機械優(yōu)化設計黃金分割法-外推法

1、鄭州大學機械優(yōu)化設計部分程序1.外推法2.黃金分割法3.二次插值法4.坐標輪換法5.隨機方向法6.四桿機構優(yōu)化設計1.外推法源程序：#include#include#define R 0.01double 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=fun(x3);whi

2、le(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);運行過程及結果：fun(2.560000)=16.953600,fun(5.120000)=11.014400,fun(10.240000)=38.4576002.黃金分割法源程序：#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,dou

3、ble 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(輸入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); 運行過程及結果：輸入a,b值和精度e值-350.0

4、001a=3.279466,b=3.279793,s=22.659008,m=3.279629,n=213.二次插值法源程序：#include#includeint 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(double x); y1=f(a1); y2=f(a2); y3=f(a3); for(i=1;1=1;i+) c1=(y3-y1)/

5、(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; 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;

6、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;運行過程及結果：a*=5.000000y*=11.0000004.坐標輪換法源程序：#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; m

7、ain() float d1003,x1003,xx3,ax1003; float a1,a2,a3,h,t,y1,y2,y3,e,a,b,l,fi; int i,k; printf(輸入初始點坐標n); scanf(%f%f,&x01,&x02); e=0.000001; l=0.618; 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=fun

8、1(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); 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

9、=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); y2=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

10、-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=fun1(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,di

11、2,axki); while(sqrt(pow(x21-x01),2)+pow(x22-x02),2)=1e-6); xx1=x21; xx2=x22; fi=fun2(xx1,xx2);printf(最優(yōu)解為nx1*=%fnx2*=%fnf*=%fnk=%dn,xx1,xx2,fi,k); 運行過程及結果：輸入初始點坐標89最優(yōu)解為x1*=5.000000x2*=6.000000f*=0.000000k=25.隨機方向法源程序：#include#include#includefloat f(float x,float y) float z; z=(x-2)*(x-2)+(y-1)*(y-1)

12、; 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 x10,x010,xl10,e10,r10,d10,h,fl,f0,fx; while(g1(x00,x01)0|g2(x00,x01)0) x00=a0+(rand()/32767.00)*(b0-a0); x01=a1+

13、(rand()/32767.00)*(b1-a1); fl=f(x00,x01);f0=f(x00,x01); while(1) h=0.01; j=1; r0=-1+(rand()/32767.00)*(1-(-1); r1=-1+(rand()/32767.00)*(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(fxfl) fl=fx; for(i=0;i2;i+)di=ei;xli

14、=xi; while(j=k) j+; r0=-1+(rand()/32767.00)*(1-(-1); r1=-1+(rand()/32767.00)*(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(fxfl) 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

15、*d0; x1=x1-h*d1; h=0.7*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(輸出最優(yōu)解為nx1*=%f,x2*=%f,y*=%fn,x0,x1,fx);運行過程及結果：輸出最優(yōu)解為x1*=0.995421,x2*=1.004521,y*=1.0092006.四桿機構優(yōu)化設計源程序：#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-