questions regarding the use of A* with the 15-square puzzle

Question

I\'m trying to build an A* solver for a 15-square puzzle.

The goal is to re-arrange the tiles so that they appear in their natural positions. You can only sli

Answer 1

What I learned

• apparently this is well-known, but it wasn't to me: the A* convergence is very sensitive to the heuristic function.
• if I write a heuristic that weights the top 2 rows more heavily than other rows, it converges much more quickly, but the path is generally much longer.
• I found the diagonal H(x) function shown here to converge much more quickly than the Manhattan distance, for the 15-square puzzle.
• even with the heuristic function that encourages speedier convergence, there is wide variance in the run time. Sometimes it finds the path in 10 seconds. Sometimes 10 minutes. Sometimes longer.
• The number of moves required in the paths found, using the diagonal heuristic, ranges from 30-ish to 110.

Answer 2

check this
import javax.swing.*; 
import java.awt.*;
import java.awt.event.*;
import java.lang.Object;

class Puzzle extends JPanel implements ActionListener
{
    JButton[] b = new JButton[16];
    Puzzle()
    {
        b[0] = new JButton("4");
        b[1] = new JButton("11");
        b[2] = new JButton("5");
        b[3] = new JButton("9");
        b[4] = new JButton("1");
        b[5] = new JButton("10");
        b[6] = new JButton("12");
        b[7] = new JButton("13");
        b[8] = new JButton("15");
        b[9] = new JButton("14");
        b[10] = new JButton("3");
        b[11] = new JButton("2"); 
        b[12] = new JButton("7");
        b[13] = new JButton("8");
        b[14] = new JButton("6");
        b[15] = new JButton("");
        GridLayout grid = new GridLayout(4,4);
        setLayout(grid);
        for(int i=0;i<16;i++)
            add(b[i]);
        for(int i=0;i<16;i++)
            b[i].addActionListener(this);
    }
    public void actionPerformed(ActionEvent e)
    {
        /*if(e.getSource()==b[11])
        {
            if(b[15].getText()=="")
            {
                b[15].setText("");
            }
        }
        else if(e.getSource()==b[3])
        {
            if(b[2].getText()=="")
            {
                b[2].setText("");
            }
        }*/
        for(int i=0;i<16;i++)
        {
            System.out.println(e.getSource());
            if(e.getSource()==b[i])
            {
                if(i==5 || i==6 || i==9 || i==10)
                {   
                    if(b[i-1].getText()=="")
                    {
                        b[i-1].setText(b[i].getText());
                        b[i].setText("");
                    }
                    else if(b[i+1].getText()=="")
                    {
                        b[i+1].setText(b[i].getText());
                        b[i].setText("");
                    }
                    else if(b[i-4].getText()=="")
                    {
                        b[i-4].setText(b[i].getText());
                        b[i].setText("");
                    }
                    else if(b[i+4].getText()=="")
                    {
                        b[i+4].setText(b[i].getText());
                        b[i].setText("");
                    }
                }
                else if(i==4 || i==8)
                {   
                    if(b[i+1].getText()=="")
                    {
                        b[i+1].setText(b[i].getText());
                        b[i].setText("");
                    }
                    else if(b[i-4].getText()=="")
                    {
                        b[i-4].setText(b[i].getText());
                        b[i].setText("");
                    }
                    else if(b[i+4].getText()=="")
                    {
                        b[i+4].setText(b[i].getText());
                        b[i].setText("");
                    }
                }
                else if(i==7 || i==11)
                {   
                    if(b[i-1].getText()=="")
                    {
                        b[i-1].setText(b[i].getText());
                        b[i].setText("");
                    }
                    else if(b[i-4].getText()=="")
                    {
                        b[i-4].setText(b[i].getText());
                        b[i].setText("");
                    }
                    else if(b[i+4].getText()=="")
                    {
                        b[i+4].setText(b[i].getText());
                        b[i].setText("");
                    }
                }
                if(i==0)
                {   
                    if(b[i+1].getText()=="")
                    {
                        b[i+1].setText(b[i].getText());
                        b[i].setText("");
                    }
                    else if(b[i+4].getText()=="")
                    {
                        b[i+4].setText(b[i].getText());
                        b[i].setText("");
                    }
                }
                if(i==3)
                {   
                    if(b[i-1].getText()=="")
                    {
                        b[i-1].setText(b[i].getText());
                        b[i].setText("");
                    }
                    else if(b[i+4].getText()=="")
                    {
                        b[i+4].setText(b[i].getText());
                        b[i].setText("");
                    }
                }
                if(i==15)
                {   
                    if(b[i-1].getText()=="")
                    {
                        b[i-1].setText(b[i].getText());
                        b[i].setText("");
                    }
                    else if(b[i-4].getText()=="")
                    {
                        b[i-4].setText(b[i].getText());
                        b[i].setText("");
                    }
                    else if(b[i+4].getText()=="")
                    {
                        b[i+4].setText(b[i].getText());
                        b[i].setText("");
                    }
                }
                if(i==12)
                {   
                    if(b[i+1].getText()=="")
                    {
                        b[i+1].setText(b[i].getText());
                        b[i].setText("");
                    }
                    else if(b[i-4].getText()=="")
                    {
                        b[i-4].setText(b[i].getText());
                        b[i].setText("");
                    }
                }
                if(i==1 || i==2)
                {   
                    if(b[i+1].getText()=="")
                    {
                        b[i+1].setText(b[i].getText());
                        b[i].setText("");
                    }
                    else if(b[i-1].getText()=="")
                    {
                        b[i-1].setText(b[i].getText());
                        b[i].setText("");
                    }                   
                    else if(b[i+4].getText()=="")
                    {
                        b[i+4].setText(b[i].getText());
                        b[i].setText("");
                    }
                }
                if(i==13 || i==14)
                {   
                    if(b[i+1].getText()=="")
                    {
                        b[i+1].setText(b[i].getText());
                        b[i].setText("");
                    }
                    else if(b[i-1].getText()=="")
                    {
                        b[i-1].setText(b[i].getText());
                        b[i].setText("");
                    }                   
                    else if(b[i-4].getText()=="")
                    {
                        b[i-4].setText(b[i].getText());
                        b[i].setText("");
                    }
                }
            }
        }
        //System.out.println(e.getActionCommand());
        }

