有约束条件下的整数规划模型及其应用
关键词 0-1整数规划 分支定界法 割平面法 整数规划模型 lingo
毕业论文设计说明书外文摘要
Title An integer programming model under constraints and its application
Abstract
Integer programming deals with the problem of optimizing an objective function subjected to equality or inequality constrains and integer variables. If all the functions are linear, the problem is of a linear integer program. Otherwise, the problem is called a nonlinear integer program.The ultimate goal in integer optimization study is to develop efficient implementable algorithms for solving problems with integer variables.The development of efficient and robust algorithms and software for linear integer programming and the advent of high-speed computers have made linear integer programming an important tool for solving many real-world problems.
This thesis mainly introduced some basic concepts of integer programming model,solution method and integer programming model in mathematical modeling.In addition,through specific examples to integer programming model is introduced in complete scheme in solving actual problems,and the model to be done the appropriate promotion,and it can play a reference role in mathematical modeling.
Keywords 0-1 Integer Programming Branch and bound algorithm Cutting-plane method Integer Programming Model Lingo
目 录
1 引言 1
1.1 研究整数规划的背景及意义 1
1.2 国内外研究整数规划模型方法综述 2
1.3 本文主要研究的内容 3
2 0-1整数规划的数学模型 4
2.1 0-1整数规划模型的特点及其作用 4
2.2 0-1变量的说明 6
2.3 0-1整数规划的实际应用 6
2.3.1 问题叙述 6
2.3.2 相关数据 7
2.3.3 变量说明 8
2.3.4 模型建立 9
2.3.5 模型求解 10
2.3.6 模型推广 11
3 一般整数规划的基本理论和数学建模思想 12
3.1 整数的基本理论 12
3.2整数规划的基本概念 12
3.2.1 整数规划的一般模型 12
3.2.2整数规划求解方法总的基本思想 12
3.3 整数规划中的数学建模思想 13
3.4 简述整数规划模型的求解方法 13
3.4.1 分支定界法的详细介绍 13
3.4.2 割平面法 16
3.4.3 求解整数规划模型的lingo解法 18
4 整数规划的应用举例 19
4.1 问题叙述 19
4.2 问题分析 19
4.3 基本假设及符号说明 20
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