机械优化设计C语言程序

1、目录 一、黄金分割法 二、二次插值法 三、最速下降法（阶梯法） 四、变尺度法 五、鲍威尔法 一、黄金分割法 #include #include #define r 0.618 #define f(x) x*x+2*x golden(float,float,float); main() float a,b,e; printf(n 请输入区间和收敛精度 :a,b,en); scanf(%f,%f,%f, golden(a,b,e); golden(float a,float b,float e) float y1,y2,a1,a2,A,Y; int n=0; a1=b-r*(b-a); a2=a+

2、r*(b-a); y1=f(a1); y2=f(a2); printf( 黄金分割法的搜索过程 :); do %d printf(n a=%f,b=%f,a1=%f,a2=%f,y1=%f,y2=%f,n,a,b,a1,a2,y1,y2); if(y1=y2) a=a1; a1=a2; y1=y2; a2=a+r*(b-a); y2=f(a2); else b=a2; a2=a1; y2=y1; a1=b-r*(b-a); y1=f(a1); n+; while(fabs(b-a)/b)=e|fabs(y2-y1)/y2)=e); A=(a+b)/2; Y=f(A); printf(n %d

3、a=%f,b=%f,a1=%f,a2=%f,n,a,b,a1,a2); printf(n 结果:n 极值点及其函数值：A=%f,Y=%fn, A,Y); 二、二次插值法 #includestdio.h #includemath.h #includeconio.h void main() float*area(float a1,float p,float a3); float f(float x); float ar,fr; float a1=10,p=0.01,e=0.000001; float pa3; area(a1,p,pa); a1=pa0; float a2=pa1; float a

4、3=pa2; float f1=f(a1); float f2=f(a2); float f3=f(a3); do ar=(a3*a3-a2*a2)*f1+(a1*a1-a3*a3)*f2+(a2*a2-a1*a1)*f3); ar=ar/2/(a3-a2)*f1+(a1-a3)*f2+(a2-a1)*f3); fr=f(ar); if(ara2) if(frf2) a3=ar; f3=fr; else if(frf2) a1=a2; f1=f2; a2=ar; f2=fr; else a3=ar; a1=a2; a2=(a1+a3)/2; f1=f2; f3=fr; f2=f(a2); el

5、se if(arf2) a1=ar; f1=fr; else if(frf2) a3=a2; f3=f2; a2=ar; f2=fr; else a1=ar; a3=a2; a2=(a1+a3)/2; f1=fr; f3=f2; f2=f(a2); if (fabs(a1-a3)=e) break; while(1); if(f2=f1) if(fabs(f2-f1)acc) p=p/2; else p=-p; else break; while(1) a3=a2+p; f3=f(a3); if(f2a3) temp=a1; a1=a3; a3=temp; a0=a1;a1=a2;a2=a3;

6、 return a; float f(float x) float y=pow(fabs(x-1),1.5)+pow(fabs(x-1),2.7); return y; 三、最速下降法 #include #include float fun1(float x1,float x2) float a; a=2*x1; return a; float fun2(float x1,float x2) float b; b=50*x2; return b; float fun3(float x1,float x2) float y; y=x1*x1+25*x2*x2; return y; main()

7、float t, e=0.01, x1=0, x2=1, a, b, y, m; a=fun1(x1,x2); b=fun2(x1,x2); m=sqrt(a*a+b*b); while(me) t=(a*a+b*b)/(2*a*a+50*b*b); x1=x1-a*t; x2=x2-b*t; a=fun1(x1,x2); b=fun2(x1,x2); m=sqrt(a*a+b*b); y=fun3(x1,x2); printf(The min is %f,y); 四、DFP变尺度法 #include #include #include #include #define tt 0.01 #de

8、fine ff 1.0e-6 #define ac 1.0e-6 #define ad 1.0e-6 #define n 2 double ia; double fny(double *x) double x1=x0,x2=x1; double f; f=x1*x1+2*x2*x2-4*x1-2*x1*x2; return f; double * iterate(double *x,double a,double *s) double *x1; int i; x1=(double *)malloc(n*sizeof(double); for(i=0;in;i+) x1i=xi+a*si; re

9、turn x1; double func(double *x,double a,double *s) double *x1; double f; x1=iterate(x,a,s); f=fny(x1); 5 / 16 return f; void finding(double a3,double f3,double *xk,double *s) double t=tt; int i; double a1,f1; a0=0;f0=func(xk,a0,s); for(i=0;i+) a1=a0+t; f1=func(xk,a1,s); if(f1=ad) t=-t; a0=a1;f0=f1;

10、else if(ia=1) return; /break t=t/2;ia=1; for(i=0;i+) a2=a1+t; f2=func(xk,a2,s); if(f2f1) break; t=2*t; a0=a1;f0=f1; a1=a2;f1=f2; if(a0a2) a1=a0; f1=f0; a0=a2; f0=f2; a2=a1; f2=f1; return; double lagrange(double *xk,double *ft,double *s) int i; double a3,f3; double b,c,d,aa; finding(a,f,xk,s); for(i=

11、0;i+) if(ia=1) aa=a1; *ft=f1; break; d=(pow(a0,2)-pow(a2,2)*(a0-a1)-(pow(a0,2)-pow(a1,2)*(a0-a2); if(fabs(d)=0) break; c=(f0-f2)*(a0-a1)-(f0-f1)*(a0-a2)/d; if(fabs(c)=0) break; b=(f0-f1)-c*(pow(a0,2)-pow(a1,2)/(a0-a1); aa=-b/(2*c); *ft=func(xk,aa,s); if(fabs(aa-a1)f1) aa=a1;break; if(aaa1) if(*ftf1)

