机械优化设计黄金分割法外推法

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fun(10.240000)=38.4576001.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;

2、 y1=y2; x2=x3; y2=y3; x3=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)=11.014400,2.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+60dou

3、ble 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);else if(y2

4、=yp) a3=a2;y3=y2; a2=ap;y2=yp;elsea1=ap;y1=yp; double x,y; if(y2=yp)x=a2;y=y2;elsex=ap;y=yp;prin tf(a*=%fn,x); prin tf(y*=%fn,y);运行过程及结果：输入a, b值和精度e值-350.0001a=3.279466,b=3.279793,s=22.659008,m=3.279629, n=213二次插值法源程序：#i nclude#in cludeint main(v oid)double a1,a2,a3,ap,y1,y2,y3,yp,c1,c2,m;double j3;

5、int i,h=1;void findin g(double a3);fin di ng(j);a1=j0;a2=j1;a3=j2;m=0.001;double f(double x);y仁 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)a仁 a2;y1=y2;a2=ap;y2=yp;elsea3=ap;y3=yp;return 0;double

6、 f(double x)double y;y=x*x-10*x+36;return y;void findin g(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;doa0=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*=5.00000

7、0y*=11.0000004坐标轮换法源程序：#i nclude #in elude #in elude vconi o.hfloat fun 1(float x,float afloat b)float y;y=x+a*b;return y;float fun 2(float x,float y)float z;z=4*(x-5)*(x-5)+(y-6)*(y-6);return 乙mai n()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);scan

8、 f(%f%f, &x01, &x02); e=0.000001;1=0.618;x21=x01;x22=x02;k=0;k-;dox01=x21;x02=x22;k+;for(i=1;iyi)h=-h;a3=a1;y3=y1;a仁 a2;a2=a3;y仁 y2;y2=y3;a3=a2+h;xi1=fu n1(xi-11,di1,a3);xi2=fu n1(xi-12,di2,a3); y3=fu n2(xi1,xi2);doa仁 a2;y1=y2;a2=a3;y2=y3;a3=a2+h;xi1=fu n1(xi-11,di1,a3); xi2=fu n1(xi-12,di2,a3); y3=

9、fu n2(xi1,xi2);while(y3a3;)t=a3;a3=a1;a1=t;t=y1;y3=y1;yi=t;a=a1;b=a3;a仁 b-l*(b-a);a2=a+l*(b-a);xi1=fu n1(xi-11,di1,a1);xi2=fu n1(xi-12,di2,a1); y1=fu n2(xi1,xi2);xi1=fu n1(xi-11,di1,a2);xi2=fu n1(xi-12,di2,a2);y2=fu n2(xi1,xi2); if(be;) if(y1=y2) a=a1;a1=a2;y1=y2; a2=a+l*(b-a);xi1=fu n1(xi-11,di1,a2

10、); xi2=fu n1(xi-12,di2,a2); y2=fu n2(xi1,xi2);elseb=a2;a2=a1;y2=y1;a仁 b-l*(b-a);xi1=fu n1(xi-11,di1,a1);xi2=fu n1(xi-12,di2,a1);y仁fun 2(xi1,xi2);elsefor(;fabs(b-a)/b)=e|fabs(y2-y1)/y2)=e; )if(y1=y2)a=a1;a仁 a2;y仁 y2;a2=a+l*(b-a);xi1=fu n1(xi-11,di1,a2);xi2=fu n1(xi-12,di2,a2);y2=fun 2(xi1,xi2);elseb=

11、a2;a2=a1;y2=y1;a仁 b-l*(b-a);xi1=fu n1(xi-11,di1,a1);xi2=fu n1(xi-12,di2,a1);y仁fun 2(xi1,xi2);axki=0.5*(a+b);xi1=fu n1(xi-11,di1,axki);xi2=fu n1(xi-12,di2,axki);while(sqrt(pow(x21-x01),2)+pow(x22-x02),2)=1e-6);xx1=x21;xx2=x22;fi=fu n2(xx1,xx2);printf(最优解为 nx1*=%fnx2*=%fnf*=%fnk=%dn,xx1,xx2,fi,k);运行过程

12、及结果：输入初始点坐标89最优解为x1*=5.000000x2*=6.000000f*=0.000000k=2源程序:5随机方向法#in clude#i nclude#i ncludefloat f(float x,float y)float 乙z=(x-2)*(x-2)+(y-1)*(y-1);return 乙float g1(float x,float y)float 乙z=x*x-y;return 乙float g2(float x,float y)float 乙z=x+y-2;return 乙void mai n()int i,j;floatk=8,c=0.000001,a0=-3,b

13、0=3,a 1=-3,b 1=3; floatx10,x010,xl10,e10,r10,d10,h,fl,f0,fx;While(g1(x00,x01)0|g2(x00,x01)0)x00=a0+(ra nd()/32767.00)*(b0-a0); x01=a1+(ra nd()/32767.00)*(b1-a1);fl=f(x00,x01);f0=f(x00,x01);while(1)h=0.01;j=1;r0=-1+(ra nd()/32767.00)*(1-(-1);r1=-1+(ra nd()/32767.00)*(1-(-1);e0=r0/sqrt(r0*r0+r1*r1);e1

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

15、,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;dox0=x0-h*d0;x1=x1-h*d1; h=0.7*h;if(h0|g2(x0,x1)0)con ti nue;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

16、结果：输出最优解为x1*=0.995421,x2*=1.004521,y*=1.0092006四杆机构优化设计源程序：#in clude#i nclude#i nclude#define Pai 3.1415926in t g(float l1,float l2)if(-l1=0)&( -I2=0)&( 6-l1-l2=0)&(1-l2-4=0)&(l2-l1-4=0)&(11*11+12*12-1.414*11*12-16=0)&(36-I1*I1-I2*I2-1.414*I1*I2v=0) return (1);elsereturn (0);float fun (float x02)flo

17、atf, a31,b31,r31,p31,q31,w31,x12;int i;p0=acos(1+x00)*(1+x00)-x01*x0 1+25)/(10+10*x00);q0=acos(1+x00)*(1+x00)-x01*x0 1-25)/(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*x0 0)/(2*ri*x01);bi=acos(ri*ri+24)/(10*ri); qi=Pai-ai-bi;wi=q0+(2*(pi-p0)*(pi-p0)/

18、(3*P ai);f=f+(Pai/60)*(qi-wi)*(qi-wi)*(pi-p i-1);return f;void mai n()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);sca nf(%f,&e);doz0=0+5*(ra nd()/32767.00); z1=0+5*(ra nd()/32767.00);while(g(z0,z1)=0);for(i=0;i=99;i+)d0i=-1+2*(ra nd()/32767.00); for(j=0;jv=99;j+) d1j=-1+2*(ra nd()/32767.00);f0=fu n(z); fl=fun( z);ss:a=0.01;for(i=0,j=0;i=99&jv=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(f=fl);if(fabs(f0-f)/f0)e) xi0=x0;xi1=x1; fx=f;printf(最优解为 nx1*=%f