📄 §2 多目标遗传算法研究.htm
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<P class=MsoNormalIndent style="TEXT-INDENT: 0cm"><SPAN lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><![if !supportEmptyParas]><![endif]> <o:p></o:p></SPAN></P><BR
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<P class=MsoNormalIndent style="TEXT-INDENT: 0cm; TEXT-ALIGN: center"
align=center><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'">图</SPAN><SPAN
lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt">4.1 </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'">加权法无法求出全部非劣解的例子</SPAN><SPAN
lang=EN-US
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<P class=MsoNormalIndent
style="TEXT-JUSTIFY: inter-ideograph; TEXT-INDENT: 0cm; 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'">的初始阶段，但是初步的计算结果非常令人振奋，故本章另一个研究重点就放在了多目标非劣解集算法的研究上。<SPAN
lang=EN-US><o:p></o:p></SPAN></SPAN></P>
<H2 style="TEXT-ALIGN: center" align=center><SPAN lang=EN-US
style="FONT-FAMILY: 'Times New Roman'">§4.2</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">基于模糊逻辑的多目标遗传算法</SPAN><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-fareast-font-family: 宋体; mso-bidi-font-size: 10.0pt"><o:p></o:p></SPAN></H2>
<H3><SPAN lang=EN-US>§4.2.1 </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">模糊逻辑简介</SPAN></H3>
<P class=MsoNormalIndent
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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'">模糊逻辑（</SPAN><SPAN
lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt">Fuzzy
Logic</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'">）是一种新型的分类方法（分类是集合论的基本概念之一）。模糊逻辑模仿人类的智慧，引入隶属度的概念，描述介于“真”与“假”中间的过渡过程。在模糊逻辑中，事件不以集合的极限值分类，而是给每一个元素赋予一个介于</SPAN><SPAN
lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt">0</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'">和</SPAN><SPAN
lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt">1</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'">之间的实数，描述其属于一个集合的强度。具体的介绍可以参考文献</SPAN><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 'Times New Roman'">【<SPAN
lang=EN-US>116】。</SPAN></SPAN><SPAN lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></SPAN></P>
<H3><SPAN lang=EN-US>§4.2.2 </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">基于模糊逻辑的多目标遗传算法的思路和具体实现</SPAN></H3>
<P class=MsoNormal
style="TEXT-JUSTIFY: inter-ideograph; 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'">通过前面的介绍，我们知道采用模糊逻辑是一种很好的反应决策者主观意愿的工具。可以用模糊逻辑的方法反应决策者对于各个目标之间重要性的“权衡”信息。众所周知，遗传算法是依据个体的适应度进行，可以认为适应度就是决策者对于个体的综合评价，因而可以依据模糊逻辑的方法，直接构造决策者对于遗传个体的适应度的取值，即决策者对个体的综合评价。并以此作为遗传进化的依据和动力。下面是初步的算法步骤：</SPAN><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></SPAN></P>
<P class=MsoNormal
style="TEXT-JUSTIFY: inter-ideograph; TEXT-ALIGN: justify"><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">1</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'">）分别求出各单目标的最优解；</SPAN><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></SPAN></P>
<P class=MsoNormal
style="TEXT-JUSTIFY: inter-ideograph; TEXT-ALIGN: justify"><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">2</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'">）以（</SPAN><SPAN
lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt">1</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'">）中的单目标的最优解和决策者协商，给出各个目标满意度的隶属函数；</SPAN><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></SPAN></P>
<P class=MsoNormal
style="TEXT-JUSTIFY: inter-ideograph; TEXT-ALIGN: justify"><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">3</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'">）通过模糊逻辑表达决策者的想法，将各目标的满意度和个体的适应度联系起来；</SPAN><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></SPAN></P>
<P class=MsoNormal
style="TEXT-JUSTIFY: inter-ideograph; TEXT-ALIGN: justify"><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">4</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'">）以（</SPAN><SPAN
lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt">3</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'">）定义的适应度为基础采用遗传算法进行求解；</SPAN><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></SPAN></P>
<P class=MsoNormal
style="TEXT-JUSTIFY: inter-ideograph; 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'">之所以首先求解各个单目标的最优解，是希望能给决策者一个比较清晰的概念，即如果单独优化某个目标，可能的最优解是多少。有了这个信息，决策者才能给出令人置信的关于不同目标的满意度的隶属曲线。如果求解单目标优化的难度很大，也可以给出对单目标最优的一个估计值。</SPAN><SPAN
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