机械优化设计外推法 黄金分割法 二次插值法 随机方向法 坐标轮换法 四杆机构.doc

《机械优化设计》上机源程序与结果—
《机械优化设计》上机源程序与结果
4
第 8 页 共 8 页

程序一：外推法
源程序：
#include
#include
#define B 0.001
double fun(double x)
{ double min;
min=x*x-10*x+36;
return min;
}
void main()
{
double h0=B,y1,y2,y3,x1,x2,x3,h;
x1=0;h=h0;x2=h;
y1=fun(x1);y2=fun(x2);
if(y2>y1)
{h=-h;
x3=x1; x1=x2; x2=x3;
y3=y1; y1=y2; y2=y3;
}
x3=x2+h;y3=fun(x3);
while(y39513)=13.720895

程序二：黄金分割法
源程序：
#include
#include
#define f(x) x*x-10*x+36

double gi(double *a,double *b,double e,int *n)
{
double x1,x2,min;
if(fabs((*b-*a)/(*b))<=e)
min=f((*b+*a)/2);
else
{
x1=*b-0.618*(*b-*a);
x2=*a+0.618*(*b-*a)
if(f(x1)>f(x2))
*a=x1;
else
*b=x2;
*n=*n+1;
min=gi(a,b,e,n);
}
return min;
}
void main()
{
double min,a,b,e,m;
int n=0;
printf("输入搜索区间a，b值和精度e\n");
scanf("%lf %lf %lf",&a,&b,&e);
min=gi(&a,&b,e,&n);
m=(a+b)/2;
printf("a=%lf,b=%lf,min=%lf,m=%lf,n=%d\n",a,b,min,m,n);
}
Press any key to continue
运行过程及结果：
a*=5.000000
y*=11.000000
程序三：二次插值法
源程序：
#include
#include
float f(float x)
{ float min;
min=x*x-10*x+36;
return min;
}
void main()
{float e=0.001,c1,c2,ap,yp,ay;
float h0=0.03,h=h0,a1=0,a2=h,y1,y2,a3,y3;
y1=f(a1);
y2=f(a2);
if(y2>y1)
{
h=-h;a3=a1;y3=y1;
a1=a2;y1=y2;a2=a3;y2=y3;
}
a3=a2+h;y3=f(a3);
while(y3a1);
y2=f(a2);
y3=f(a3);
c1=(y3-y1)/(a3-a1);
c2=((y2-y1)/(a2-a1)-c1)/(a2-a3);
ap=0.5*(a1+a3-c1/c2);
yp=f(ap);
while(abs((y2-yp)/y2)>=e)
{if((ap-a2)*h>0){if(y2>=yp){a1=a2;y1=y2;a2=ap;y2=yp;}
else{a3=ap;y3=yp;}}
else{if(y2>=yp){a3=a2;y3=y2;a2=ap;y2=yp;}
else{a1=ap;y1=yp;}}
}
if(y2
#include
#include io.h>

float fun1(float x,float a,float b)
{float y;
y=x+a*b;
return y;
}
float fun2(float x,float y)
{float z;
z=4*(x-5)*(x-5)+(y-6)*(y-6);
return z;
}
main()
{float d[100][3],x[100][3],xx[3],ax[100][3];
float a1,a2,a3,h,t,y1,y2,y3,e,a,b,l,fi;
int i,k;
printf("输入初始点坐标\n");
scanf("%f%f",&x[0][1],&x[0][2]);
e=0.000001;
l=0.618;
x[2][1]=x[0][1];
x[2][2]=x[0][2];
k=0;
k--;
do
{x[0][1]=x[2][1];
x[0][2]=x[2][2];
k++;

for(i=1;i<=2;i++)
{
if(i==1)
{d[i][1]=1;
d[i][2]=0;
}

else
{d[i][1]=0;
d[i][2]=1;
}

h=0.1;
a1=0;
a2=h;
x[i][1]=fun1(x[i-1][1],d[i][1],a1);
x[i][2]=fun1(x[i-1][2],d[i][2],a1);
y1=fun2(x[i][1],x[i][2]);
x[i][1]=fun1(x[i-1][1],d[i][1],a2);
x[i][2]=fun1(x[i-1][2],d[i][2],a2);
y2=fun2(x[i][1],x[i][2]);

