浅谈多目标规划及解法
摘 要：本文对多目标规划问题的解决方法进行了归纳和总结，并且进行了1定的评论。基本方法有主要目标法、分层序列法；评价函数法，理想点法、线行加权和法、平方和权法；功效系数法。特别地介绍了1种关于线性多目标规划求最优解的方法。通过归纳和总结，熟知各解决方法的特点，以便以后在实际中能够得到更好的应用。并且给出了1种新的评价函数。
关键词: 多目标规划；解决方法；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 录
中文题目………………………………………………………………………………………(1)
中文摘要和关键词………………………………………………………………………(1)
英文题目………………………………………………………………………………………(1)
英文摘要和关键词………………………………………………………………………(1)
前言……………………………………………………………………………………………(2)
正文……………………………………………………………………………………………(3)
1 有关多目标规划的基本概念…………………………………………………………(3)
1.1 标准形式………………………………………………………………………………(3)
1.2 多目标规划的解………………………………………………………………………(4)
2 基本方法 …………………………………………………………………………………(4)
2.1主要目标法………………………………………………………………………………(5)
2.2 分层序列法 ……………………………………………………………………………(5)
2.2.1不容许宽容…………………………………………………………………………(5)
2.2.2允许宽容……………………………………………………………………………(6)
2.3评估函数…………………………………………………………………………………(7)
2.3.1理想点法……………………………………………………………………………(7)
2.3.2线性加权和法………………………………………………………………………(8)
2.3.3平方加权法…………………………………………………………………………(8)
2.4功效系数法………………………………………………………………………………(8)
2.4.1直线法………………………………………………………………………………(9)
2.4.2指数法………………………………………………………………………………(10)
2.5 线行多目标规划最优解求法…………………………………………………………(10)
2.5.1(LVP)弱有效解的解集性质与求解方法…………………………………………(10)
2.5.2 决策者满意解的确定方法……………………………………………………………(15)
2.5.3 算法步骤………………………………………………………………………………(15)
2.6确定权数法 …………………………………………………………………………………(16)
2.7新的评价函数………………………………………………………………………………(17)
3 结束语…………………………………………………………………………………………(17)
参考文献 …………………………………………………………………………………………(18)
致谢 ………………………………………………………………………………………………(20)
[数学毕业论文参考]
摘 要：本文对多目标规划问题的解决方法进行了归纳和总结，并且进行了1定的评论。基本方法有主要目标法、分层序列法；评价函数法，理想点法、线行加权和法、平方和权法；功效系数法。特别地介绍了1种关于线性多目标规划求最优解的方法。通过归纳和总结，熟知各解决方法的特点，以便以后在实际中能够得到更好的应用。并且给出了1种新的评价函数。
关键词: 多目标规划；解决方法；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 录
中文题目………………………………………………………………………………………(1)
中文摘要和关键词………………………………………………………………………(1)
英文题目………………………………………………………………………………………(1)
英文摘要和关键词………………………………………………………………………(1)
前言……………………………………………………………………………………………(2)
正文……………………………………………………………………………………………(3)
1 有关多目标规划的基本概念…………………………………………………………(3)
1.1 标准形式………………………………………………………………………………(3)
1.2 多目标规划的解………………………………………………………………………(4)
2 基本方法 …………………………………………………………………………………(4)
2.1主要目标法………………………………………………………………………………(5)
2.2 分层序列法 ……………………………………………………………………………(5)
2.2.1不容许宽容…………………………………………………………………………(5)
2.2.2允许宽容……………………………………………………………………………(6)
2.3评估函数…………………………………………………………………………………(7)
2.3.1理想点法……………………………………………………………………………(7)
2.3.2线性加权和法………………………………………………………………………(8)
2.3.3平方加权法…………………………………………………………………………(8)
2.4功效系数法………………………………………………………………………………(8)
2.4.1直线法………………………………………………………………………………(9)
2.4.2指数法………………………………………………………………………………(10)
2.5 线行多目标规划最优解求法…………………………………………………………(10)
2.5.1(LVP)弱有效解的解集性质与求解方法…………………………………………(10)
2.5.2 决策者满意解的确定方法……………………………………………………………(15)
2.5.3 算法步骤………………………………………………………………………………(15)
2.6确定权数法 …………………………………………………………………………………(16)
2.7新的评价函数………………………………………………………………………………(17)
3 结束语…………………………………………………………………………………………(17)
参考文献 …………………………………………………………………………………………(18)
致谢 ………………………………………………………………………………………………(20)
[数学毕业论文参考]
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