工程优化一维搜索算法C程序实现

5 抛物线法
#include<stdio.h> #include<stdlib.h> #include<math.h> #include<string.h> #include<time.h> #define F(x) 3*x*x*x-4*x+2 int main(void){ double x1,x2,x3,x; double y1,y2,y3,y;
7 三次插值法
#include<stdio.h> #include<stdlib.h> #include<math.h> #include<string.h> #include<time.h> #define F(x) 3*x*x*x-4*x+2 #define F1(x) 9*x*x-4 int main(void){ double a=0,b,h=1,x; double v,u,s,z,w; time_t start,end; start=clock(); v=F1(a); x=a; while(abs(v)>0.2){ if(v<0){ h=abs(h); } else{ h=-abs(h); } l: b=a+h; u=F1(b); if(abs(u)<0.2){ x=b; goto end; } while(u*v>0){ h=2*h; v=u; a=b; goto l; } s=3*(F(a)-F(b))/(b-a); z=s-u-v; w=sqrt(pow(z,2)-u*v); if(v>0){ a=a-(b-a)*v/(z-w-v);
} else{ a=a-(b-a)*v/(z+w-v); } v=F1(a); h=h/10; x=a; } end:printf("%.3f,%.3f\n",x,F(x)); end=clock(); printf("the time is %.3fm\n",double(end-start)/CLOCKS_PER_SEC); system("pause"); }
8 D.S.C法
#include<stdio.h> #include<stdlib.h> #include<math.h> #include<string.h> #include<time.h> #define F(x) 3*x*x*x-4*x+2 int main(void){ double x0=0,x1,x2,x3,y0,y1,y2,y3,h=1,num,den; time_t start,end; start=clock(); l:y0=F(x0); x1=x0+h; y1=F(x1); if(y0<y1){ h=-h; x1=x0+h; y1=F(x1); } while(y1<y0){ x0=x1; y0=F(x0); x1=x0+h; y1=F(x1); h=h+h;
3 平分法
#include<stdio.h> #include<stdlib.h> #include<math.h> #include<string.h> #include<time.h> #define F(x) 3*x*x*x-4*x+2 #define f(x) 9*x*x-4 int main(void){ double a=0,b=2,c,e; double y,result; time_t start,end; start=clock(); e=b-a; c=(a+b)/2; while(e>0.2){ y=f(c); if(y==0){ goto l; } else if(y>0){ b=c; e=b-a; c=(a+b)/2; } else{ a=c; e=b-a; c=(a+b)/2; } } result=F(c); l:printf("%.3f,%.3f\n",c,result); end=clock(); printf("the time is %.3fm\n",(double(end-start))/CLOCKS_PER_SEC); system("pause"); }
6 简化的抛物线法
#include<stdio.h> #include<stdlib.h> #include<math.h> #include<string.h> #include<time.h> #define F(x) 3*x*x*x-4*x+2 int main(void){ double x1,x2,x3,x; double y1,y2,y3,y; double num,den; time_t start,end; start=clock(); x1=0; x2=1; x3=2; y1=F(x1); y2=F(x2); y3=F(x3); num=(y3-y1)/(x3-x1); den=((y2-y1)/(x2-x1)-num)/(x2-x3); x=0.5*(x1+x3-num/den); y=F(x); while(abs(y-y2)>0.2){ if(x>x2){ x1=x2; x2=x; y1=y2; y2=y; } else if(x<x2){ x3=x2; x2=x; y3=y2; y2=y; } num=(y3-y1)/(x3-x1); den=((y2-y1)/(x2-x1)-num)/(x2-x3); x=0.5*(x1+x3-num/den); y=F(x); } printf("%.3f,%.3f\n",x,y); end=clock(); printf("the time is %.3fm\n",(double(end-start))/CLOCKS_PER_SEC); system("pause"); }
Hale Waihona Puke 1 成功失败法#include<stdio.h> #include<stdlib.h> #include<math.h> #include<time.h> #define F(x) 3*x*x*x-4*x+2 int main(void){ double h=1.0,e=0.2,x=0; double y1,y2,minx,t; time_t start,end; start=clock(); y1=F(x); t=x+h; y2=F(t); l:while(y1>y2){ printf("%.3f,%.3f;%.3f,%.3f;\n",x,y1,x+h,y2); x=x+h; y1=y2; h=2*h; t=x+h; y2=F(t); } if(abs(h)<=e){ minx=x; } else{ h=-h/4; t=x+h; y2=F(t); goto l; } printf("%.3f\n",minx); end=clock(); printf("It takes %.3fm.",(double(end-start))/CLOCKS_PER_SEC); system("pause"); }
2 0.618法
#include<stdio.h>
#include<stdlib.h> #include<math.h> #include<string.h> #include<time.h> #define F(x) 3*x*x*x-4*x+2 int main(void){ double e,a=0,b=2; double x1,x2,y1,y2,minx,miny; time_t start,end; start=clock(); x1=a+0.382*(b-a); x2=a+0.618*(b-a); y1=F(x1); y2=F(x2); e=b-a; while(e>0.2){ if(y1<y2){ b=x2; y2=y1; x2=x1; x1=a+0.382*(b-a); y1=F(x1); } else{ a=x1; x1=x2; y1=y2; x2=a+0.618*(b-a); y2=F(x2); } e=b-a; } minx=(a+b)/2; miny=F(minx); printf("%.3f,%.3f\n",minx,miny); end=clock(); printf("the time is %.3f",(double(end-start))/CLOCKS_PER_SEC); system("pause"); }
} h=h/2; x3=x1; x2=x3-h; x1=x0; x0=x1-h; y3=F(x3); y2=F(x2); y1=F(x1); y0=F(x0); if(y1>y2){ num=(y1-y3)*h; den=2*(y1-2*y2+y3); x0=x2+num/den; if(abs((y1-y3)/y1)>0.1){ h=h/4; goto l; } } else{ num=(y0-y2)*h; den=2*(y0-2*y1+y2); x0=x1+num/den; if(abs((y0-y2)/y0)>0.1){ h=h/4; goto l; } } printf("%.3f,%.3f\n",x0,F(x0)); end=clock(); printf("the time is %.3fm\n",double(end-start)/CLOCKS_PER_SEC); system("pause"); }