电气优化设计作业2、用黄金分割法求目标函数107)(2+-=x x x f 的极小点，初始搜索区间[a ，b]=[1，7]，迭代精度取0.2。

答：程序如下function xmin=golden(f,a,b,e)k=0; a1 =b-0.618*(b-a); a2 =a+0.618*(b-a);while b-a>ey1=subs(f,a1); y2=subs(f,a2);if y1>y2 a=a1; a1=a2; y1=y2; a2=a+0.618*(b-a);else b=a2; a2=a1; y2=y1; a1=b-0.618*(b-a);endk=k+1;endxmin=(a+b)/2; fmin=subs(f,xmin) fprintf('k=\n'); disp(k);将程序保存后在命令窗口输入以下指令并输入回车：syms x a b a3 e h; a=input('搜索区间的第一点\a='); b=input('搜索区间的第二点\b='); e=input('搜索精度\ne='); disp('需求的优化函数f=f(x)，调用xmin=golden(f,a,b,e)');按照提示将搜索区间、目标函数及迭代精度输入，键入指令xmin=golden(f,a,b,e)')，回车可得结果如下（k 为迭代次数）： fmin=-2.2497，k=8，xmin=3.48343、用牛顿法求10)1(2)1(4)(212221+++-++=x x x x X f 的最优解，设X （0）=[0, 0]T 。

答：程序如下：syms x1 x2;f=4*(x1+1)^2+2*(x2-1)^2+x1+x2+10; v=[x1,x2]; df=jacobian(f,v); df=df.'; G=jacobian(df,v);epson=1e-12;x0=[0,0]'; g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)}); G1=subs(G,{x1,x2},{x0(1,1),x0(2,1)}); k=0;mul_count=0;sum_count=0; mul_count=mul_count+12; sum_count=sum_count+6; while(norm(g1)>epson)p=-G1\g1; x0=x0+p; g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});G1=subs(G ,{x1,x2},{x0(1,1),x0(2,1)}); k=k+1;mul_count=mul_count+16;sum_count=sum_count+11;end;x0结果为：x0 =( -1.1250，0.7500)4、用拉格朗日乘子法求解以下约束最优化问题：06)( ..60410)(min 121212221=-=+---+=x X h t s x x x x x x X f答：程序如下syms x1 x2 lamaf=x1^2+x2^2-x1*x2-10*x1-4*x2+60+lama*(x1-6); dx1=diff(f,x1); dx2=diff(f,x2); dlama=diff(f,lama); x1x1=solve(dx1,x1); x2x2=solve(dx2,x2); ff=subs(dlama,{x1,x2},{x1x1,x2x2}); lamao=solve(ff); xo=subs(x1x1,lama,lamao) yo=subs(x2x2,lama,lamao) fo=subs(f,{x1,x2,lama},{xo,yo,lamao}) 结果为：x1=6，x2=5,minf(x)=11。

5、用二进制遗传算法求解以下约束整数优化问题：105 63 157 ..)(min 321321≤≤≤≤≤≤++=x x x t s x x x X f答：程序如下：function pop=initpop(popsize,chromlength)pop=round(rand(popsize,chromlength));function pop2=decodebinary(pop)[px,py]=size(pop);for i=1:pypop1(:,i)=2.^(py-i).*pop(:,i);endpop2=sum(pop1,2);function pop2=decodechrom(pop,spoint,length)pop1=pop(:,spoint:spoint+length-1); pop2=decodebinary(pop1);function [eval]=f(sol)numv=size(sol,3); x=sol(1:numv); eval=x1+x2+x3;function [sol,eval]=fitness(sol,options)numv=size(sol,3)-1; x=sol(1:numv); eval=f(x); eval=-eval;bounds=ones(3,1)*[7<=x1<=15,3<=x2<=6,5<=x3<=10]; [p,endPop,bestSols,trace]=ga(bounds,'fitness') function fitvalue=calfitvalue(objvalue)global Cmin; Cmin=0; [px,py]=size(objvalue);for i=1:pxif objvalue(i)+Cmin>0temp=Cmin+objvalue(i);elsetemp=0.0;endfitvalue(i)=temp;endfitvalue=fitvalue';function [newpop]=selection(pop,fitvalue)totalfit=sum(fitvalue); fitvalue=fitvalue/totalfit; fitvalue=cumsum(fitvalue); [px,py]=size(pop); ms=sort(rand(px,1)); fitin=1; newin=1;while newin<=pxif(ms(newin))<fitvalue(fitin)newpop(newin)=pop(fitin); newin=newin+1;else fitin=fitin+1;endendfunction [newpop]=crossover(pop,pc)[px,py]=size(pop); newpop=ones(size(pop));for i=1:2:px-1if(rand<pc) cpoint=round(rand*py); newpop(i,:)=[pop(i,1:cpoint),pop(i+1,cpoint+1:py)];newpop(i+1,:)=[pop(i+1,1:cpoint),pop(i,cpoint+1:py)];else newpop(i,:)=pop(i); newpop(i+1,:)=pop(i+1);endendfunction [newpop]=mutation(pop,pm)[px,py]=size(pop); newpop=ones(size(pop));for i=1:pxif(rand<pm)mpoint=round(rand*py);if mpoint<=0mpoint=1;endnewpop(i)=pop(i);if any(newpop(i,mpoint))==0newpop(i,mpoint)=1;else newpop(i,mpoint)=0;endelse newpop(i)=pop(i);endendfunction [bestindividual,bestfit]=best(pop,fitvalue)[px,py]=size(pop); bestindividual=pop(1,:); bestfit=fitvalue(1);for i=2:pxif fitvalue(i)<bestfitbestindividual=pop(i,:); bestfit=fitvalue(i);endendclearclfpopsize=20; chromlength=10; pc=0.6; pm=0.001; pop=initpop(popsize,chromlength); for i=1:20[objvalue]=calobjvalue(pop);fitvalue=calfitvalue(objvalue);[newpop]=selection(pop,fitvalue);[newpop]=crossover(pop,pc);[newpop]=mutation(pop,pc);[bestindividual,bestfit]=best(pop,fitvalue);y(i)=min(bestfit);n(i)=i;pop5=bestindividual;x(i)=decodechrom(pop5,1,chromlength)*10/1023;pop=newpop;endfplot('10*sin(5*x)+7*cos(4*x)',[0 10])hold onplot(x,y,'r*')hold off[z index]=max(y);x5=x(index)y=z结果如下：min f(x)=15，x1=7，x2=3，x3=5。