淺談多目標規劃及解法
摘 要：本文對多目標規劃問題的解決方法進行了歸納和總結，並且進行了1定的評論。基本方法有主要目標法、分層序列法；評價函數法，理想點法、線行加權和法、平方和權法；功效係數法。特別地介紹了1種關於線性多目標規劃求最優解的方法。通過歸納和總結，熟知各解決方法的特點，以便以後在實際中能夠得到更好的應用。並且給出了1種新的評價函數。
關鍵詞: 多目標規劃；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)
中文摘要和關鍵詞………………………………………………………………………(1)
英文題目………………………………………………………………………………………(1)
英文摘要和關鍵詞………………………………………………………………………(1)
前言……………………………………………………………………………………………(2)
正文……………………………………………………………………………………………(3)
1 有關多目標規劃的基本概念…………………………………………………………(3)
1.1 標準形式………………………………………………………………………………(3)
1.2 多目標規劃的解………………………………………………………………………(4)
2 基本方法 …………………………………………………………………………………(4)
2.1主要目標法………………………………………………………………………………(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…………………………………………………………………………………(7)
2.3.1理想點法……………………………………………………………………………(7)
2.3.2線性加權和法………………………………………………………………………(8)
2.3.3平方加權法…………………………………………………………………………(8)
2.4功效係數法………………………………………………………………………………(8)
2.4.1直線法………………………………………………………………………………(9)
2.4.2指數法………………………………………………………………………………(10)
2.5 線行多目標規劃最優解求法…………………………………………………………(10)
2.5.1(LVP)弱有效解的解集性質與求解方法…………………………………………(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確定權數法 …………………………………………………………………………………(16)
2.7新的評價函數………………………………………………………………………………(17)
3 結束語…………………………………………………………………………………………(17)
參考文獻 …………………………………………………………………………………………(18)
致謝 ………………………………………………………………………………………………(20)
[數學畢業論文參考]
摘 要：本文對多目標規劃問題的解決方法進行了歸納和總結，並且進行了1定的評論。基本方法有主要目標法、分層序列法；評價函數法，理想點法、線行加權和法、平方和權法；功效係數法。特別地介紹了1種關於線性多目標規劃求最優解的方法。通過歸納和總結，熟知各解決方法的特點，以便以後在實際中能夠得到更好的應用。並且給出了1種新的評價函數。
關鍵詞: 多目標規劃；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)
中文摘要和關鍵詞………………………………………………………………………(1)
英文題目………………………………………………………………………………………(1)
英文摘要和關鍵詞………………………………………………………………………(1)
前言……………………………………………………………………………………………(2)
正文……………………………………………………………………………………………(3)
1 有關多目標規劃的基本概念…………………………………………………………(3)
1.1 標準形式………………………………………………………………………………(3)
1.2 多目標規劃的解………………………………………………………………………(4)
2 基本方法 …………………………………………………………………………………(4)
2.1主要目標法………………………………………………………………………………(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…………………………………………………………………………………(7)
2.3.1理想點法……………………………………………………………………………(7)
2.3.2線性加權和法………………………………………………………………………(8)
2.3.3平方加權法…………………………………………………………………………(8)
2.4功效係數法………………………………………………………………………………(8)
2.4.1直線法………………………………………………………………………………(9)
2.4.2指數法………………………………………………………………………………(10)
2.5 線行多目標規劃最優解求法…………………………………………………………(10)
2.5.1(LVP)弱有效解的解集性質與求解方法…………………………………………(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確定權數法 …………………………………………………………………………………(16)
2.7新的評價函數………………………………………………………………………………(17)
3 結束語…………………………………………………………………………………………(17)
參考文獻 …………………………………………………………………………………………(18)
致謝 ………………………………………………………………………………………………(20)
[數學畢業論文參考]
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