📄 §2 多目标遗传算法研究.htm
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</SPAN></SPAN><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">实际的工程优化问题大多数是多目标优化问题，目标之间一般都是互相冲突的。多目标优化很早就得到了人们的重视，到目前已经发展了较多的求解多目标优化的方法。下面先介绍多目标优化最重要的关于非劣解以及非劣解集的定义。</SPAN><SPAN
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style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt">1</SPAN></B><B
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style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">成立（</SPAN><SPAN
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style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">为目标数），且其中至少有一个严格不等式成立，则称</SPAN><SPAN
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style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">是多目标优化的一个非劣解（</SPAN><SPAN
lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt">Noninferior
Solution</SPAN><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">）。所有非劣解构成的集叫非劣解集（</SPAN><SPAN
lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt">Noninferior
Set</SPAN><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">）。</SPAN><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></SPAN></P>
<P class=MsoNormalIndent
style="TEXT-JUSTIFY: inter-ideograph; TEXT-INDENT: 0cm; TEXT-ALIGN: justify"><SPAN
lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><SPAN
style="mso-spacerun: yes">
</SPAN></SPAN><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">一个多目标优化如果存在非劣解，往往存在无穷多个，形成非劣解集。在求解实际问题时，过多的非劣解是无法直接应用的。决策者只能选择令其最满意的一个非劣解作为最终解。求最终解主要有三类方法，一类是求非劣解的生成法，即先求出大量的非劣解，构成非劣解的一个子集，然后按照决策者的意图找出最终解，另一类为交互法，不先求出很多的非劣解，而是通过分析者与决策者对话的方式，逐步求出最终解。最后一类是事先要求决策者提供目标之间的相对重要程度，算法以此为依据，将多目标问题转化为单目标问题进行求解，该类方法也可以被认为是第一类方法的一个子方法，该类方法的难点在于，如何得到决策者真实的权重信息，本章将提出一种基于模糊逻辑的，能比较好反映决策者权重的多目标遗传算法。</SPAN><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></SPAN></P>
<P class=MsoNormalIndent
style="TEXT-JUSTIFY: inter-ideograph; TEXT-INDENT: 0cm; TEXT-ALIGN: justify"><SPAN
lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><SPAN
style="mso-spacerun: yes">
</SPAN></SPAN><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">生成法主要有加权法</SPAN><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 'Times New Roman'">﹑</SPAN><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">约束法</SPAN><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 'Times New Roman'">﹑</SPAN><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">加权法和约束法结合的混合法以及多目标遗传算法。而交互法主要有用于求解线性约束多目标优化的</SPAN><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt">Geoffrion</SPAN><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">法</SPAN><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 'Times New Roman'">﹑求解线性多目标</SPAN><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">优化</SPAN><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 'Times New Roman'">的逐步法（<SPAN
lang=EN-US>STEM）和Zionts-Wallenius方法以及代替价值交换法。<o:p></o:p></SPAN></SPAN></P>
<P class=MsoNormalIndent
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style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 'Times New Roman'">作者认为相对而言生成法对决策者更有吸引力，首先目前没有比较好的多目标非线性优化的交互法，其次在只给决策者有限信息的前提下，往往要求决策者回答一些似是而非的问题，决策者在交互过程中将会很被动，也就是说交互法在某种程度上将问题的矛盾转嫁给了决策者。如果我们能求得非劣解的一个较好的近似解集，决策者就有了一个对问题比较全面的认识，从而能更好地进行决策和折衷。<SPAN
lang=EN-US><o:p></o:p></SPAN></SPAN></P>
<P class=MsoNormalIndent
style="TEXT-JUSTIFY: inter-ideograph; TEXT-INDENT: 24pt; TEXT-ALIGN: justify"><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 'Times New Roman'">生成法中，常用的加权法有其固有的缺点，对于非劣解集的某些区域不可能求出。如图<SPAN
lang=EN-US>4.1就是一个两个目标的例子，箭头所指非劣解曲线凹的部分无法用加权法求出，出现该现象的原因是，加权法实际上是优化各个目标函数正线性组合而成的单个目标。即采用正加权系数计算的单目标最优必然是非劣解，而某些非劣解可能找不到一组正加权系数来进行求解。采用约束法可以避免该现象，但是计算代价过大，且过程很繁杂，应用前景也不乐观。利用多目标遗传算法求解非劣解集是最近几年新出现的一种求解思路，目前还处在研究<o:p></o:p></SPAN></SPAN></P>
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