if(y2>y1)
{h=-h;
a3=a1;
y3=y1;
a1=a2;
a2=a3;
y1=y2;
y2=y3;
}
a3=a2+h;
x[i][1]=fun1(x[i-1][1],d[i][1],a3);
x[i][2]=fun1(x[i-1][2],d[i][2],a3);
y3=fun2(x[i][1],x[i][2]);
do
{a1=a2;
y1=y2;
a2=a3;
y2=y3;
a3=a2+h;
x[i][1]=fun1(x[i-1][1],d[i][1],a3);
x[i][2]=fun1(x[i-1][2],d[i][2],a3);
y3=fun2(x[i][1],x[i][2]);
}
while(y3a3;)
{t=a3;
a3=a1;
a1=t;
t=y1;
y3=y1;
y1=t;
}
a=a1;
b=a3;
a1=b-l*(b-a);
a2=a+l*(b-a);
x[i][1]=fun1(x[i-1][1],d[i][1],a1);
x[i][2]=fun1(x[i-1][2],d[i][2],a1);
y1=fun2(x[i][1],x[i][2]);
x[i][1]=fun1(x[i-1][1],d[i][1],a2);
x[i][2]=fun1(x[i-1][2],d[i][2],a2);
y2=fun2(x[i][1],x[i][2]);
if(b<1e-3)
{
for(;fabs(b-a)>e;)
{
if(y1>=y2)
{a=a1;
a1=a2;
y1=y2;

a2=a+l*(b-a);
x[i][1]=fun1(x[i-1][1],d[i][1],a2);
x[i][2]=fun1(x[i-1][2],d[i][2],a2);
y2=fun2(x[i][1],x[i][2]);
}
else
{b=a2;
a2=a1;
y2=y1;
a1=b-l*(b-a);
x[i][1]=fun1(x[i-1][1],d[i][1],a1);
x[i][2]=fun1(x[i-1][2],d[i][2],a1);
y1=fun2(x[i][1],x[i][2]);
}
}
}
else
{
for(;fabs((b-a)/b)>=e||fabs((y2-y1)/y2)>=e;)
{
if(y1>=y2)
{a=a1;
a1=a2;
y1=y2;
a2=a+l*(b-a);
x[i][1]=fun1(x[i-1][1],d[i][1],a2);
x[i][2]=fun1(x[i-1][2],d[i][2],a2);
y2=fun2(x[i][1],x[i][2]);
}
else
{b=a2;
a2=a1;
y2=y1;
a1=b-l*(b-a);
x[i][1]=fun1(x[i-1][1],d[i][1],a1);
x[i][2]=fun1(x[i-1][2],d[i][2],a1);
y1=fun2(x[i][1],x[i][2]);
}
}
}
ax[k][i]=0.5*(a+b);
x[i][1]=fun1(x[i-1][1],d[i][1],ax[k][i]);
x[i][2]=fun1(x[i-1][2],d[i][2],ax[k][i]);

}
}
while(sqrt(pow((x[2][1]-x[0][1]),2)+pow((x[2][2]-x[0][2]),2))>=1e-6);
xx[1]=x[2][1];
xx[2]=x[2][2];
fi=fun2(xx[1],xx[2]);
printf("最优解为\nx1*=%f\nx2*=%f\nf*=%f\nk=%d\n",xx[1],xx[2],fi,k);

}
运行过程及结果：
输入初始点坐标
1 9
最优解为
x1*=5.000000
x2*=6.000000
f*=0.000000
k=2
Press any key to continue
程序五：随机方向法
源程序：
#include
#include
#include
float f(float x,float y)
{
float z;
z=(x-2)*(x-2)+(y-1)*(y-1);
return z;
}
float g1(float x,float y)
{
float z;
z=x*x-y;
return z;
}
float g2(float x,float y)
{
float z;
z=x+y-2;
return z;
}
void main()
{
int i,j;
float k=8,c=0.000001,a0=-3,b0=3,a1=-3,b1=3;
float x[10],x0[10],xl[10],e[10],r[10],d[10],h,fl,f0,fx;

