黄金分割法-机械优化设计程序

#include"stdio.h"

#include"stdlib.h"

#include"math.h"

double objf(double x[])

{double ff;

ff=x[0]*x[0]+x[1]*x[1]-x[0]*x[1]-10*x[0]-4*x[1]+60;

return(ff);

}

double gold(double a[],double b[],double eps,int n,double xx[]) {int i;

double f1,f2,*x[2],ff,q,w;

for(i=0;i<2;i++)

x[i]=(double*)malloc(n*sizeof(double));

for(i=0;i

{*(x[0]+i)=a[i]+0.618*(b[i]-a[i]);

*(x[1]+i)=a[i]+0.382*(b[i]-a[i]);

}

f1=objf(x[0]);

f2=objf(x[1]);

do

{if(f1>f2)

{for(i=0;i

{b[i]=*(x[0]+i);

*(x[0]+i)=*(x[1]+i);

}

f1=f2;

for(i=0;i

*(x[1]+i)=a[i]+0.382*(b[i]-a[i]);

f2=objf(x[1]);

}

else

{for(i=0;i

{a[i]=*(x[1]+i);

*(x[1]+i)=*(x[0]+i);}

f2=f1;

for(i=0;i

*(x[0]+i)=a[i]+0.618*(b[i]-a[i]);

f1=objf(x[0]);

}

q=0;

for(i=0;i

q=q+(b[i]-a[i])*(b[i]-a[i]);

w=sqrt(q);

}while(w>eps);

for(i=0;i

xx[i]=0.5*(a[i]+b[i]);

ff=objf(xx);

for(i=0;i<2;i++)

free(x[i]);

return(ff);

}

void jtf(double x0[],double h0,double s[],int n,double a[],double b[]) {int i;

double*x[3],h,f1,f2,f3;

for(i=0;i<3;i++)

x[i]=(double*)malloc(n*sizeof(double));

h=h0;

for(i=0;i

*(x[0]+i)=x0[i];

f1=objf(x[0]);

for(i=0;i

*(x[1]+i)=*(x[0]+i)+h*s[i];

f2=objf(x[1]);

if(f2>=f1)

{h=-h0;

for(i=0;i

*(x[2]+i)=*(x[0]+i);

f3=f1;

for(i=0;i

{*(x[0]+i)=*(x[1]+i);

*(x[1]+i)=*(x[2]+i);

}

f1=f2;

f2=f3;

}

for(;;)

{h=2*h;

for(i=0;i

*(x[2]+i)=*(x[1]+i)+h*s[i];

f3=objf(x[2]);

if(f2

else

{for(i=0;i

{*(x[0]+i)=*(x[1]+i);

*(x[1]+i)=*(x[2]+i);

}

f1=f2;

f2=f3;

}

}

if(h<0)

for(i=0;i

{a[i]=*(x[2]+i);

b[i]=*(x[0]+i);

}

else

for(i=0;i

{a[i]=*(x[0]+i);

b[i]=*(x[2]+i);

}

for(i=0;i<3;i++)

free(x[i]);

}

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,double eps,double epsg,int n,double x[]) {int i,j,m;

double*xx[4],*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

{for(j=0;j<=n;j++)

*(ss+i*(n+1)+j)=0;

*(ss+i*(n+1)+i)=1;

}

for(i=0;i<4;i++)

xx[i]=(double*)malloc(n*sizeof(double));

for(i=0;i

*(xx[0]+i)=p[i];

for(;;)

{for(i=0;i

{*(xx[1]+i)=*(xx[0]+i);

x[i]=*(xx[1]+i);

}

f0=f1=objf(x);

dlt=-1;

for(j=0;j

{for(i=0;i

{*(xx[0]+i)=x[i];

*(s+i)=*(ss+i*(n+1)+j);

}

f=oneoptim(xx[0],s,h0,epsg,n,x);

df=f0-f;

if(df>dlt)

{dlt=df;

m=j;

}

}

sdx=0;

for(i=0;i

sdx=sdx+fabs(x[i]-(*(xx[1]+i)));

if(sdx

{free(ss);