机械优化设计C语言程序.docx
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机械优化设计C语言程序.docx
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机械优化设计机械优化设计C语言程序语言程序一、黄金分割法二、二次插值法三、最速下降法(阶梯法)四、变尺度法五、鲍威尔法一、黄金分割法#include#include#definer0.618#definef(x)x*x+2*xgolden(float,float,float);main()floata,b,e;printf(n请输入区间和收敛精度:
a,b,en);scanf(%f,%f,%f,&a,&b,&e);golden(a,b,e);golden(floata,floatb,floate)floaty1,y2,a1,a2,A,Y;intn=0;a1=b-r*(b-a);a2=a+r*(b-a);y1=f(a1);y2=f(a2);printf(黄金分割法的搜索过程:
);doprintf(n%da=%f,b=%f,a1=%f,a2=%f,y1=%f,y2=%f,n,a,b,a1,a2,y1,y2);if(y1=y2)a=a1;a1=a2;y1=y2;a2=a+r*(b-a);y2=f(a2);elseb=a2;a2=a1;y2=y1;a1=b-r*(b-a);y1=f(a1);n+;while(fabs(b-a)/b)=e|fabs(y2-y1)/y2)=e);A=(a+b)/2;Y=f(A);printf(n%da=%f,b=%f,a1=%f,a2=%f,n,a,b,a1,a2);printf(n结果:
n极值点及其函数值:
A=%f,Y=%fn,A,Y);二、二次插值法#includestdio.h#includemath.h#includeconio.hvoidmain()float*area(floata1,floatp,floata3);floatf(floatx);floatar,fr;floata1=10,p=0.01,e=0.000001;floatpa3;area(a1,p,pa);a1=pa0;floata2=pa1;floata3=pa2;floatf1=f(a1);floatf2=f(a2);floatf3=f(a3);doar=(a3*a3-a2*a2)*f1+(a1*a1-a3*a3)*f2+(a2*a2-a1*a1)*f3);ar=ar/2/(a3-a2)*f1+(a1-a3)*f2+(a2-a1)*f3);fr=f(ar);if(ara2)if(frf2)a3=ar;f3=fr;elseif(frf2)a1=a2;f1=f2;a2=ar;f2=fr;elsea3=ar;a1=a2;a2=(a1+a3)/2;f1=f2;f3=fr;f2=f(a2);elseif(arf2)a1=ar;f1=fr;elseif(frf2)a3=a2;f3=f2;a2=ar;f2=fr;elsea1=ar;a3=a2;a2=(a1+a3)/2;f1=fr;f3=f2;f2=f(a2);if(fabs(a1-a3)=e)break;while
(1);if(f2=f1)if(fabs(f2-f1)acc)p=p/2;elsep=-p;elsebreak;while
(1)a3=a2+p;f3=f(a3);if(f2a3)temp=a1;a1=a3;a3=temp;a0=a1;a1=a2;a2=a3;returna;floatf(floatx)floaty=pow(fabs(x-1),1.5)+pow(fabs(x-1),2.7);returny;三、最速下降法#include#includefloatfun1(floatx1,floatx2)floata;a=2*x1;returna;floatfun2(floatx1,floatx2)floatb;b=50*x2;returnb;floatfun3(floatx1,floatx2)floaty;y=x1*x1+25*x2*x2;returny;main()floatt,e=0.01,x1=0,x2=1,a,b,y,m;a=fun1(x1,x2);b=fun2(x1,x2);m=sqrt(a*a+b*b);while(me)t=(a*a+b*b)/(2*a*a+50*b*b);x1=x1-a*t;x2=x2-b*t;a=fun1(x1,x2);b=fun2(x1,x2);m=sqrt(a*a+b*b);y=fun3(x1,x2);printf(Theminis%f,y);四、DFP变尺度法#include#include#include#include#definett0.01#defineff1.0e-6#