界,分别记为max J和min J。

The general type of pure linear integer programming is: IP-1 max CX stAX≤BX≥0 Integer where: C = [C_1, C_2 ......, C_n] X = [X_1, X_2 ...... X_n] ~ TB = [b_1 , b_2, ... b_m] ~ T The feasible field ΩE_n of linear integer programming. Let J = sum from i = 1 to n X_1 be called variable order, if J∈Ω, then let J be a feasible order. Otherwise JΩ, J is called non-feasible order. Because X must take an integer, order J must also be an integer order. (The sum of integers is still an integer.) If Ω is a finite n-dimensional real number space, that is, for all i: a_i≤X_i≤b_i, then the feasible order J of linear integer programming must have upper and lower bounds, respectively max J and min J.