基于概率的剪枝算法

以alpha-beta剪枝算法为研究对象,提出一种基于alpha-beta剪枝和概率剪枝因素相结合的概率剪枝算法,来解决博弈树搜索问题。利用概率剪枝算法,可减少博弈树搜索深度,从而加快搜索进程。     

双人博弈问题中的蒙特卡洛树搜索算法的改进

蒙特卡洛树搜索(MCTS)是一种针对决策类博弈游戏,运用蒙特卡洛模拟方法进行评估博弈策略的启发式搜索算法。但是,在面对计算机围棋这种复杂的决策过程时,简单的蒙特卡洛树搜索过程往往由于计算量大,收敛速度非常慢。 由于双人博弈游戏中的蒙特卡洛树搜索不能收敛于双人博弈的最佳决策策略,因此提出蒙特卡洛树搜索结合极大极小值算法的改进算法,使得搜索结果不会因为蒙特卡洛方法的随机性而失真。为了进一步提高复杂双人博弈游戏中搜索算法的计算效率,还结合了几种常见的剪枝策略。实验结果说明,所提算法显著改进了蒙特卡洛树搜索的准确性和效率。     

基于PVM的博弈树的网络并行搜索

通过分析博弈理论和a-b剪枝搜索过程,提出了使用PVM构造并行搜索网络.设计和实现了基于PVM的博弈树并行搜索过程.在博弈树搜索中通过构造的并行搜索网络和使用分而治之的策略把搜索过程分布在多个计算机上同时进行,在叶计算机结点的搜索中,通过a-b剪枝技术,剪枝了大量的搜索结点.全局并行搜索和局部剪枝技术的使用,加快了搜索的速度,解决了使用单计算机搜索速度和时间不可行的问题.该博弈并行搜索模型,适用于一般的博弈树搜索问题.     

博弈树启发式搜索的α-β剪枝技术研究

博弈是启发式搜索的一个重要应用领域,博弈的过程可以用一棵博弈搜索树表示,通过对博弈树进行搜索求取问题的解,搜索策略常采用α-β剪枝技术。在深入研究α-β剪枝技术的基础上,提出在扩展未达到规定深度节点时,对扩展出的子节点按照估价函数大小顺序插入到搜索树中,从而在α-β剪枝过程中剪掉更多的分枝,提高搜索效率。     

博弈算法在黑白棋中的应用

计算机博弈是一种对策性游戏，是人工智能的主要研究领域之一．它涉及人工智能中的搜索方法、推理技术和决策规划等。目前广泛研究的是确定的、二人、零和、完备信息的博弈搜索。文中通过一个黑白棋程序的设计，将生成的博弈树节点的估值过程和对博弈树搜索过程相结合，采用传统的Alpha—Beta剪枝和极大一极小原则方法给出了博弈程序设计的核心内容：包括博弈树搜索和估值函数两个方面，提出了对原算法的一种改进，该算法提高了搜索速度。实验结果验证了算法的有效性。     

使用R树进行k-NN搜索

在地理信息系统中经常要做k-NN搜索，进行这些查询用到的算法与位置和范围查询的算法不同，需要专门进行研究，介绍了一种分支界限遍历R树算法，并将该算法概括为k-NN算法。文中讨论了两种方法。对R树进行结点内MBR的排序以及剪枝过程，以减少搜索空间中需访问结点的数量，有效地进行k-NN搜索。     

基于父子等价剪枝策略的最大频繁项集挖掘

在传统剪枝策略中,具有相同事务集的父子结点搜索空间没有充分剪枝,效率较低.为此,提出父子等价的剪枝策略.采用深度优先搜索集合枚举树,对于父子结点中具有相同事务集的搜索空间进行剪枝,有效地缩小搜索空间,减少频繁项计算的次数,给出基于该剪枝策略的最大频繁项集挖掘算法.实验结果表明,该算法可缩短同一支持度下的最大频繁项集挖掘时间.     

改进的FLWAP的Web访问序列模式挖掘方法

为了提高序列模式挖掘的FLWAP-mine算法挖掘海量数据的效率和性能,基于减少数据库访问次数原则和序列模式的Apriori性质对FLWAP-mine算法进行改进,构造FLWAP-tree过程中只扫描一次访问序列数据库,对树进行剪枝删除非频繁事件。模式挖掘过程中采取投影数据库思想,只搜索当前模式的投影树,对构造的投影树判断剪枝,去除非频繁事件,进一步缩小搜索范围。实验表明,当数据量较大或支持度阈值较小时,改进的FLWAP-mine算法比FLWAP-mine算法有更好的性能。     

基于Expectimax搜索与Double DQN的非完备信息博弈算法

麻将作为典型的非完备信息博弈游戏主要通过传统Expectimax搜索算法实现,其剪枝策略与估值函数基于人工先验知识设计,存在假设不合理等问题。提出一种结合Expectimax搜索与Double DQN强化学习算法的非完备信息博弈算法。在Expectimax搜索树扩展过程中,采用Double DQN输出的估值设计估值函数并在限定搜索层数内获得分支估值,同时设计剪枝策略对打牌动作进行排序与部分扩展实现搜索树剪枝。在Double DQN模型训练过程中,将麻将信息编码为特征数据输入神经网络获得估值,使用Expectimax搜索算法得到最优动作以改进探索策略。实验结果表明,与Expectimax搜索算法、Double DQN算法等监督学习算法相比,该算法在麻将游戏上胜率与得分更高,具有更优异的博弈性能。     