while(g1(x0[0],x0[1])>0||g2(x0[0],x0[1])>0)
{
x0[0]=a0+(rand()/32767.00)*(b0-a0);
x0[1]=a1+(rand()/32767.00)*(b1-a1);
}
fl=f(x0[0],x0[1]);
f0=f(x0[0],x0[1]);
while(1)
{
h=0.01;
j=1;
r[0]=-1+(rand()/32767.00)*(1-(-1));
r[1]=-1+(rand()/32767.00)1-(-1));
e[0]=r[0]/sqrt(r[0]*r[0]+r[1]*r[1]);
e[1]=r[1]/sqrt(r[0]*r[0]+r[1]*r[1]);
x[0]=x0[0]+h*e[0];
x[1]=x0[1]+h*e[1];
if(g1(x[0],x[1])<=0&&g2(x[0],x[1])<=0)
{
fx=f(x[0],x[1]);
if(fx fl=fx;
for(i=0;i<2;i++)
{d[i]=e[i];xl[i]=x[i];}
}
}
while(j<=k)
{
j++;
r[0]=-1+(rand()/32767.00)*(1-(-1));
r[1]=-1+(rand()/32767.00)*(1-(-1));
e[0]=r[0]/sqrt(r[0]*r[0]+r[1]*r[1]);
e[1]=r[1]/sqrt(r[0]*r[0]+r[1]*r[1]);
x[0]=x0[0]+h*e[0];
x[1]=x0[1]+h*e[1];
if(g1(x[0],x[1])<=0&&g2(x[0],x[1])<=0)
{
fx=f(x[0],x[1]);
if(fx
{d[i]=e[i];xl[i]=x[i];}
}
}
}
x[0]=xl[0];
x[1]=xl[1];
while(1)
{
h=1.3*h;
x[0]=x[0]+h*d[0];
x[1]=x[1]+h*d[1];
if(g1(x[0],x[1])>0||g2(x[0],x[1])>0)
break;
fx=f(x[0],x[1]);
if(fx if(g1(x[0],x[1])>0||g2(x[0],x[1])>0)
continue;
fx=f(x[0],x[1]);
}
while(fx>=fl);
if(fabs((f0-fx)/f0)>=c)
{
x0[0]=x[0];
x0[1]=x[1];
fl=fx;
f0=fx;
}
else
break;
}
printf("输出最优解为\nx1*=%f,x2*=%f,y*=%f\n",x[0],x[1],fx);
}
输出最优解为
x1*=0.995421,x2*=1.004521,y*=1.009200
Press any key to continue
程序六：四杆机构
源程序：
#include
#include
#include
#define Pai 3.1415926
int g(float l1,float l2)
{
if((1-l1<=0)
&&(1-l2<=0)
&&(6-l1-l2<=0)
&&(1-l2-4<=0)
&&(l2-l1-4<=0)
&&(l1*l1+l2*l2-1.414*l1*l2-16<=0)
&&(36-l1*l1-l2*l2-1.414*l1*l2<=0))
return (1);
else
return (0);
}
float fun(float x0[2])
{
float f,a[31],b[31],r[31],p[31],q[31],w[31],x1[2];
int i;
p[0]=acos(((1+x0[0])*(1+x0[0])-x0[1]*x0[1]+25)/(10+10*x0[0]));
q[0]=acos(((1+x0[0])*(1+x0[0])-x0[1]*x0[1]-25)/(10*x0[1]));
f=0;
for(i=1;i<=30;i++)
{
p[i]=p[0]+(Pai/60)*i;
r[i]=sqrt(26-10*cos(p[i]));
a[i]=acos((r[i]*r[i]+x0[1]*x0[1]-x0[0]*x0[0])/(2*r[i]*x0[1]));
b[i]=acos((r[i]*r[i]+24)/(10*r[i]));
q[i]=Pai-a[i]-b[i];
w[i]=q[0]+(2p[i]-p[0])*(p[i]-p[0]))/(3*Pai);
f=f+(Pai/60)*(q[i]-w[i])*(q[i]-w[i])*(p[i]-p[i-1]);
}
return f;
}
void main()
{

float a,q,f,fl,f0,l[2],z[2],d0[100],d1[100],x[2],xi[2],fx,m0,m1,e;
int i,j,n,k;
printf("请输入收敛精度e：");
scanf("%f",&e);
do
{
z[0]=0+5*(rand()/32767.00);
z[1]=0+5*(rand()/32767.00);
}
while(g(z[0],z[1])==0);
for(i=0;i<=99;i++)
{
d0[i]=-1+2*(rand()/32767.00);
}
for(j=0;j<=99;j++)
{
d1[j]=-1+2*(rand()/32767.00);
}
f0=fun(z);
fl=fun(z);
ss:
a=0.01;
for(i=0,j=0;i<=99&&j<=99;i++,j++)
{n=1/sqrt((d0[i])*(d0[i])+d1[j]*d1[j]);
d0[i]=d0[i]/sqrt((d0[i])*(d0[i])+d1[j]*d1[j]);
d1[j]=d1[j]/sqrt((d0[i])*(d0[i])+d1[j]*d1[j]);
x[0]=z[0]+a*d0[i];
x[1]=z[1]+a*d1[j];
if(g(x[0],x[1])==1)
{
f=fun(x);
if(f
x[0]=l[0];
x[1]=l[1];
do
{
a=1.3*a;
x[0]=x[0]+a*m0;
x[1]=x[1]+a*m1;
if(g(z[0],z[1])==0)
break;
f=fun(x);
if(f0]=x[0]+a*m0;
x[1]=x[1]+a*m1;
if(g(z[0],z[1])==1)
f=fun(x);
}
while(f>=fl);
if(fabs((f0-f)/f0)