defineac1.0e-6#definead1.0e-6#definen2doubleia;doublefny(double*x)doublex1=x0,x2=x1;doublef;f=x1*x1+2*x2*x2-4*x1-2*x1*x2;returnf;double*iterate(double*x,doublea,double*s)double*x1;inti;x1=(double*)malloc(n*sizeof(double);for(i=0;in;i+)x1i=xi+a*si;returnx1;doublefunc(double*x,doublea,double*s)double*x1;doublef;x1=iterate(x,a,s);f=fny(x1);returnf;voidfinding(doublea3,doublef3,double*xk,double*s)doublet=tt;inti;doublea1,f1;a0=0;f0=func(xk,a0,s);for(i=0;i+)a1=a0+t;f1=func(xk,a1,s);if(f1=ad)t=-t;a0=a1;f0=f1;elseif(ia=1)return;/breakt=t/2;ia=1;for(i=0;i+)a2=a1+t;f2=func(xk,a2,s);if(f2f1)break;t=2*t;a0=a1;f0=f1;a1=a2;f1=f2;if(a0a2)a1=a0;f1=f0;a0=a2;f0=f2;a2=a1;f2=f1;return;doublelagrange(double*xk,double*ft,double*s)inti;doublea3,f3;doubleb,c,d,aa;finding(a,f,xk,s);for(i=0;i+)if(ia=1)aa=a1;*ft=f1;break;d=(pow(a0,2)-pow(a2,2)*(a0-a1)-(pow(a0,2)-pow(a1,2)*(a0-a2);if(fabs(d)=0)break;c=(f0-f2)*(a0-a1)-(f0-f1)*(a0-a2)/d;if(fabs(c)=0)break;b=(f0-f1)-c*(pow(a0,2)-pow(a1,2)/(a0-a1);aa=-b/(2*c);*ft=func(xk,aa,s);if(fabs(aa-a1)f1)aa=a1;break;if(aaa1)if(*ftf1)a2=aa;f2=*ft;elseif(*ftf1)a0=aa;f0=*ft;elseif(*ftf1)*ft=f1;aa=a1;returnaa;double*gradient(double*xk)double*g,f1,f2,q;inti;g=(double*)malloc(n*sizeof(double);f1=fny(xk);for(i=0;in;i+)q=ff;xki=xki+q;f2=fny(xk);gi=(f2-f1)/q;xki=xki-q;returng;double*bfgs(double*xk)doubleun,vn,hnn,dxn,dgn,sn;doubleaa,ib;double*ft,*xk1,*g1,*g2,*xx,*x0=xk;doublefi;inti,j,k;ft=(double*)malloc(sizeof(double);xk1=(double*)malloc(n*sizeof(double);for(i=0;in;i+)si=0;for(j=0;jn;j+)hij=0;if(j=i)hij=1;g1=gradient(xk);fi=fny(xk);x0=xk;for(k=0;kn;k+)ib=0;if(ia=1)xx=xk;break;ib=0;for(i=0;in;i+)si=0;for(i=0;in;i+)for(j=0;jn;j+)si+=-hij*g1j;aa=lagrange(xk,ft,s);xk1=iterate(xk,aa,s);g2=gradient(xk1);for(i=0;i=ac)&(fabs(g2i-g1i)=ac)ib=ib+1;if(ib=0)xx=xk1;break;fi=*ft;if(k=n-1)intj;xk=xk1;for(i=0;in;i+)for(j=0;jn;j+)hij=0;if(j=i)hij=1;g1=g2;k=-1;elseintj;doublea1=0,a2=0;for(i=0;in;i+)dgi=g2i-g1i;dxi=xk1i-xki;for(i=0;in;i+)intj;ui=0;vi=0;for(j=0;jn;j+)ui=ui+dgj*hji;vi=vi+dgj*hij;for(j=0;jn;j+)a1+=dxj*dgj;a2+=vj*dgj;if(fabs(a1)!
