Minimax博弈树
1. Minimax博弈树
Minimax Game Trees(简称MGT)是游戏AI中一种很重要的数据结构,用于双方轮流博弈,每次执行一步。MGT是一棵包含了所有可能的执行步骤的树,每个节点可拥有任意数目的子节点。
2. Minimax搜索
Minimax搜索算法是一种找出失败的最大可能性中的最小值的算法,一般以递归方式实现。其假定博弈双方都尽自己的最大努力获得好结果。该算法是零和算法,即一方要选择将其优势最大化的走法,另一方则选择令对手优势最小化的走法,其输赢的总和为零。
3. Alpha-Beta剪枝
预测的步数越多,生成的MGT越庞大,搜索的消耗会很大。为了提高搜索的效率,引入了通过对评估值的上下限进行估计,从而减少需要进行评估的节点的范围的优化,即Alpha-Beta剪枝,它能够快速裁剪掉不必要的搜索分支,从而提高搜索的效率。
下面是Minimax Alpha-Beta剪枝的核心代码:
int minimax(const Node &node, int depth, int min_, int max_)
{
if ( isLeaf(node) || depth == 0 )
{
return evaluate(node);
}
if ( isMaxNode(node) )
{
int score = min_;
for(auto it = node.children.cbegin(); it != node.children.cend(); ++it)
{
int newScore = minimax(*it, depth-1, score, max_);
if(newScore > score) score = newScore;
if(score > max_) return max_;
}
return score;
}
if ( isMinNode(node) )
{
int score = max_;
for(auto it = node.children.cbegin(); it != node.children.cend(); ++it)
{
int newScore = minimax(*it, depth-1, min_, score);
if(newScore < score) score = newScore;
if(score < min_) rturn min_;
}
return score;
}
}
4. 适用场合
MGT最适合完全信息博弈(games of perfect information),即博弈双方能看到博弈的全部信息,比如棋类游戏(国际象棋、五子棋、围棋等)。但是有些游戏,比如扑克,因为一方不能看另一方手上的牌,所以很难判断对手的走法,所以MGT就不怎么适用。
5. 参考文献
题图来自:AI Horizon <AI Horizon: Computer Science and Artificial Intelligence Programming Resources>
AI Horizon: Minimax Game Tree Programming, Part 1
AI Horizon: Minimax Game Tree Programming, Part 2
一年多前的技术文,再发是否考虑适当修改,比如代码等等。技术日新月异,不可能一年毫无变化吧。
谢谢你的建议,这几天忙,有空我更新下,比如加入蒙特卡洛树的介绍
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