中科大《优化设计》课程大作业之约束优化实验报告(共8页)

1、精选优质文档-倾情为你奉上约束优化设计实验报告力学系型号：联想y470CPU：i5-2450M内存：2GB系统：win7-64位求解问题：如上是以下三个约束方法共同需要求解的问题，预估结果：在（x1,x2,x3）（23,13,12）点附近存在极值。其中，每个方法对应的初始条件分别为：（1）随机试验法设计变量范围：随机试验点数：N=1000精度：eps=0.001（2）随机方向法初始点：x0=(25,15,5)初始步长：a0=0.5精度：eps=0.001（3）线性规划单纯形法初始复合形：X=20 23 25 30;10 13 15 20;10 9 5 0顶点个数：n=4精度：eps=0.01计

2、算结果：约束方法所需时间迭代次数极值点极值随机试验法28.230（22.63,12.63,12.06）3445.50随机方向法0.6549（22.67,12.67,11.98）3441.99线性规划单纯形法6.235（22.59,12.59,12.12）3445.61程序说明：主程序为main，运行main后按提示即可得到相应约束方法的求解结果。程序如下：1、 主程序clear;global kk;kk=0;disp('1.随机试验法');disp('2.随机方向法');disp('3.线性规划单纯形法');while 1 n0=input(&#

3、39;请输入上面所想选择约束优化方法的编号（1、2、3）：'); if n0=1|n0=2|n0=3 break; end disp('此次输入无效.');end disp(' ');disp('');xx,yy=fmins(n0);fprintf('迭代次数为： %8.0fn', kk);disp('所求极值点的坐标向量为：');fprintf(' %16.5fn', xx);fprintf('所求函数的极值为： %16.5fn', yy);2、 调用函数function

4、xx,yy=fmins(n0)if n0=1 tic;xx,yy=suijishiyan();toc;elseif n0=2 tic;xx,yy=suijifangxiang();toc;elseif n0=3 tic;xx,yy=danchunxing();toc;endend3、 单纯形法function xx,yy=danchunxing()clear;global kk;syms a b c;f=-a*b*c;g=-a+2*b+2*c>=0;a+2*b+2*c<=72;abs(a-b-10)<=1e-3;b>=10;b<=20;X=20 23 25 30;

5、10 13 15 20;10 9 5 0;alpha=1.3;sita=0.5;gama=1;beta=0.7;var=a;b;c;eps=0.001;N=size(X);n=N(2);FX=zeros(1,n);while 1 for i=1:n FX(i)=double(subs(f,var,X(:,i); end XS,IX=sort(FX); Xsorted=X(:,IX); px=sum(Xsorted(:,1:(n-1),2)/(n-1); Fpx=double(subs(f,var,px); SumF=0; for i=1:n SumF=SumF+(FX(IX(i)-Fpx)2;

6、 end SumF=sqrt(SumF/(n-1); if SumF<=eps xx=Xsorted(:,1); break; else bcon_1=1; cof_alpha=alpha; while bcon_1 x2=px+cof_alpha*(px-Xsorted(:,n); gx2=double(subs(g,var,x2); if min(gx2)>0 bcon_1=0; else cof_alpha=0.7*(cof_alpha); end end fx2=double(subs(f,var,x2); if fx2<XS(1) cof_gama=gama; bc

7、on_2=1; while bcon_2 x3=x2+cof_gama*(x2-px); gx3=double(subs(g,var,x3); fx3=double(subs(f,var,x3); if min(gx3)>0 bcon_2=0; if fx3<XS(1) count=1; else count=2; end else bcon_2=0; count=3; end end if count=1 Xsorted(:,n)=x3; X=Xsorted; continue else Xsorted(:,n)=x2; X=Xsorted; continue end else

8、if fx2<XS(n-1) Xsorted(:,n)=x2; X=Xsorted; continue else if fx2<XS(n) Xsorted(:,n)=x2; cof_beta=beta; bcon_3=1; while bcon_3<4 x4=Xsorted(:,n)+cof_beta*(px-Xsorted(:,n); gx4=double(subs(g,var,x4); if min(gx4)>0 bcon_3=5; else cof_beta=cof_beta/2; bcon_3=bcon_3+1; end end if min(gx4)>0

9、 fx4=double(subs(f,var,x4); FNnew=double(subs(f,var,Xsorted(:,n); if fx4<FNnew Xsorted(:,n)=x4; X=Xsorted; continue else x0=Xsorted(:,1); for i=1:n Xsorted(:,i)=x0+sita*(Xsorted(:,i)-x0); end end else x0=Xsorted(:,1); for i=1:n Xsorted(:,i)=x0+sita*(Xsorted(:,i)-x0); X=Xsorted; continue end end e

10、lse x0=Xsorted(:,1); for i=1:n Xsorted(:,i)=x0+sita*(Xsorted(:,i)-x0); X=Xsorted; continue end end end end end X=Xsorted; kk=kk+1;endyy=-double(subs(f,var,xx);end4、 随机方向法function xx,yy=suijifangxiang()clear;global kk;x0 = 25;15;5;n = 3;eps = 0.001;a0 = 0.5;k = 10000;f0 = -x0(1)*x0(2)*x0(3);fl = -x0(

11、1)*x0(2)*x0(3);i = 1;while 1 a = a0; r = -1 + 2*rand(n,k); for j = 1:k ss=(sum(abs(r(:,j)0.5; e = r(:,j)./ss; x = x0 + a*e; if (-x(1)+2*x(2)+2*x(3)>=0)&& (x(1)+2*x(2)+2*x(3)<=72)&&(abs(x(1)-x(2)-10)<=1e-3)&&(x(2)>=10)&&(x(2)<=20) f =-x(1)*x(2)*x(3); if

12、f < fl fl = f; d = e; xl = x; end end end while 1 x = xl; a = 1.3*a; x = x+a*d; if (-x(1)+2*x(2)+2*x(3)>=0)&& (x(1)+2*x(2)+2*x(3)<=72)&&(abs(x(1)-x(2)-10)<=1e-3)&&(x(2)>=10)&&(x(2)<=20) f =-x(1)*x(2)*x(3); if f < fl fl = f; else break end else bre

13、ak end kk=kk+1; end for b = 1:50 x = x - a*d; a = 0.7*a; x = x + a*d; if (-x(1)+2*x(2)+2*x(3)>=0)&& (x(1)+2*x(2)+2*x(3)<=72)&&(abs(x(1)-x(2)-10)<=1e-3)&&(x(2)>=10)&&(x(2)<=20) f =-x(1)*x(2)*x(3); if f < fl fl = f; break end end end epsl = abs(f0-fl)/

14、f0); if epsl < eps&&x(1)<23 break else i = i+1; x0 = x; f0 = f; fl = f; end kk=kk+1;endxx = x;yy =-f;end5、 随机试验法function xx,yy=suijishiyan()format longN=1000;x1=;x2=;x3=;zmax=-inf;x10=unifrnd(20,30,N,1);x20=unifrnd(10,20,N,1);x30=unifrnd(-10,16,N,1);for i=1:N for j=1:N for k=1:N if (-x10(i)+2*x20(j)+2*x30