如何实现高效的Alpha-Beta修剪游戏搜索树?

时间:2013-03-25 23:21:54

标签: java android artificial-intelligence game-theory alpha-beta-pruning

我正在尝试了解人工智能以及如何在程序中实现它。最简单的起点可能是简单的游戏(在这种情况下是Tic-Tac-Toe)和游戏搜索树(递归调用;不是实际的数据结构)。 I found this关于该主题的讲座非常有用的视频。

我遇到的问题是对算法的第一次调用需要花费很长时间(大约15秒)才能执行。我已经在整个代码中放置了调试日志输出,似乎它调用了算法的一部分过多次。

以下是为计算机选择最佳移动的方法:

    public Best chooseMove(boolean side, int prevScore, int alpha, int beta){
    Best myBest = new Best(); 
    Best reply;

    if (prevScore == COMPUTER_WIN || prevScore == HUMAN_WIN || prevScore == DRAW){
        myBest.score = prevScore;
        return myBest;
    }

    if (side == COMPUTER){
        myBest.score = alpha;
    }else{
        myBest.score = beta;
    }
    Log.d(TAG, "Alpha: " + alpha + " Beta: " + beta + " prevScore: " + prevScore);
    Move[] moveList = myBest.move.getAllLegalMoves(board);
    for (Move m : moveList){
        String choice;
        if (side == HUMAN){
            choice = playerChoice;
        }else if (side == COMPUTER && playerChoice.equals("X")){
            choice = "O";
        }else{
            choice = "X";
        }
        Log.d(TAG, "Current Move: column- " + m.getColumn() + " row- " + m.getRow());
        int p = makeMove(m, choice, side);
        reply = chooseMove(!side, p, alpha, beta);
        undoMove(m);
        if ((side == COMPUTER) && (reply.score > myBest.score)){
            myBest.move = m;
            myBest.score = reply.score;
            alpha = reply.score;
        }else if((side == HUMAN) && (reply.score < myBest.score)){
            myBest.move = m;
            myBest.score = reply.score;
            beta = reply.score;
        }//end of if-else statement
        if (alpha >= beta) return myBest;
    }//end of for loop
    return myBest;
}

如果点是空的,makeMove方法移动并返回一个值(-1 - 人类获胜,0 - 抽奖,1 - 计算机获胜,-2或2 - 否则)。虽然我认为错误可能在getAllLegalMoves方法中:

    public Move[] getAllLegalMoves(String[][] grid){
    //I'm unsure whether this method really belongs in this class or in the grid class, though, either way it shouldn't matter.
    items = 0;
    moveList = null;
    Move move = new Move();

    for (int i = 0; i < 3; i++){
        for(int j = 0; j < 3; j++){
            Log.d(TAG, "At Column: " + i + " At Row: " + j);
            if(grid[i][j] == null || grid[i][j].equals("")){
                Log.d(TAG, "Is Empty");
                items++;
                if(moveList == null || moveList.length < items){
                    resize();
                }//end of second if statement
                move.setRow(j);
                move.setColumn(i);
                moveList[items - 1] = move;
            }//end of first if statement
        }//end of second loop
    }//end of first loop
    for (int k = 0; k < moveList.length; k++){
        Log.d(TAG, "Count: " + k + " Column: " + moveList[k].getColumn() + " Row: " + moveList[k].getRow());
    }
    return moveList;
}

private void resize(){
    Move[] b = new Move[items];
    for (int i = 0; i < items - 1; i++){
        b[i] = moveList[i];
    }
    moveList = b;
}

总结一下:我的电话是什么,选择最好的举动,花了这么长时间?我错过了什么?有没有更简单的方法来实现此算法?任何帮助或建议将不胜感激,谢谢!

2 个答案:

答案 0 :(得分:7)

具有alpha beta修剪的minimax树应该可视化为树,树的每个节点都是可能的移动,许多转向未来,其子节点可以从中获取所有移动。

为了尽可能快,并保证你只需要前方向移动数量的空间线性,你需要进行深度优先搜索并从一侧进行“扫描”。如果你想象整个树正在构建中,你的程序实际上只会一次构建一个从一个到一个根的单个链,并丢弃它完成的任何部分。