12、 a2=aa;f2=*ft; else if(*ftf1) a0=aa;f0=*ft; else if(*ftf1) *ft=f1;aa=a1; return aa; double *gradient(double *xk) double *g,f1,f2,q; int i; g=(double*)malloc(n*sizeof(double); f1=fny(xk); for(i=0;in;i+) q=ff; xki=xki+q; f2=fny(xk); gi=(f2-f1)/q; xki=xki-q; return g; double * bfgs(double *xk) double u

13、n,vn,hnn,dxn,dgn,sn; double aa,ib; double *ft,*xk1,*g1,*g2,*xx,*x0=xk; double fi; int i,j,k; ft=(double *)malloc(sizeof(double); xk1=(double *)malloc(n*sizeof(double); for(i=0;in;i+) si=0; for(j=0;jn;j+) hij=0; if(j=i) hij=1; g1=gradient(xk); 7 / 16 fi=fny(xk); x0=xk; for(k=0;kn;k+) ib=0; if(ia=1) x

14、x=xk; break; ib=0; for(i=0;in;i+) si=0; for(i=0;in;i+) for(j=0;jn;j+) si+= -hij*g1j; aa=lagrange(xk,ft,s); xk1=iterate(xk,aa,s); g2=gradient(xk1); for(i=0;i=ac) if(ib=0) xx=xk1; break; fi=*ft; if(k=n-1) int j; xk=xk1; for(i=0;in;i+) for(j=0;jn;j+) hij=0; if(j=i) hij=1; g1=g2; k=-1; else int j; doubl

15、e a1=0,a2=0; for(i=0;in;i+) dgi=g2i-g1i; dxi=xk1i-xki; for(i=0;in;i+) int j; ui=0;vi=0; for(j=0;jn;j+) ui=ui+dgj*hji; vi=vi+dgj*hij; for(j=0;jn;j+) a1+=dxj*dgj; a2+=vj*dgj; if(fabs(a1)!=0) a2=1+a2/a1; for(i=0;in;i+) for(j=0;jfi) *ft=fi; xx=xk; xk=x0; return xx; void main () int k; double *xx,f; doub

16、le xkn=1,1; xx=bfgs(xk); f=fny(xx); printf(nnThe Optimal Design Result Is:n); for(k=0;kn;k+) printf(ntx%d*=%f,k+1,xxk); printf(ntf*=%f,f); getch(); # / 16 五、鲍威尔法 #include stdio.h #include stdlib.h #include math.h double objf(double x) double ff; ff=x0*x0+2*x1*x1-4*x0-2*x0*x1; return(ff); n,double a

17、,double b ) void jtf(double x0 ,double h0,double s ,int int i; double *x3,h,f1,f2,f3; for (i=0;i3;i+) xi=(double *)malloc (n*sizeof(double); h=h0; for(i=0;in;i+) *(x0+i)=x0i; f1=objf(x0); for(i=0;i=f1) h= -h0; for (i=0;in;i+) *(x2+i)=*(x0+i); f3=f1; for(i=0;in;i+) *(x0+i)= *(x1+i); *(x1+i)= *(x2+i);

18、 f1=f2; f2=f3; for(;) h=2. *h; for(i=0;in;i+) *(x2+i)=* (x1+i) +h*si; f3= objf(x2); if(f2f3) break; else for(i=0;in;i+) *(x0+i)= *(x1+i); *(x1+i)= *(x2+i); f1=f2; f2=f3; if(h0. ) for(i=0;in;i+) ai=*(x2+i); bi=*(x0+i); else for(i=0;in;i+) ai=*(x0+i); bi=*(x2+i); for(i=0;i3;i+) free(xi); double gold(d

19、ouble a,double b,double eps,int n,double xx) int i; double f1,f2,*x2,ff,q,w; for(i=0;i2;i+) xi=(double*)malloc (n*sizeof(double); for(i=0;if2) for(i=0;in;i+) bi=*(x0+i); *(x0+i)=*(x1+i); f1=f2; for(i=0;in;i+) *(x1+i)=ai+0.382*(bi-ai); f2=objf(x1); else for(i=0;in;i+) ai=*(x1+i); *(x1+i)=*(x0+i); f2=

20、f1; for(i=0;in;i+) *(x0+i)=ai+0.618*(bi-ai); f1=objf(x0); q=0; for(i=0;ieps); for(i=0;in;i+) xxi=0.5*(ai+bi); ff=objf(xx); for(i=0;i2;i+) free(xi); return(ff); double oneoptim(double x0,double s,double h0,double epsg,int n,double x) double *a,*b,ff; a=(double *)malloc(n*sizeof(double); b=(double *)m

21、alloc(n*sizeof(double); jtf(x0,h0,s,n,a,b); ff=gold(a,b,epsg,n,x); free(a); free(b); return(ff); double powell(double p,double h0,double eps,double epsg,int n,double x) int i,j,m; double *xx4,*ss,*s; double f,f0,f1,f2,f3,fx,dlt,df,sdx,q,d; ss=(double *)malloc(n*(n+1)*sizeof(double); s=(double *)mall

22、oc(n*sizeof(double); for (i=0;in;i+) 11 / 16 for (j=0;j=n;j+) *(ss+i*(n+1)+j)=0; *(ss+i*(n+1)+i)=1; for (i=0;i4;i+) xxi=(double *)malloc(n*sizeof(double); for (i=0;in;i+) *(xx0+i)=pi; for(;) for (i=0;in;i+) *(xx1+i)=*(xx0+i); xi=*(xx1+i); f0=f1=objf(x); dlt=-1; for (j=0;jn;j+) for (i=0;idlt) dlt=df; m=j; sdx=0.; for (i=0