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。     

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。     

面向多智能体博弈的并行蒙特卡洛树搜索算法研究

蒙特卡洛树搜索算法是一种常用的强化学习算法,博弈过程中动态空间的指数级增长是制约该算法学习效率的因素。基于并行方法对蒙特卡洛树搜索算法进行优化,提出基于胜率估值传递的并行蒙特卡洛树搜索算法。改进后的并行博弈搜索策略框架包含一个主进程和多个子进程,其中子进程用于探索,主进程根据子进程传递的胜率估值数据进行决策。结合多智能体博弈平台Pommerman进行实验验证,与传统的蒙特卡罗树搜索算法相比,并行蒙特卡罗树搜索算法有效提高了资源利用率、博弈胜率及决策效率。      

面向目标的博弈搜索策略及其应用

博弈是人工智能研究的重要分支,它涉及人工智能中的推理技术、搜索方法和决策规划。而搜索策略是博弈问题的关键。针对搜索技术中存在的由于搜索空间巨大而引起的搜索效率下降的缺点,结合五子棋的特点,探讨了相应博弈问题的求解策略,提出一种结合PVS算法、静态着法启发、历史启发算法的搜索策略。实验结果证明,该算法不但能保证博弈水平,还能得到较好的搜索效率。     

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。     

面向目标的博弈搜索策略及其应用

博弈是人工智能研究的重要分支，它涉及人工智能中的推理技术、搜索方法和决策规划。而搜索策略是博弈问题的关键。针对搜索技术中存在的由于搜索空间巨大而引起的搜索效率下降的缺点，结合五子棋的特点，探讨了相应博弈问题的求解策略，提出一种结合PVS、静态着法启发、历史启发算法的搜索策略。实验结果证明，该算法不但能保证博弈水平，还能得到较好的搜索效率。     

一种博弈树静态估值算法——ΔFeature状态估值

在考虑下棋操作对棋盘影响的局部性后,提出了棋博弈的Δfeature状态估值算法,通过计算博弈树中相邻结点的特征变化来避免在叶结点上扫描整个棋盘,有效地减少了静态估值的时间开销。若棋子影响的局部范围足够小,还可以考虑将局部范围的所有情况列成表,以查表代替棋形匹配。ΔFeature状态估值算法也可以与其它优化博弈树搜索的方法一同使用,达到更好的效果。     

五子棋智能博弈的研究与设计

机器博弈是人工智能的一个重要研究分支,该文通过设计一个五子棋智能博奕程序,采用传统的博弈树算法,利用剪枝和极大极小树搜索最佳位置,从而实现人机智能博弈。并对现有算法存在的问题进行探究改进,最后给出程序实例,结果表明效果较为理想。     

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。     

一种博弈树静态估值算法--△Feature状态估值

在考虑下棋操作对棋盘影响的局部性后，提出了棋博弈的△feature状态估值算法，通过计算博弈树中相邻结点的特征变化来避免在叶结点上扫描整个棋盘，有效地减少了静态估值的时间开销。若棋子影响的局部范围足够小，还可以考虑将局部范围的所有情况列成表，以查表代替棋形匹配。ΔAFeature状态估值算法也可以与其它优化博弈树搜索的方法一同使用，达到更好的效果。     

约束逻辑程序设计的变量压缩事件分析

该文涉及的约束逻辑程序设计(CLP)是一在二叉树上进行搜索的过程,提高搜索效率是CLP的主要研究方向之一。在CLP中约束推理机是核心,由变量组、约束过滤器、临时容器、推理引擎组成。在介绍了约束推理机激活过滤器,对变量进行区间压缩后,提出引入变量事件,总结为三种类型:SINGLE、BOUND和DOMCHG,用于减少过滤器的激发次数。实验结果表明,变量事件能够促进约束推理机的搜索效率,缩短二叉树搜索的时间,可以更快寻找到答案。     

Selecting evaluation functions in Opponent-Model search

Opponent-Model search is a game-tree search method that explicitly uses knowledge of the opponent. There is some risk involved in using Opponent-Model search. For adequate forecasting, two conditions should be imposed. Both the prediction of the opponent's moves and the judgement of future positions should be of good quality. The two conditions heavily depend on the evaluation functions used.In the article we distinguish evaluation functions by type. Three fundamentally different types are introduced. Thorough analysis of a variety of characteristics leads to eight possible orderings. The role of the evaluation functions is studied by attempting to answer five research questions. Moreover, actual computer game-playing programs investigate the research questions by a series of experiments in which Opponent-Model search is performed. The game of Bao is our test bed, it was selected because of its relatively narrow game tree, which allowed for an appropriate search depth in the experiments. We restrict ourselves to five evaluation functions generated with the help of machine-learning techniques. A set of round-robin tournaments between these evaluation functions show that when the above conditions are met, Opponent-Model search can be applied successfully. Answers to the research questions are given in the conclusions.     

Using the primal-dual interior point algorithm within the branch-price-and-cut method

Branch-price-and-cut has proven to be a powerful method for solving integer programming problems. It combines decomposition techniques with the generation of both columns and valid inequalities and relies on strong bounds to guide the search in the branch-and-bound tree. In this paper, we present how to improve the performance of a branch-price-and-cut method by using the primal-dual interior point algorithm. We discuss in detail how to deal with the challenges of using the interior point algorithm with the core components of the branch-price-and-cut method. The effort to overcome the difficulties pays off in a number of advantageous features offered by the new approach. We present the computational results of solving well-known instances of the vehicle routing problem with time windows, a challenging integer programming problem. The results indicate that the proposed approach delivers the best overall performance when compared with a similar branch-price-and-cut method which is based on the simplex algorithm.     

