📄 §2 多目标遗传算法研究.htm
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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'">具体的计算方法和模糊控制的计算方法基本相同，也分为模糊化（</SPAN><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt">Fuzzification</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
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'">模糊推理（</SPAN><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt">Fuzzy-Inference</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
style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 'Times New Roman'">和去模糊化（<SPAN
lang=EN-US>Defuzzification）三部分组成。在作者算法中，模糊推理采用的是最大最小法，而去模糊化采用的是面积重心法。详见</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'">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>
<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'">下面以十杆桁架双目标优化为例详细叙述算法过程。</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'">参考图</SPAN><SPAN
lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt">3.4</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'">，位移目标是指节点</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-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-hansi-font-family: 'Times New Roman'">﹑<SPAN
lang=EN-US>3﹑4的最大<SUB><!--[if gte vml 1]><v:shape id=_x0000_i1043
style="WIDTH: 11.25pt; HEIGHT: 12.75pt" o:ole="" type = "#_x0000_t75" coordsize
= "21600,21600" fillcolor = "winColor(17)"> <v:imagedata o:title="" src =
"./Chapter4.files/image016.wmz"></v:imagedata></v:shape><![endif]--><![if !vml]><img width=15 height=17
src="./Chapter4.files/image017.gif" v:shapes="_x0000_i1043"><![endif]></SUB><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1043"
DrawAspect="Content" ObjectID="_1123618138">
</o:OLEObject>
</xml><![endif]-->向位移最小。这里最大<SUB><!--[if gte vml 1]><v:shape id=_x0000_i1044
style="WIDTH: 11.25pt; HEIGHT: 12.75pt" o:ole="" type = "#_x0000_t75" coordsize
= "21600,21600" fillcolor = "winColor(17)"> <v:imagedata o:title="" src =
"./Chapter4.files/image018.wmz"></v:imagedata></v:shape><![endif]--><![if !vml]><img width=15 height=17
src="./Chapter4.files/image019.gif" v:shapes="_x0000_i1044"><![endif]></SUB><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1044"
DrawAspect="Content" ObjectID="_1123618139">
</o:OLEObject>
</xml><![endif]-->向位移指的是绝对值最大。</SPAN></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'">这样我们就有了两个目标，即同时极小化位移和重量，可以建立比较简单的模糊逻辑如下：</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'">）如果重量轻并且位移小那么设计的适应度高；</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'">显然上式同时对两个目标都提出了要求。而如果我们只关心重量则可以建立如下的模糊逻辑：</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'">）如果重量轻不管位移大或小设计的适应度都应高；</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'">我们可以将模糊逻辑表示得更加精细，更符合决策者实际的想法：</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">3-1</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'">）如果重量轻而且位移小那么设计的适应度很高；</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">3-2</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'">）如果重量轻而且位移中等那么设计的适应度高；</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">3-3</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'">）如果重量轻而且位移大那么设计的适应度一般；</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">3-4</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'">）如果重量中等而且位移小那么设计的适应度高；</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">3-5</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'">）如果重量中等而且位移中等那么设计的适应度中等；</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">3-6</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'">）如果重量中等而且位移大那么设计的适应度低；</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">3-7</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'">）如果重量大而且位移小那么设计的适应度中等；</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">3-8</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'">）如果重量大而且位移中等那么设计的适应度低；</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">3-9</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'">）如果重量大而且位移大那么设计的适应度很低；</SPAN><SPAN
lang=EN-US
style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></SPAN></P>
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