淺談多目標(biāo)規(guī)劃及解法

淺談多目標(biāo)規(guī)劃及解法

摘 要：本文對多目標(biāo)規(guī)劃問題的解決方法進(jìn)行了歸納和總結(jié)，并且進(jìn)行了1定的'評論。基本方法有主要目標(biāo)法、分層序列法；評價函數(shù)法，理想點法、線行加權(quán)和法、平方和權(quán)法；功效系數(shù)法。特別地介紹了1種關(guān)于線性多目標(biāo)規(guī)劃求最優(yōu)解的方法。通過歸納和總結(jié)，熟知各解決方法的特點，以便以后在實際中能夠得到更好的應(yīng)用。并且給出了1種新的評價函數(shù)。
關(guān)鍵詞: 多目標(biāo)規(guī)劃；解決方法；弱有效解；算法

On multi-objective programming and Its Solution

Abstract: This article has carried on the induction and the summary to the multi-objective programming, and has carried on the certain commentary. The main method has the primary-object method，Lexicographic method，evaluation function methods，robustness estimate，linearity weighted sum method, involution weighted sum method efficiency coefficient method .Specially introduced one kind of method of optimal solution about muti-objective linear programming. Through the induction and the summary, knows very well each solution the characteristic, in order to later in will be actual can obtain a better application. And has produced one kind of new evaluation function.
Keywords： multi-objective programming; solution; weak efficient solution; algorithm

目 錄

中文題目………………………………………………………………………………………(1)
中文摘要和關(guān)鍵詞………………………………………………………………………(1)
英文題目………………………………………………………………………………………(1)
英文摘要和關(guān)鍵詞………………………………………………………………………(1)
前言……………………………………………………………………………………………(2)
正文……………………………………………………………………………………………(3)
　 1 有關(guān)多目標(biāo)規(guī)劃的基本概念…………………………………………………………(3)
1.1 標(biāo)準(zhǔn)形式………………………………………………………………………………(3)
1.2 多目標(biāo)規(guī)劃的解………………………………………………………………………(4)
2 基本方法　…………………………………………………………………………………(4)
2.1主要目標(biāo)法………………………………………………………………………………(5)
2.2 分層序列法 ……………………………………………………………………………(5)
2.2.1不容許寬容…………………………………………………………………………(5)
2.2.2允許寬容……………………………………………………………………………(6)
2.3評估函數(shù)…………………………………………………………………………………(7)
2.3.1理想點法……………………………………………………………………………(7)
2.3.2線性加權(quán)和法………………………………………………………………………(8)
2.3.3平方加權(quán)法…………………………………………………………………………(8)
2.4功效系數(shù)法………………………………………………………………………………(8)
2.4.1直線法………………………………………………………………………………(9)
2.4.2指數(shù)法………………………………………………………………………………(10)
2.5 線行多目標(biāo)規(guī)劃最優(yōu)解求法…………………………………………………………(10)
2.5.1(LVP)弱有效解的解集性質(zhì)與求解方法…………………………………………(10)
2.5.2 決策者滿意解的確定方法……………………………………………………………(15)
2.5.3 算法步驟………………………………………………………………………………(15)
2.6確定權(quán)數(shù)法 …………………………………………………………………………………(16)
2.7新的評價函數(shù)………………………………………………………………………………(17)
3 結(jié)束語…………………………………………………………………………………………(17)
參考文獻(xiàn)　…………………………………………………………………………………………(18)
致謝　………………………………………………………………………………………………(20)