我现在要复制维基百科的伪代码,因为它真的非常简洁明了:

function alphabeta(node, depth, α, β, Player)         
    if  depth = 0 or node is a terminal node
        return score
    if  Player = MaxPlayer
        for each child of node
            α := max(α, alphabeta(child, depth-1, α, β, not(Player) ))     
            if β ≤ α
                break                             (* Beta cut-off *)
        return α
    else
        for each child of node
            β := min(β, alphabeta(child, depth-1, α, β, not(Player) ))     
            if β ≤ α
                break                             (* Alpha cut-off *)
        return β

注意:

- '对于节点的每个子节' - 不是编辑当前板的状态,而是创建一个全新的板,这是应用移动的结果。通过使用不可变对象,您的代码一般来说,它不会容易出错,也更容易推理。

- 要使用此方法,请为当前状态下的每个可能移动调用它,为其提供深度-1,-Afinity为alpha和+ Infinity为beta,它应该从非移动玩家开始转入每个调用 - 返回最高值的调用是最好的调用。

这在概念上非常简单。如果你正确编码,那么你永远不会同时实例化多个(深度)板,你永远不会考虑无意义的分支等等。

答案 1 :(得分:0)

我不会为你描述你的代码,但因为这是一个很好的编码kata我写了一个小的ai tic tac toe:

import java.math.BigDecimal;

public class Board {

    /**
     * -1: opponent
     * 0: empty
     * 1: player
     */
    int[][] cells = new int[3][3];

    /**
     * the best move calculated by eval(), or -1 if no more moves are possible
     */
    int bestX, bestY;

    int winner() {
        // row
        for (int y = 0; y < 3; y++) {
            if (cells[0][y] == cells[1][y] && cells[1][y] == cells[2][y]) {
                if (cells[0][y] != 0) {
                    return cells[0][y];
                }
            }
        }

        // column
        for (int x = 0; x < 3; x++) {
            if (cells[x][0] == cells[x][1] && cells[x][1] == cells[x][2]) {
                if (cells[x][0] != 0) {
                    return cells[x][0];
                }
            }
        }

        // 1st diagonal
        if (cells[0][0] == cells[1][1] && cells[1][1] == cells[2][2]) {
            if (cells[0][0] != 0) {
                return cells[0][0];
            }
        }

        // 2nd diagonal
        if (cells[2][0] == cells[1][1] && cells[1][1] == cells[0][2]) {
            if (cells[2][0] != 0) {
                return cells[2][0];
            }
        }

        return 0; // nobody has won
    }

    /**
     * @return 1 if side wins, 0 for a draw, -1 if opponent wins
     */
    int eval(int side) {
        int winner = winner();
        if (winner != 0) {
            return side * winner;
        } else {
            int bestX = -1;
            int bestY = -1;
            int bestValue = Integer.MIN_VALUE;
        loop:
            for (int y = 0; y < 3; y++) {
                for (int x = 0; x < 3; x++) {
                    if (cells[x][y] == 0) {
                        cells[x][y] = side;
                        int value = -eval(-side);
                        cells[x][y] = 0;

                        if (value > bestValue) {
                            bestValue = value;
                            bestX = x;
                            bestY = y;
                            if (bestValue == 1) {
                                // it won't get any better, we might as well stop thinking
                                break loop;
                            }
                        }
                    }
                }
            }
            this.bestX = bestX;
            this.bestY = bestY;
            if (bestValue == Integer.MIN_VALUE) {
                // there were no moves left, it must be a draw!
                return 0;
            } else {
                return bestValue;
            }
        }
    }

    void move(int side) {
        eval(side);
        if (bestX == -1) {
            return;
        }
        cells[bestX][bestY] = side;
        System.out.println(this);

        int w = winner();
        if (w != 0) {
            System.out.println("Game over!");
        } else {
            move(-side);
        }
    }

    @Override
    public String toString() {
        StringBuilder sb = new StringBuilder();
        char[] c = {'O', ' ', 'X'};
        for (int y = 0; y < 3; y++) {
            for (int x = 0; x < 3; x++) {
                sb.append(c[cells[x][y] + 1]);
            }
            sb.append('\n');
        }
        return sb.toString();
    }

    public static void main(String[] args) {
        long start = System.nanoTime();
        Board b = new Board();
        b.move(1);
        long end = System.nanoTime();
        System.out.println(new BigDecimal(end - start).movePointLeft(9));
    }
}

精明的读者会注意到我不使用alpha / beta截止。不过,在我有点过时的笔记本上,这会在0.015秒内完成游戏......

没有对您的代码进行分析,我无法确定问题是什么。但是,在搜索树中的每个节点上记录每个可能的移动可能与它有关。