机械参考资料优化设计C语言程序

1、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<stdio.h>#include<math.h>#define r 0.618#define f(x) x*x+2*xgolden(float,float,float);main()float a,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(float a,float b,float

2、 e)float y1,y2,a1,a2,A,Y;int n=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)

3、/b)>=e|fabs(y2-y1)/y2)>=e);A=(a+b)/2;Y=f(A);printf("n %d a=%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#include"stdio.h"#include"math.h"#include"conio.h"void main()float*area(float a1,float p,float a3);f

4、loat f(float x);float ar,fr;float a1=10,p=0.01,e=0.000001;float pa3;area(a1,p,pa);a1=pa0;float a2=pa1;float a3=pa2;float f1=f(a1);float f2=f(a2);float f3=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(ar>a2) if(fr>f2) a3=ar;

5、 f3=fr; else if(fr<f2) a1=a2; f1=f2;a2=ar; f2=fr; else a3=ar; a1=a2; a2=(a1+a3)/2;f1=f2; f3=fr; f2=f(a2); else if(ar<a2) if(fr>f2) a1=ar; f1=fr; else if(fr<f2) a3=a2; f3=f2;a2=ar; f2=fr; else a1=ar; a3=a2; a2=(a1+a3)/2; f1=fr; f3=f2; f2=f(a2); if (fabs(a1-a3)<=e) break; while(1);if(f2

6、<fr) ar=a2; fr=f2; printf("nx=%fnf(x*)=%f",ar,fr);float*area(float a1,float p,float a3)float f(float x);float a2,f2,a3,f3,temp;float acc=0.00001;float f1=f(a1);float storep=p;while(1) a2=a1+p; f2=f(a2);if(f2>=f1) if(fabs(f2-f1)<acc) p=p/2;elsep=-p;else break;while(1) a3=a2+p; f3=f

7、(a3);if(f2<=f3) break;p=2*p;a1=a2; f1=f2;a2=a3; f2=f3;if(a1>a3) temp=a1; a1=a3; a3=temp; a0=a1;a1=a2;a2=a3;return a;float f(float x)float y=pow(fabs(x-1),1.5)+pow(fabs(x-1),2.7); return y;三、最速下降法#include <stdio.h>#include <math.h>float fun1(float x1,float x2)float a;a=2*x1;return a

8、;float fun2(float x1,float x2)float b;b=50*x2;return b;float fun3(float x1,float x2)float y;y=x1*x1+25*x2*x2;return y;main() float t, 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(m>e) 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=

9、sqrt(a*a+b*b);y=fun3(x1,x2);printf("The min is %f",y);四、DF陛尺度法#include<stdio.h>#include<stdlib.h>#include<math.h>#include<conio.h>#define tt 0.01#define ff 1.0e-6#define ac 1.0e-6#define ad 1.0e-6#define n 2double ia;double fny(double *x)double x1=x0,x2=x1;double f;

10、f=x1*x1+2*x2*x2-4*x1-2*x1*x2;return f;double * iterate(double *x,double a,double *s)double *x1;int i;x1=(double *)malloc(n*sizeof(double);for(i=0;i<n;i+)x1i=xi+a*si;return x1;double func(double *x,double a,double *s)double *x1;double f;x1=iterate(x,a,s);f=fny(x1);return f;void finding(double a3,d

11、ouble f3,double *xk,double *s)double t=tt;int i;double a1,f1;a0=0;f0=func(xk,a0,s);for(i=0;i+)a1=a0+t;f1=func(xk,a1,s);if(f1<f0) break;if(fabs(f1-f0)>=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(f2>f1) break;t=2*t;a0=a1;f0=f1;a1=a2;f1=f2;

12、if(a0>a2)a1=a0;f1=f0;a0=a2;f0=f2;a2=a1;f2=f1;return;double lagrange(double *xk,double *ft,double *s)int i;double a3,f3;double b,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-

13、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)<=ad) if(*ft>f1) aa=a1;break;if(aa>a1)if(*ft>f1) a2=aa;f2=*ft;else if(*ft<f1) a0=a1;a1=aa;f0=f1;f1=*ft;else if(*ft=f1)a2=aa;a0=a1;f2=*ft;f0=f1;a1=(a0+a2)/2;f1=func(xk

14、,a1,s);elseif(*ft>f1) a0=aa;f0=*ft;else if(*ft<f1) a2=a1;a1=aa;f2=f1;f1=*ft;else if(*ft=f1)a0=aa;a2=a1;f0=*ft;f2=f1;a1=(a0+a2)/2;f1=func(xk,a1,s);if(*ft>f1) *ft=f1;aa=a1;return aa;double *gradient(double *xk)double *g,f1,f2,q;int i;g=(double*)malloc(n*sizeof(double);f1=fny(xk);for(i=0;i<

15、n;i+)q=ff;xki=xki+q; f2=fny(xk);gi=(f2-f1)/q; xki=xki-q;return g;double * bfgs(double *xk)double un,vn,hnn,dxn,dgn,sn;double aa,ib;double *ft,*xk1,*g1,*g2,*xx,*x0=xk;double fi;int i,j,k;ft=(double *)malloc(sizeof(double);xk1=(double *)malloc(n*sizeof(double);for(i=0;i<n;i+)si=0;for(j=0;j<n;j+)