    public static void main(String[] args)
    {
        JFrame frame = new JFrame("15-Puzzle");             

        //frame.setContentPane(panel);

JComponent newContentPane = new Puzzle();
        //newContentPane.setOpaque(true); //content panes must be opaque
        frame.setContentPane(newContentPane);





        //panel.add(button);  
        frame.setSize(400,400);


        frame.setVisible(true);
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    }
}

Answer 3

I have programmed such an algorithm once (windowsApp) and I have the following experience

1) it is most fun to see the robot in action if it uses an (near) optimal solution. (For the human observer it is impossible to understand how the robot "thinks" and the transaction from chaos to order is sudden)

2) if you like to find the optimal solution your h() function must underestimate true distance. If you overestimate it you will not find the optimum.

3) The potential state-space is huge, 15!/2 (10^12). If you use a bad heuristic function your data sets will grow far beyond the size of your main-memory and every data access will require multiple disc-accesses. If this happens the execution time will be "infinite".

Answer 4

Maybe it will converge quicker if you shoot for intermediate goals first. For instance, only score the top and right rows. It shouldn't take very long to get those rows in place, then you can solve the remaining 3x3.

Answer 5

Use IDA* instead of A*. You need much less memory. As a heuristics, the "Walking distance" developed by Ken'ichiro Takahashi is much more effective, though using only 25 kB of memory.
Here and here is English translation.

Answer 6

Yes, that's how I've heard of this problem being done. g(x) is the number of tile slides that have taken place, and h(x) is the total distance that all tiles are from their required squares. I hadn't seen anything used but this approach (the Manhattan heuristic) before today, but just found this so-called diagonal shortcut -- you might want to check it out.