机械优化设计黄金分割法外推法

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1、郑州大学机械优化设计部分程序1. 外推法2. 黄金分割法3. 二次插值法4. 坐标轮换法5. 随机方向法6. 四杆机构优化设计1. 外推法源程序：#include #include #define R 0.01 double fun(double x) double m;m=x*x-10*x+36; return m;void main()double h0=R,y1,y2,y3,x1,x2,x3,h; x1=0;h=h0;x2=h; y1=fun(x1);y2=fun(x2);if(y2y1) h=-h; x3=x1; y3=y1; x1=x2; y1=y2; x2=x3; y2=y3; x

2、3=x2+h;y3=fun(x3); while(y3y2) h*=2.0; x1=x2; y1=y2; x2=x3; y2=y3; x3=x2+h; y3=fun(x3); printf(fun(%f)=%f,fun(%f)=%f,fun(%f)=%fn,x1,y1,x2,y2,x3,y3); 运行过程及结果： fun(2.560000)=16.953600, fun(5.120000)=11.014400, fun(10.240000)=38.4576002. 黄金分割法源程序：#include#include#define f(x) x*x*x*x-5*x*x*x+4*x*x-6*x+6

3、0double hj(double *a,double *b,double e,int *n)double x1,x2,s;if(fabs(*b-*a)/(*b)f(x2)*a=x1;else*b=x2;*n=*n+1;s=hj(a,b,e,n);return s;void main()double s,a,b,e,m;int n=0;printf(输入a, b值和精度e值n);scanf(%lf %lf %lf,&a,&b,&e);s=hj(&a,&b,e,&n);m=(a+b)/2;printf(a=%lf,b=%lf,s=%lf,m=%lf,n=%dn,a,b,s,m,n);运行过程及结

4、果：输入a, b值和精度e值a2=ap;y2=yp;-3elsea1=ap;y1=yp;50.0001double x,y;a=3.279466,b=3.279793,s=22.659008,m=3.279if(y2=yp)629,n=213. 二次插值法源程序：#include #include int main(void)double a1,a2,a3,ap,y1,y2,y3,yp,c1,c2,m; double j3;int i,h=1;void finding(double a3); finding(j);a1=j0;a2=j1;a3=j2; m=0.001;double f(doub

5、le x);y1=f(a1);y2=f(a2);y3=f(a3); for(i=1;1=1;i+) c1=(y3-y1)/(a3-a1); c2=(y2-y1)/(a2-a1)-c1)/(a2-a3); ap=0.5*(a1+a3-c1/c2);yp=f(ap); if(fabs(y2-yp)/y2)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;x=a2;y=y2;elsex=ap;y=yp;printf(a*=%fn,x); printf(y*=%fn,y);return 0;

6、double f(double x)double y; y=x*x-10*x+36; return y;void finding(double a3)int h,i;double y3;a0=0;h=1;a1=h;y0=f(a0);y1=f(a1); if(y1y0)h=-h;a2=a0;y2=y0;do a0=a1;a1=a2; y0=y1;y1=y2; a2=a1+h;y2=f(a2);h=2*h;while(y2=1;i+) a2=a1+h;y2=f(a2); if(y2=y1)break;h=2*h;a0=a1;y0=y1; a1=a2;y1=y2;return;运行过程及结果：a*=

7、5.000000y*=11.0000004. 坐标轮换法源程序：#include #include #include 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 d1003,x1003,xx3,ax1003;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(%

8、f%f,&x01,&x02); e=0.000001;l=0.618;x21=x01;x22=x02;k=0;k-;dox01=x21;x02=x22;k+;for(i=1;iy1)h=-h;a3=a1;y3=y1;a1=a2;a2=a3;y1=y2;y2=y3;a3=a2+h;xi1=fun1(xi-11,di1,a3);xi2=fun1(xi-12,di2,a3);y3=fun2(xi1,xi2);doa1=a2;y1=y2;a2=a3;y2=y3;a3=a2+h;xi1=fun1(xi-11,di1,a3);xi2=fun1(xi-12,di2,a3);y3=fun2(xi1,xi2);

9、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);xi1=fun1(xi-11,di1,a1);xi2=fun1(xi-12,di2,a1);y1=fun2(xi1,xi2);xi1=fun1(xi-11,di1,a2);xi2=fun1(xi-12,di2,a2);y2=fun2(xi1,xi2);if(be;)if(y1=y2)a=a1;a1=a2;y1=y2;a2=a+l*(b-a);xi1=fun1(xi-11,di1,a2);xi2=fun1(xi-12,di2,a2); y

10、2=fun2(xi1,xi2);elseb=a2;a2=a1;y2=y1;a1=b-l*(b-a);xi1=fun1(xi-11,di1,a1);xi2=fun1(xi-12,di2,a1);y1=fun2(xi1,xi2);elsefor(;fabs(b-a)/b)=e|fabs(y2-y1)/y2)=e;)if(y1=y2)a=a1;a1=a2;y1=y2;a2=a+l*(b-a);xi1=fun1(xi-11,di1,a2);xi2=fun1(xi-12,di2,a2);y2=fun2(xi1,xi2);elseb=a2;a2=a1;y2=y1;a1=b-l*(b-a); xi1=fun