=0)a2=1+a2/a1;for(i=0;in;i+)for(j=0;jfi)*ft=fi;xx=xk;xk=x0;returnxx;voidmain()intk;double*xx,f;doublexkn=1,1;xx=bfgs(xk);f=fny(xx);printf(nnTheOptimalDesignResultIs:
n);for(k=0;kn;k+)printf(ntx%d*=%f,k+1,xxk);printf(ntf*=%f,f);getch();五、鲍威尔法#includestdio.h#includestdlib.h#includemath.hdoubleobjf(doublex)doubleff;ff=x0*x0+2*x1*x1-4*x0-2*x0*x1;return(ff);voidjtf(doublex0,doubleh0,doubles,intn,doublea,doubleb)inti;double*x3,h,f1,f2,f3;for(i=0;i3;i+)xi=(double*)malloc(n*sizeof(double);h=h0;for(i=0;in;i+)*(x0+i)=x0i;f1=objf(x0);for(i=0;i=f1)h=-h0;for(i=0;in;i+)*(x2+i)=*(x0+i);f3=f1;for(i=0;in;i+)*(x0+i)=*(x1+i);*(x1+i)=*(x2+i);f1=f2;f2=f3;for(;)h=2.*h;for(i=0;in;i+)*(x2+i)=*(x1+i)+h*si;f3=objf(x2);if(f2f3)break;elsefor(i=0;in;i+)*(x0+i)=*(x1+i);*(x1+i)=*(x2+i);f1=f2;f2=f3;if(h0.)for(i=0;in;i+)ai=*(x2+i);bi=*(x0+i);elsefor(i=0;in;i+)ai=*(x0+i);bi=*(x2+i);for(i=0;i3;i+)free(xi);doublegold(doublea,doubleb,doubleeps,intn,doublexx)inti;doublef1,f2,*x2,ff,q,w;for(i=0;i2;i+)xi=(double*)malloc(n*sizeof(double);for(i=0;if2)for(i=0;in;i+)bi=*(x0+i);*(x0+i)=*(x1+i);f1=f2;for(i=0;in;i+)*(x1+i)=ai+0.382*(bi-ai);f2=objf(x1);elsefor(i=0;in;i+)ai=*(x1+i);*(x1+i)=*(x0+i);f2=f1;for(i=0;in;i+)*(x0+i)=ai+0.618*(bi-ai);f1=objf(x0);q=0;for(i=0;ieps);for(i=0;in;i+)xxi=0.5*(ai+bi);ff=objf(xx);for(i=0;i2;i+)free(xi);return(ff);doubleoneoptim(doublex0,doubles,doubleh0,doubleepsg,intn,doublex)double*a,*b,ff;a=(double*)malloc(n*sizeof(double);b=(double*)malloc(n*sizeof(double);jtf(x0,h0,s,n,a,b);ff=gold(a,b,epsg,n,x);free(a);free(b);return(ff);doublepowell(doublep,doubleh0,doubleeps,doubleepsg,intn,doublex)inti,j,m;double*xx4,*ss,*s;doublef,f0,f1,f2,f3,fx,dlt,df,sdx,q,d;ss=(double*)malloc(n*(n+1)*sizeof(double);s=(double*)malloc(n*sizeof(double);for(i=0;in;i+)for(j=0;j=n;j+)*(ss+i*(n+1)+j)=0;*(ss+i*(n+1)+i)=1;for(i=0;i4;i+)xxi=(double*)malloc(n*sizeof(double);for(i=0;in;i+)*(xx0+i)=pi;for(;)for(i=0;in;i+)*(xx1+i)=*(xx0+i);xi=*(xx1+i);f0=f1=objf(x);dlt=-1;for(j=0;jn;j+)for(i=0;idlt)dlt=df;m=j;sdx=0.;for(i=0;in;i+)sdx=sdx+fabs(xi-(*(xx1+i);if(sdxeps)free(ss);free(s);for(i=0;i4;i+)free(xxi);return(f);for(i=0;in;i+)*(xx2+i)=xi;f2=f;for(i=0;in;i+)*(xx3+i)=2.*(*(xx2+i)-(*(xx1+i);xi=*(xx3+i);fx=objf(x);f3=fx;q=(f1-2*f2+f3)*(f1-f2-dlt)*(f1-f2-dlt);d=0.5*dlt*(f1-f3)*(f1-f3);if(f3f1)|(qd)if(f2=f3)for(i=0;in;i+)*(xx0+i)=*(xx2+i);elsefor(i=0;in;i+)*(xx0+i)=*(xx3+i);elsefor(i=0;in;i+)*(ss+(i+1)*(n+1)=xi-(*(xx1+i);*(s+i)=*(ss+(i+1)*(n+1);f=oneoptim(xx0,s,h0,epsg,n,x);for(i=0;in;i+)*(xx0+i)=xi;for(j=m+1;j=n;j+)for(i=0;in;i+)*(ss+i*(n+1)+j-1)=*(ss+i*(n+1)+j);voidmain()doublep=1,1;doubleff,x2;ff=powell(p,0.3,0.001,0.0001,2,x);printf(输出最优点及其目标函数值:
n);printf(x0=%f,x1=%f,ff=%f,x0,x1,ff);
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