机械优化设计黄金分割法外推法.pdf

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1、1/8 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 2/8 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;x3=x2

2、+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)=38.457600 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(doubl

3、e*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);3/8 运行过程及结果：输入 a，b 值和精度

4、 e 值-3 5 0.0001 a=3.279466,b=3.279793,s=22.659008,m=3.279629,n=21 3.二次插值法 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(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;while(y2=1;i+)a2=a1+

6、h;y2=f(a2);if(y2=y1)break;4/8 h=2*h;a0=a1;y0=y1;a1=a2;y1=y2;return;运行过程及结果：a*=5.000000 y*=11.000000 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,ax1

7、003;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,&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=fun1(xi-12,di2,a3);y3=fun2(xi1,xi2);do a1=a2;y1=y2;a2=a3;y

8、2=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;5/8 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=y

9、2)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);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);x

10、i2=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);axki=0.5*(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*=

11、%fnx2*=%fn f*=%fnk=%dn,xx1,xx2,fi,k);运行过程及结果：输入初始点坐标 8 9 最优解为 x1*=5.000000 x2*=6.000000 f*=0.000000 k=2 5.随机方向法 源程序：6/8#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-

12、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+(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+(

13、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=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

14、);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 7/8 x0=x0-h*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(输出最

15、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*=0.995421,x2*=1.004521,y*=1.009200 6.四杆机构优化设计 源程序：#include#include#include#define Pai 3.1415926 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*l2-1.414*l1*l2-16=0)&(36-l1*l1-l2*l2-1.414*l1*l2=0)return(1);els

16、e return(0);float fun(float x02)floatf,a31,b31,r31,p31,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

17、-bi;wi=q0+(2*(pi-p0)*(pi-p0)/(3*Pai);f=f+(Pai/60)*(qi-wi)*(qi-wi)*(pi-pi-1);return f;void 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()/32767.00);z1=0+5*(rand()/32767.00);while(g(z0,z1)=0);for(i=0;i=99;i+)8/8 d0i=-1+2*(rand()/32767

18、.00);for(j=0;j=99;j+)d1j=-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(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;do a=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);do x0=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*=%fn fx=%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 0.001 最优解为 x1*=4.161386 x2*=2.311257 fx=0.000021