11、1(xi-11,di1,a1); xi2=fun1(xi-12,di2,a1); y1=fun2(xi1,xi2);axki=0.5*(a+b);xi1=fun1(xi-11,di1,axki);xi2=fun1(xi-12,di2,axki);while(sqrt(pow(x21-x01),2)+pow(x2 2-x02),2)=1e-6);xx1=x21;xx2=x22;fi=fun2(xx1,xx2);printf( 最优解为 nx1*=%fnx2*=%fnf*=%fnk=%dn,xx1,xx2,fi,k);运行过程及结果：输入初始点坐标89最优解为x1*=5.000000x2*=6.0

12、00000f*=0.000000k=25. 随机方向法源程序：#include#include#includefloat f(float x,float y)float z;z=(x-2)*(x-2)+(y-1)*(y-1);return z;while(j=k)float g1(float x,float y)j+;float z;z=x*x-y;r0=-1+(rand()/32767.00)*(1-(-1);return z;r1=-1+(rand()/32767.00)*(1-(-1);float g2(float x,float y)e0=r0/sqrt(r0*r0+r1*r1);fl

13、oat z;z=x+y-2;e1=r1/sqrt(r0*r0+r1*r1);return z;x0=x00+h*e0;x1=x01+h*e1;void main()if(g1(x0,x1)=0&g2(x0,x1)=0)int i,j;floatfx=f(x0,x1);k=8,c=0.000001,a0=-3,b0=3,a1=-3,b1=3;if(fxfl)floatx10,x010,xl10,e10,r10,d10,h,fl,f0,fx;fl=fx;for(i=0;i0|g2(x00,x01)0) x00=a0+(rand()/32767.00)*(b0-a0);x01=a1+(rand()/

14、32767.00)*(b1-a1);x0=xl0;x1=xl1;fl=f(x00,x01);while(1)f0=f(x00,x01);while(1)h=1.3*h;x0=x0+h*d0;h=0.01;j=1;x1=x1+h*d1;r0=-1+(rand()/32767.00)*(1-(-1);if(g1(x0,x1)0|g2(x0,x1)0)r1=-1+(rand()/32767.00)*(1-(-1);break;e0=r0/sqrt(r0*r0+r1*r1);fx=f(x0,x1);e1=r1/sqrt(r0*r0+r1*r1);if(fxfl) fl=fx;x0=x00+h*e0;e

15、lse break;x1=x01+h*e1; doif(g1(x0,x1)=0&g2(x0,x1)=0)x0=x0-h*d0;fx=f(x0,x1);x1=x1-h*d1;if(fxfl)h=0.7*h;if(hc)fl=fx;break;for(i=0;i0|g2(x0,x1)0) continue;fx=f(x0,x1);while(fx=fl); if(fabs(f0-fx)/f0)=c) x00=x0;x01=x1;fl=fx;f0=fx;elsebreak;printf( 输出最优解为 nx1*=%f,x2*=%f,y*=%fn,x0,x1,fx);运行过程及结果：输出最优解为x1*

16、=0.995421,x2*=1.004521,y*=1.0092006. 四杆机构优化设计源程序：#include#include#include#define Pai 3.1415926int g(float l1,float l2)if(-l1=0)&(-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);elsereturn (0);float fun(float x02)floatf,a31,b31,r31,p

17、31,q31,w31,x12;int i;p0=acos(1+x00)*(1+x00)-x01*x01+25)/(10+10*x00);q0=acos(1+x00)*(1+x00)-x01*x01-25)/(10*x01);f=0;for(i=1;i=30;i+)pi=p0+(Pai/60)*i; ri=sqrt(26-10*cos(pi);ai=acos(ri*ri+x01*x01-x00*x00)/(2*ri*x01); bi=acos(ri*ri+24)/(10*ri); qi=Pai-ai-bi;wi=q0+(2*(pi-p0)*(pi-p0)/(3*P ai);f=f+(Pai/60

18、)*(qi-wi)*(qi-wi)*(pi-pi-1);return f;void main()floata,q,f,fl,f0,l2,z2,d0100,d1100,x2,xi2,f x,m0,m1,e;int i,j,n,k;printf(输入精度);scanf(%f,&e);doz0=0+5*(rand()/32767.00); z1=0+5*(rand()/32767.00);while(g(z0,z1)=0);for(i=0;i=99;i+)d0i=-1+2*(rand()/32767.00);for(j=0;j=99;j+) d1j=-1+2*(rand()/32767.00);f0

19、=fun(z);fl=fun(z);ss:a=0.01;for(i=0,j=0;i=99&j=99;i+,j+)n=1/sqrt(d0i)*(d0i)+d1j*d1j);d0i=n*d0i;d1j=n*d1j;x0=z0+a*d0i;x1=z1+a*d1j; if(g(x0,x1)=1) f=fun(x);if(ffl)fl=f;m0=d0i;m1=d1j;l0=x0;l1=x1;elsef0=f; fl=f; z0=x0; z1=x1; goto ss; 运行过程及结果： 输入精度 0.001 最优解为 x1*=4.161386 x2*=2.311257fx=0.000021x0=l0;x1=l1;doa=1.3*a;x0=x0+a*m0;x1=x1+a*m1;if(g(z0,z1)=0)break;f=fun(x);if(ffl) fl=f; else break; while(g(z0,z1)=1); dox0=x0-a*m0; x1=x1-a*m1; a=0.7*a; if(a=fl);if(fabs(f0-f)/f0)e) xi0=x0;xi1=x1; fx=f;printf( 最优解为 nx1*=%fnx2*=%fnfx=%fn,xi0,xi1,fx);