逻辑语言剪枝算子的过程语义及其实现

论述了逻辑程序设计中剪枝算子的作用及传统剪枝算子的过程性语义和说明性语义不一致问题;介绍了新型逻辑程序语言〔淑划中的COTRTT11t剪枝算子;通过引入一组定义描述其过程语义,并进一步阐述了剪枝算子和延迟计算规则之间的关系,讨论了Godel语言的剪枝策略及控制机制,从而为逻辑程序语言的实现提供了依据。     

基于混合搜索的含逻辑“与”“或”的RM优化算法

相对于标准约束优化问题,广义约束优化问题（或称析取优化问题）的等式或不等式约束条件中不仅包含逻辑“与”关系,还含有逻辑“或”关系.单调速率（RM）优化问题是广义约束优化问题的一个重要应用.目前RM优化问题已有的解法包括函数变换、混合整数规划、线性规划搜索等算法.随着任务数的增多,这些算法的求解时间较长.提出一种基于线性规划的深度广度混合搜索算法（LPHS）,将广义约束优化问题拆分成若干子问题,建立线性规划搜索树,合理选择搜索顺序,利用动态剪枝算法减小子问题的规模,最终求得最优解.实验结果表明,LPHS算法比其他方法有明显的效率提升.研究成果与计算机基础理论中的可满足性模理论的研究相结合,有助于提高可满足性模理论问题的求解效率,促进该理论在程序验证、符号执行等领域的进一步应用.     

A distributed processing algorithm for solving integer programs using a cluster of workstations

The sequential branch and bound algorithm is the most established method for solving mixed integer and discrete programming problems. It is based on the tree search of the possible subproblems of the original problem. There are two goals in carrying out a tree search, namely, (i) finding a good and ultimately the best integer solution, and (ii) to prove that the best solution has been found or no integer feasible solution exists. We call these the stage 1 and stage 2 of tree search. In general it is extremely difficult to choose the ideal search strategy in stage 1 or stage 2 for a given integer programming (IP) problem. On the other hand by investigating a number of different strategies (and hence different search trees) a good solution can be reached quickly in respect of many practical IP problems. Starting from this observation a parallel branch and bound algorithm has been designed which exploits this two stage approach. In the first stage we investigate a number of alternative search trees (forest search) in the hope of finding a good solution quickly. This we call the multiple heuristic search (MHS). In this approach the best integer solution is broadcast to other processors involved in MHS tree development. In the second stage we reorganise the search to investigate branches of a chosen tree in parallel. This two stage algorithm has been implemented on a cluster of SUN workstations using the Parallel Virtual Machine (PVM) harness [12]. The results of our investigation for a range of well known test problems taken from the MIPLIB set and others from the literature are reported here.     

An Edit Distance between Quotiented Trees

In this paper we propose a dynamic programming algorithm to compare two quotiented trees using a constrained edit distance. A quotiented tree is a tree defined with an additional equivalent relation on vertices and such that the quotient graph is also a tree. The core of the method relies on an adaptation of an algorithm recently proposed by Zhang for comparing unordered rooted trees. This method is currently being used in plant architecture modelling to quantify different types of variability between plants represented by quotiented trees.     

A PLANNING APPROACH TO DECLARER PLAY IN CONTRACT BRIDGE

Although game-tree search works well in perfect-information games, it is less suitable for imperfect-information games such as contract bridge. The lack of knowledge about the opponents' possible moves gives the game tree a very large branching factor, making it impossible to search a significant portion of this tree in a reasonable amount of time.
This paper describes our approach for overcoming this problem. We represent information about bridge in a task network extended to represent multi-agency and uncertainty. Our game-playing procedure uses this task network to generate game trees in which the set of alternative choices is determined not by the set of possible actions, but by the set of available tactical and strategic schemes.
We have tested this approach on declarer play in the game of bridge, in an implementation called Tignum 2. On 5000 randomly generated notrump deals, Tignum 2 beat the strongest commercially available program by 1394 to 1302, with 2304 ties. These results are statistically significant at the α= 0.05 level. Tignum 2 searched an average of only 8745.6 moves per deal in an average time of only 27.5 seconds per deal on a Sun SPARCstation 10. Further enhancements to Tignum 2 are currently underway.     

基于Matlab的线性规划问题求解

线性规划是运筹学中研究较早、发展较快、应用广泛、方法成熟的一个重要分支,它是辅助人们进行科学管理的一种重要的数学方法.文章首先介绍了线性规划的基本概念及标准形式,着重讨论了线性规划问题的三种常用解法:单纯形法、直接搜索法以及遗传算法,最后在Matlab R2009a环境下进行了仿真.通过结果可以看出,用Matlab求解线性规划问题,可以避免手工的烦琐计算,大大地提高工作效率和结果的准确性.     

An Edit Distance between Quotiented Trees

Abstract. In this paper we propose a dynamic programming algorithm to compare two quotiented trees using a constrained edit distance. A quotiented tree is a tree defined with an additional equivalent relation on vertices and such that the quotient graph is also a tree. The core of the method relies on an adaptation of an algorithm recently proposed by Zhang for comparing unordered rooted trees. This method is currently being used in plant architecture modelling to quantify different types of variability between plants represented by quotiented trees.