matlab遗传算法工具箱函数及实例讲解 zz.htm

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style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">指定精度</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">) 
<BR><BR>(2)function [x,endPop,bPop,traceInfo] = 
ga(bounds,evalFN,evalOps,startPop,opts,... <BR>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp; 
&nbsp; 
termFN,termOps,selectFN,selectOps,xOverFNs,xOverOps,mutFNs,mutOps)--</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">遗传算法函数</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> 
<BR></SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">【输出参数】</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> <BR>&nbsp; 
&nbsp;&nbsp;&nbsp;x--</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">求得的最优解</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> <BR>&nbsp; 
&nbsp;&nbsp;&nbsp;endPop--</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">最终得到的种群</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> <BR>&nbsp; 
&nbsp;&nbsp;&nbsp;bPop--</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">最优种群的一个搜索轨迹</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> 
<BR></SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">【输入参数】</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> <BR>&nbsp; 
&nbsp;&nbsp;&nbsp;bounds--</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">代表变量上下界的矩阵</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> <BR>&nbsp; 
&nbsp;&nbsp;&nbsp;evalFN--</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">适应度函数</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> <BR>&nbsp; 
&nbsp;&nbsp;&nbsp;evalOps--</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">传递给适应度函数的参数</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> <BR>&nbsp; 
&nbsp;&nbsp;&nbsp;startPop-</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">初始种群</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> <BR>&nbsp; 
&nbsp;&nbsp;&nbsp;opts[epsilon prob_ops display]--opts(1:2)</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">等同于</SPAN><SPAN 
lang=EN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">initializega</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">的</SPAN><SPAN 
lang=EN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">options</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">参数，第三个参数控制是否输出，一般为</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">0</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">。如</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">[1e-6 1 0] 
<BR>&nbsp; &nbsp;&nbsp;&nbsp;termFN--</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">终止函数的名称</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">,</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">如</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">['maxGenTerm'] 
<BR>&nbsp; &nbsp;&nbsp;&nbsp;termOps--</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">传递个终止函数的参数</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">,</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">如</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">[100] 
<BR>&nbsp; &nbsp;&nbsp;&nbsp;selectFN--</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">选择函数的名称</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">,</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">如</SPAN><SPAN 
lang=EN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">['normGeomSelect'] 
<BR>&nbsp; &nbsp;&nbsp;&nbsp;selectOps--</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">传递个选择函数的参数</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">,</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">如</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">[0.08] 
<BR>&nbsp; &nbsp;&nbsp;&nbsp;xOverFNs--</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">交叉函数名称表，以空格分开，如</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">['arithXover 
heuristicXover simpleXover'] <BR>&nbsp; &nbsp;&nbsp;&nbsp;xOverOps--</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">传递给交叉函数的参数表，如</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">[2 0;2 3;2 0] 
<BR>&nbsp; &nbsp;&nbsp;&nbsp;mutFNs--</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">变异函数表，如</SPAN><SPAN 
lang=EN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">['boundaryMutation 
multiNonUnifMutation nonUnifMutation unifMutation'] <BR>&nbsp; 
&nbsp;&nbsp;&nbsp;mutOps--</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">传递给交叉函数的参数表</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">,</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">如</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">[4 0 0;6 100 
3;4 100 3;4 0 0] <BR><BR></SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">注意】</SPAN><SPAN 
lang=EN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">matlab</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">工具箱函数必须放在工作目录下</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> 
<BR></SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">【问题】求</SPAN><SPAN 
lang=EN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">f(x)=x+10*sin(5x)+7*cos(4x)</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">的最大值，其中</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">0&lt;=x&lt;=9 
<BR></SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">【分析】选择二进制编码，种群中的个体数目为</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">10</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">，二进制编码长度为</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">20</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">，交叉概率为</SPAN><SPAN 
lang=EN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">0.95,</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">变异概率为</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">0.08 
<BR></SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">【程序清单】</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> <BR>&nbsp; 
&nbsp; %</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">编写目标函数</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> <BR>&nbsp; 
&nbsp;&nbsp; &nbsp;function[sol,eval]=fitness(sol,options) <BR>&nbsp; 
&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;x=sol(1); <BR>&nbsp; &nbsp;&nbsp; 
&nbsp;&nbsp;&nbsp;eval=x+10*sin(5*x)+7*cos(4*x); <BR>&nbsp; &nbsp; %</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">把上述函数存储为</SPAN><SPAN 
lang=EN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">fitness.m</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">文件并放在工作目录下</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> <BR>&nbsp; 
&nbsp;&nbsp;&nbsp;<BR>&nbsp; &nbsp; initPop=initializega(10,[0 
9],'fitness');%</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">生成初始种群，大小为</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">10 <BR>&nbsp; 
&nbsp; [x endPop,bPop,trace]=ga([0 9],'fitness',[],initPop,[1e-6 1 
1],'maxGenTerm',25,'normGeomSelect',... <BR>&nbsp; &nbsp;&nbsp; 
&nbsp;[0.08],['arithXover'],[2],'nonUnifMutation',[2 25 3]) %25</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">次遗传迭代</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> 
<BR><BR></SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">运算借过为：</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">x = <BR>&nbsp; 
&nbsp; 7.8562 24.8553(</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">当</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">x</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">为</SPAN><SPAN 
lang=EN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">7.8562</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">时，</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">f</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">（</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">x</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">）取最大值</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">24.8553) 
<BR><BR></SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">注：遗传算法一般用来取得近似最优解，而不是最优解。另外遗传算法的收敛性跟其初始值有关，大家运行上面的命令所得到的借过可能跟我的借过不同或是差别很大。但多执行几次上面的命令（随即取不同的初始群体）一定可以得到近似最优解。</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> 
<BR><BR><BR><BR></SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">遗传算法实例</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">2 
<BR><BR></SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">【问题】在－</SPAN><SPAN 
lang=EN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">5&lt;=Xi&lt;=5,i=1,2</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">区间内，求解</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> <BR>&nbsp; 
&nbsp;&nbsp; 
&nbsp;&nbsp;&nbsp;f(x1,x2)=-20*exp(-0.2*sqrt(0.5*(x1.^2+x2.^2)))-exp(0.5*(cos(2*pi*x1)+cos(2*pi*x2)))+22.71282</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">的最小值。</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma"> 
<BR></SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">【分析】种群大小</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">10</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">，最大代数</SPAN><SPAN 
lang=EN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">1000</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">，变异率</SPAN><SPAN 
lang=EN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">0.1,</SPAN><SPAN 
style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: 宋体; mso-hansi-font-family: Tahoma; mso-ascii-font-family: Tahoma; mso-bidi-font-family: Tahoma">交叉率</SPAN><SPAN 
lang=EN style="FONT-SIZE: 9pt; COLOR: black; FONT-FAMILY: Tahoma">0.3