若干運(yùn)籌學(xué)優(yōu)化方法的MATLAB實(shí)現(xiàn)

信息計算科學(xué)論文編號:XXLW078 論文字?jǐn)?shù):11586,頁數(shù):34

目  錄

摘     要 i
Abstract ii
目  錄 iii
第一章 前  言 1
第二章  線性規(guī)劃問題的MATLAB實(shí)現(xiàn) 2
2.1  線性規(guī)劃數(shù)學(xué)原理 2
2.2   MATLAB函數(shù)Linprog簡介 3
2.3 線性規(guī)劃算例 4
2.3.1問題提出 4
2.3.2模型分析 4
2.3.3 模型建立和求解 7
2.3.4結(jié)果分析 14
第三章  整數(shù)規(guī)劃的MATLAB實(shí)現(xiàn) 15
3.1  指派問題介紹 15
3.2 指派問題算例 16
3.2.1  問題提出 16
3.2.2問題分析 16
3.2.3問題求解 17
3.2.4 結(jié)果解釋 18
3.2.5結(jié)果分析 18
第四章  動態(tài)規(guī)劃算法的MATLAB實(shí)現(xiàn) 19
4.1  動態(tài)規(guī)劃算法介紹 19
4.2 Floyd算法介紹 19
4.2.1核心思路 19
4.2.2 算法基本步驟 20
4.2.3 算法描述 20
4.3 最短路線實(shí)例 21
4.3.1問題提出 21
4.3.2問題分析 21
4.3.3問題求解 22
4.3.4結(jié)果分析 22
第五章  結(jié)論 23
致  謝 24
參考文獻(xiàn) 25
附錄  26

摘     要
 本文選擇了運(yùn)籌學(xué)優(yōu)化方法的其中三種方法進(jìn)行了Matlab實(shí)現(xiàn)。第一種方法是線性規(guī)劃方法，在分析了線性規(guī)劃的數(shù)學(xué)原理的基礎(chǔ)上，利用MATLAB工具箱中線性規(guī)劃的經(jīng)典函數(shù)Linprog函數(shù)，很好的解決了所提出的求解余姚市城鄉(xiāng)最低生活保障保準(zhǔn)問題。第二種方法是整數(shù)規(guī)劃方法，其實(shí)更是特殊的整數(shù)規(guī)劃，特殊的0—1規(guī)劃，文中利用枚舉法編寫Matlab程序，很好的解決了一個非標(biāo)準(zhǔn)的人員分配指派問題。第三種方法是動態(tài)規(guī)劃方法，在分析了動態(tài)規(guī)劃方法的特征和求解步驟后，提出了用動態(tài)規(guī)劃方法來解決最短路線問題，利用動態(tài)規(guī)劃算法—Flyod算法，一個求解網(wǎng)絡(luò)上任意兩點(diǎn)間的最短路的經(jīng)典算法，準(zhǔn)確而快速的找到了杭州到青川最短公路行駛路線。最后，結(jié)合以上三種方法的求解過程及所得結(jié)果，對Matlab語言在運(yùn)籌學(xué)中的應(yīng)用做了客觀的評價，同時也指出本文中的優(yōu)缺點(diǎn)。
 
關(guān)鍵詞：線性規(guī)劃 整數(shù)規(guī)劃 動態(tài)規(guī)劃 Matlab Linprog Floyd
 
Abstract

 The article chooses 3 methods of Operations research for Matlab implementing.The first method is Linear Programming.On the basis of the mathematics principle of Linear Programming,we use the classic function called Linprog function of Linear Programming in the MATLAB Toolbox to solve the problem that solving the minimum living standard of urban and rural in Yuyao city sucessfully.
 The second method is Integer Programming.It is a special Integer Programming,a special 0-1 programming,we use Enumeration method to programming in Matlab,and it solve a non-standard assignment problem successfully.
 The third method is Dynamic Programming.After analysising the features and the solution steps of Dynamic Programming,we propose that using Dynamic Programming to solve the problem of the shortest route.we use Dynamic Programming algorithm-flyod algorithm, a classic algorithm of searching the shortest path between any two in the network,and we find the shortest road route from Hangzhou to Qingchuan accurately and fastly.At last,combining the solution procedures and solution results of the above 3 methods,we give a objective eva luation of the Matlab language in the application of operations research, and also point out the advantages and disadvantages of this article.
 
Keywords: Linear Programming;Integer Programming;Dynamic Programming;Matlab;Linprog;Floyd