爬山算法

爬山算法
一.实验目的
通过上机实现爬山算法，了解并掌握爬山搜索算法的内涵。

通过动态演示搜索全过程深刻理解该算法。

二. 实验内容与要求
用爬山法求f(x,y)=1/(x 2+y 2+2)的最大值，设计出具体的程序，使之能够动态演示爬山搜索过程。

三．参考算法
1. 给定初值x (0)及精度ε，若||▽f(x (0))||2≤ε则x (0)
即为近似极小值 2222121||||,),,()(n T n
x x x X x f x f X f +++=∂∂∂∂=∇ 2．若||▽f(x (0)
)||2>ε，用适当步长0λ按下式计算 )()0(0)0()1(X f X X ∇-=λ
3．一般，若||▽f(x (k))||2≤ε，则x (k)
为近似极小值，否则用适当步长k λ确定下一个近似值，直到满足精度为止。

)()()()1(k k k k X f X X ∇-=+λ
四．源代码
import java.awt.*;
import java.awt.event.*;
import javax.swing.*;
public class hill
{
/**
* Creates a new instance of <code>Newton</code>.
*/
public hill() {
}
/**
* @param args the command line arguments
*/
public static void main(String[] arg)
{
new newFrame().init();
}
}
class newFrame extends JFrame
{
public void init()
{
MyPanel hello=new MyPanel();
getContentPane().add(hello);
hello.thread.start();
//以下代码设置JFrame窗体的外观
setSize(400,400);
setLocation(200,200);
setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
setVisible(true);
}
}
class MyPanel extends JPanel implements Runnable
{
Thread thread;
double xpoint[],ypoint[];
double z,step=0.5,e=0.00001;
double x=-3.0,y=-3.0;
int hh=0,k=1;
public MyPanel()
{
xpoint=new double[145];
ypoint=new double[145];
setSize(500, 500);
thread=new Thread(this);
}
double f(double x,double y)
{
return(1.0/(x*x+y*y+2));
}
double fx(double x,double y)
{
return(-2.0*x/((x*x+y*y+2)*(x*x+y*y+2)));
}
double fy(double x,double y)
{
return(-2.0*y/((x*x+y*y+2)*(x*x+y*y+2)));
}
double fxy2(double x,double y)
{
return((4*(x*x+y*y))/((x*x+y*y+2)*(x*x+y*y+2)*(x*x+y*y+2)*(x*x+y*y+2))); }
public void run()
{
z=f(x,y);
repaint();
xpoint[0]=x;
ypoint[0]=z;
try
{
thread.sleep(500);
}
catch(InterruptedException e)
{
}
while(fxy2(x,y)>e)
{
x = x + step * fx(x, y);
y = y + step * fy(x, y);
z = f(x,y);
xpoint[k]=x;
ypoint[k]=z;
k++;
repaint();
try
{
thread.sleep(50);
}
catch(InterruptedException e)
{
}
}
hh=1;
repaint();
}
public void paintComponent(Graphics g)
{
g.setColor(Color.white);
g.clearRect(0, 0, 400, 440);
//画坐标轴
g.setColor(Color.red);
g.drawLine(0, 300, 400, 300); //x轴
g.drawLine(200, 400, 200, 0); //y轴
g.translate(200,300);
g.setColor(Color.blue);
//g.drawLine((int)(x*60),-(int)(z*200),0,-(int)(z*200));
g.fillOval((int)(x*60-2),-(int)(z*200+2),4,4);
if(hh==1)
{
for(int i=0;i<144;i++)
{
g.drawLine((int)(xpoint[i]*60),-(int)(ypoint[i]*200),(int)(xpoint[i+1]*60),-(int)(ypoint[i+1]* 200));
}
g.setColor(Color.red);
g.drawLine(0,0,0,-200);
g.setColor(Color.black);
g.drawString("发现极值：x="+x,-180,-280);
g.drawString("y="+y,-180,-260);
g.drawString("f(x,y)="+z,-180,-240);
}
}
}
五．运行结果截图。