机械优化设计黄金分割法 外推法.docx

1、机械优化设计黄金分割法 外推法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 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;x3=x2+h;y3

2、=fun(x3);while(y3y2)h*=;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=,fun=,fun=2.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+60 double hj(double *a,double *b,double e,int *n) double x1,x2,s; if(fabs(*b-*a)/(*b

3、)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); 运行过程及结果：输入a，b值和精度e值-35a=,b=,s=,m=,n=213.二次插值法源程序：#include#includeint main

4、(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=; double f(double 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=*(a1+a3-c1/c2); yp=f(ap); if(fabs(y2-yp)/y2)0) i

5、f(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; elsea1=ap;y1=yp; double x,y; if(y2y0) 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

6、结果：a*=y*=4.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(%f%

7、f,&x01,&x02); e=; l=; x21=x01; x22=x02; k=0; k-; do x01=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); do a1=a2; y1=y2; a2=a3; y2=y3; a3=a2+h; xi1=fun1(xi-11,di1,a3); xi2=fun1(xi-12,di2,a3); y3

8、=fun2(xi1,xi2); 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(

9、xi-11,di1,a2); xi2=fun1(xi-12,di2,a2); y2=fun2(xi1,xi2); else b=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); 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); xi1=fun1(xi-11,di1,a2); xi2=fun1(xi-12,di2,a2); y

10、2=fun2(xi1,xi2); else b=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); axki=*(a+b); xi1=fun1(xi-11,di1,axki); xi2=fun1(xi-12,di2,axki); while(sqrt(pow(x21-x01),2)+pow(x22-x02),2)=1e-6); xx1=x21; xx2=x22; fi=fun2(xx1,xx2);printf(最优解为nx1*=%fnx2*=%fnf*

11、=%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*=x2*=f*=k=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;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

12、=8,c=,a0=-3,b0=3,a1=-3,b1=3; float x10,x010,xl10,e10,r10,d10,h,fl,f0,fx; while(g1(x00,x01)0|g2(x00,x01)0) x00=a0+(rand()/*(b0-a0); x01=a1+(rand()/*(b1-a1); fl=f(x00,x01); f0=f(x00,x01); while(1) h=; j=1; r0=-1+(rand()/*(1-(-1); r1=-1+(rand()/*(1-(-1); e0=r0/sqrt(r0*r0+r1*r1); e1=r1/sqrt(r0*r0+r1*r1)

13、; x0=x00+h*e0; x1=x01+h*e1; if(g1(x0,x1)=0&g2(x0,x1)=0) fx=f(x0,x1); if(fxfl) fl=fx; for(i=0;i2;i+) di=ei;xli=xi; while(j=k) j+; r0=-1+(rand()/*(1-(-1); r1=-1+(rand()/*(1-(-1); e0=r0/sqrt(r0*r0+r1*r1); e1=r1/sqrt(r0*r0+r1*r1); x0=x00+h*e0; x1=x01+h*e1; if(g1(x0,x1)=0&g2(x0,x1)=0) fx=f(x0,x1); if(fxf

14、l) fl=fx; for(i=0;i0|g2(x0,x1)0) break; fx=f(x0,x1); if(fxfl) fl=fx; else break; do x0=x0-h*d0; x1=x1-h*d1; h=*h; if(h0|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; else break; 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*=,x2*

15、=,y*=6.四杆机构优化设计源程序：#include#include#include#define Pai int 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*l1*l2-16=0) &(36-l1*l1-l2*l1*l2=0) return (1); else return (0);float fun(float x02) floatf, a31,b31,r31,p31,q31,w31,x12; int i; p0=acos(1+x00)*(1+x00)-x

16、01*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*Pai); f=f+(Pai/60)*(qi-wi)*(qi-wi)*(pi-pi-1); return f;v

17、oid main() float a,q,f,fl,f0,l2,z2,d0100,d1100,x2,xi2,fx,m0,m1,e; int i,j,n,k; printf(输入精度); scanf(%f,&e); doz0=0+5*(rand()/; z1=0+5*(rand()/; while(g(z0,z1)=0); for(i=0;i=99;i+) d0i=-1+2*(rand()/; for(j=0;j=99;j+) d1j=-1+2*(rand()/; f0=fun(z); fl=fun(z);ss: a=; for(i=0,j=0;i=99&j=99;i+,j+) n=1/sqrt

18、(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; x0=l0;x1=l1;doa=*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); do x0=x0-a*m0; x1=x1-a*m1; a=*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); else f0=f; fl=f; z0=x0; z1=x1; goto ss; 运行过程及结果：输入精度最优解为x1*=x2*=fx=