16、hij=0;if(j=i) hij=1;g1=gradient(xk);fi=fny(xk);xO=xk;for(k=0;k<n;k+)(ib=O;if(ia=1) xx=xk; break; ib=O;for(i=0;i<n;i+) si=O;for(i=0;i<n;i+)forQ=0;j<n;j+)si+= -hiU*g1U;aa=lagrange(xk,ft,s);xk1 =iterate(xk,aa,s);g2=gradient(xk1);for(i=0;i<n;i+)if(fabs(g2i)>=ac)&&(fabs(g2i-g1i)

17、>=ac)ib=ib+1;if(ib=O) xx=xk1; break; fi=*ft;if(k=n-1) intj;xk=xk1;for(i=0;i<n;i+)for(j=0;j<n;j+)(hiU=O;ifO=i) hiU=1;g1=g2; k=-1;else(intj;double a1=0,a2=0;for(i=0;i<n;i+)(dgi=g2i-gli;dxi=xk1i-xki;for(i=0;i<n;i+)int j;ui=0;vi=0;for(j=0;j<n;j+)ui=ui+dgj*hji;vi=vi+dgj*hij;for(j=0;j<

18、;n;j+)a1+=dxj*dgj;a2+=vj*dgj;if(fabs(a1)!=0)a2=1+a2/a1;for(i=0;i<n;i+)for(j=0;j<n;j+)hij+=(a2*dxi*dxj-vi*dxj-dxi*uj)/a1;xk=xk1; g1=g2;if(*ft>fi) *ft=fi; xx=xk;xk=x0; return xx;void main ()int k;double *xx,f;double xkn=1,1;xx=bfgs(xk);f=fny(xx);printf("nnThe Optimal Design Result Is:n&q

19、uot;);for(k=0;k<n;k+)printf("ntx%d*=%f",k+1,xxk); printf("ntf*=%f",f);getch();五、鲍威尔法#include "stdio.h"#include "stdlib.h"#include "math.h"double objf(double x)double ff;ff=x0*x0+2*x1*x1-4*x0-2*x0*x1;return(ff);void jtf(double x0 ,double h0,double

20、s ,int n,double a ,double b )int i;double *x3,h,f1,f2,f3;for (i=0;i<3;i+)xi=(double *)malloc (n*sizeof(double);h=h0;for(i=0;i<n;i+)*(x0+i)=x0i;f1=objf(x0);for(i=0;i<n;i+)*(x1+i)=*(x0+i)+h*si;f2=objf(x1);if(f2>=f1)h= -h0;for (i=0;i<n;i+)*(x2+i)=*(x0+i);f3=f1;for(i=0;i<n;i+)*(x0+i)=

21、*(x1+i);*(x1+i)= *(x2+i);f1=f2;f2=f3;for(;)h=2. *h;for(i=0;i<n;i+)*(x2+i)=* (x1+i) +h*si;f3= objf(x2);if(f2<f3)break;else for(i=0;i<n;i+)*(x0+i)= *(x1+i);*(x1+i)= *(x2+i);f1=f2;f2=f3;if(h<0. )for(i=0;i<n;i+)ai=*(x2+i);bi=*(x0+i);elsefor(i=0;i<n;i+)ai=*(x0+i);bi=*(x2+i);for(i=0;i<

22、;3;i+) free(xi); double gold(double a,double b,double eps,int n,double xx) int i;double f1f2,*x2,ff,q,w;for(i=0;i<2;i+)xi=(double*)malloc (n*sizeof(double);for(i=0;i<n;i+)*(x0+i)=ai+0.618*(bi-ai);*(x1+i)=ai+0.382*(bi-ai);f1=objf(x0);f2=objf(x1);doif(f1>f2)for(i=0;i<n;i+)bi=*(x0+i);*(x0+i

23、)=*(x1+i);f1=f2;for(i=0;i<n;i+)*(x1+i)=ai+0.382*(bi-ai);f2=objf(x1);elsefor(i=0;i<n;i+)ai=*(x1+i);*(x1+i)=*(x0+i);f2=f1;for(i=0;i<n;i+)*(x0+i)=ai+0.618*(bi-ai);f1=objf(x0);q=0;for(i=0;i<n;i+)q=q+(bi-ai)*(bi-ai);w=sqrt(q);while(w>eps);for(i=0;i<n;i+)xxi=0.5*(ai+bi);ff=objf(xx);for(i

24、=0;i<2;i+)free(xi);return(ff);double oneoptim(double x0,double s,double h0,double epsg,int n,double x) 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);double powell(double p,double h0,doubl

25、e eps,double epsg,int n,double x)int i,j,m;double *xx4,*ss,*s;double f,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;i<n;i+)for (j=O;j<=n;j+)*(ss+i*(n+1)+j)=0;*(ss+i*(n+1)+i)=1;for (i=0;i<4;i+)xxi=(double *)malloc(n*sizeof(double);for (i=0;i<n;i+)*(xx0+i)=pi;for(;)for (i=0;i<n;i+)*(xx1+i)=*(xx0+i);xi=*(xx1+i);f0=f1=objf(x);dlt=-1;for 0=O;j<n;j+)for (i=0;i<n;i+)*(xx0+i)=xi;*(s+i)=*