博弈算法在黑白棋中的应用

计算机博弈是一种对策性游戏,是人工智能的主要研究领域之一,它涉及人工智能中的搜索方法、推理技术和决策规划等。目前广泛研究的是确定的、二人、零和、完备信息的博弈搜索。文中通过一个黑白棋程序的设计,将生成的博弈树节点的估值过程和对博弈树搜索过程相结合,采用传统的Alpha-Beta剪枝和极大-极小原则方法给出了博弈程序设计的核心内容:包括博弈树搜索和估值函数两个方面,提出了对原算法的一种改进,该算法提高了搜索速度。实验结果验证了算法的有效性。     

Challenging state-of-the-art move ordering with Adaptive Data Structures

The field of game playing is a particularly well-studied area within the context of AI, leading to the development of powerful techniques, such as the alpha-beta search, capable of achieving competitive game play against an intelligent opponent. It is well-known that tree pruning strategies, such as alpha-beta, benefit strongly from proper move ordering, i.e., by searching the best element first. A wide range of techniques have been developed over the years to achieve good move ordering, and improved tree pruning, in the field, in general and in particular, in the alpha-beta search, have been extensively studied. Inspired by the formerly unrelated field of Adaptive Data Structures (ADSs), we had previously introduced the History-ADS technique, which employs an adaptive list to achieve effective and dynamic move ordering, in a domain independent fashion. Our previous results confirmed that it performs well in a very wide range of cases, and in varied types of board games. However, our previous work did not compare the performance of the History-ADS heuristic to any established move ordering strategy. In an attempt to address this problem, we present here a comparison to two well-known, acclaimed strategies, which operate on a similar philosophy to the History-ADS, namely, the History Heuristic, and the Killer Moves technique. We also introduce, in this work, a mechanism by which these established move ordering strategies can be approximated, or directly implemented, in terms of ADSs. We confirm that, in a wide range of two-player and multi-player games, at various points in the game’s progression, the History-ADS performs at least as well as these strategies, and, in fact, outperforms them in the majority of cases.     

On the branching factor of the alpha-beta pruning algorithm

An analysis of the alpha-beta pruning algorithm is presented which takes into account both shallow and deep cut-offs. A formula is first developed to measure the average number of terminal nodes examined by the algorithm in a uniform tree of degree n and depth d when ties are allowed among the bottom positions: specifically, all bottom values are assumed to be independent identically distributed random variables drawn from a discrete probability distribution. A worst case analysis over all possible probability distributions is then presented by considering the limiting case when the discrete probability distribution tends to a continuous probability distribution. The branching factor of the alpha-beta pruning algorithm is shown to grow with n as Θ(n/lnn), therefore confirming a claim by Knuth and Moore that deep cut-offs only have a second order effect on the behavior of the algorithm.     

博弈树置换表启发式算法研究

博弈树搜索对于计算机博弈至关重要。优秀的搜索算法通过搜索较少的节点就可以获得最佳路径,从而提高计算机的博弈水平。论文以中国象棋计算机博弈作为背景,在alpha-beta基本搜索算法上,详细阐述了置换表启发算法的原理和哈希冲突,引进了双层置换表的概念及其替换策略,增强了引擎的搜索效率。实验结果表明了该算法的有效性。     

基于覆盖树的可扩展邻近搜索方法

针对邻近搜索技术受限于网络协议的支持以及存在空间嵌入误差的问题,提出一种基于覆盖树的可扩展邻近搜索方法CPS,包括覆盖树构建与维护协议和k近邻搜索算法两部分。节点自主计算自身所处层次,构造一棵层次化树。邻居维护协议负责维护覆盖树结构,确保其适应动态的网络环境。k近邻搜索算法通过对覆盖树剪枝,构造各层候选节点集合,提高搜索效率。实验结果表明,CPS的搜索精度优于典型的邻近搜索方法Tiers。     

The history heuristic and alpha-beta search enhancements inpractice

Many enhancements to the alpha-beta algorithm have been proposed to help reduce the size of minimax trees. A recent enhancement, the history heuristic, which improves the order in which branches are considered at interior nodes is described. A comprehensive set of experiments is reported which tries all combinations of enhancements to determine which one yields the best performance. In contrast, previous work on assessing their performance has concentrated on the benefits of individual enhancements or a few combinations. The aim is to find the combination that provides the greatest reduction in tree size. Results indicate that the history heuristic combined with transposition tables significantly outperforms other alpha-beta enhancements in application-generated game trees. For trees up to depth 8, this combination accounts for 99% of the possible reductions in tree size, with the other enhancements yielding insignificant gains     

An analysis of alpha-beta pruning

The alpha-beta technique for searching game trees is analyzed, in an attempt to provide some insight into its behavior. The first portion of this paper is an expository presentation of the method together with a proof of its correctness and a historical discussion. The alpha-beta procedure is shown to be optimal in a certain sense, and bounds are obtained for its running time with various kinds of random data.