zyh.c

最优化课程中要用到的所有最优化算法

                //////////////////////////////
                //////   最优化      /////////
                //////信号与信息处理 /////////
                //////    刘君       /////////
                //////06020810021009//////////
                //////////////////////////////

//此程序使用0.618法，用于计算目标函数在给定区间和精度的条件下的最小值//

//////////////////////////////////////////////////////
#include <stdio.h>
#include <math.h>
////////other defination//////////////////////////////
#define   BOOL  int

////////the area of calculation///////////////////////
#define   MIN   0        //区间下界
#define   MAX   1        //区间上界
#define   L     0.2      //计算精度
#define   FUN   "exp( -x ) + x*x"

////////the function of destionation////////////////// 
float fun( float x)
{
	float result;
	result = exp( -x ) + x*x;
	return result;
}

////////determine whether the fun is single peak///////
BOOL single_peak( void )
{
	return 1; //还不知道怎样用程序判断一个函数为单峰函数
}

////////the main process function//////////////////////
int fun_MIN( float *a_min, float *b_min )
{
	float a = MIN, b = MAX;
	float ak = a, bk = b;
	float y, u;
	float fun_y, fun_u;
	int   k = 1;

	y = a + 0.382 * ( b - a );
	u = a + 0.618 * ( b - a );

	fun_y = fun( y );
    fun_u = fun( u );
	
	printf( "计算过程如下: \n\n" );
	printf( " k  ak       bk       yk       uk       f(yk)    f(uk)\n\n" );
	

LOOP:
	printf( " %-3d%-9f%-9f%-9f%-9f%-9f%-9f\n",k,ak,bk,y,u,fun_y,fun_u );
	if( ( bk - ak ) <= L )
	{
		*a_min = ak;
		*b_min = bk;
		return k;
	}


	if( fun_y > fun_u )
	{
		ak = y;
		y  = u;
		u  = ak + 0.618*( bk - ak );
		fun_y = fun_u;
		fun_u = fun( u );

		k += 1;
		goto LOOP;
	}
	else
	{
		bk = u;
		u  = y;
		y  = ak + 0.382*( bk - ak );
		fun_u = fun_y;
		fun_y = fun( y );

		k += 1;
		goto LOOP;
	}


}
////////the main funciton/////////////////////////////
int main( void )
{
	BOOL  s_p;
	float a_min, b_min;
	float result;
	float x;
	int   k;
	float min = MIN, max = MAX;
	float l = L;
	
	///////determine whether it is single peak//////////
	s_p = single_peak();
	if( !s_p )
	{
		printf( "输入的不是单峰函数，请重新输入！\n" );
		return 0;
	}
    
	///////stat/////////
	printf( "本题使用0.618法求目标函数最小值\n" );
	printf( "输入的目标函数为: " );
	printf( FUN );
	printf( "\n" );
	printf( "区间为：[ %f, %f]\n", min, max );
	printf( "精度为：L <= %f\n", l );
    
    
	k = fun_MIN( &a_min, &b_min );

    x = ( a_min + b_min ) / 2;

	printf( "\n经过%d次迭代，目标函数最小值是%.3f \n", k, x );

	while(1);
    
	return 1;
		
}