Alpha-beta Search Research Articles

Monte Carlo tree search for dynamic shortest‐path interdiction

AbstractWe present a reinforcement learning‐based heuristic for a two‐player interdiction game called the dynamic shortest path interdiction problem (DSPI). The DSPI involves an evader and an interdictor who take turns in the problem, with the interdictor selecting a set of arcs to attack and the evader choosing an arc to traverse at each step of the game. Our model employs the Monte Carlo tree search framework to learn a policy for the players using randomized roll‐outs. This policy is stored as an asymmetric game tree and can be further refined as the game unfolds. We leverage alpha–beta pruning and existing bounding schemes in the literature to prune suboptimal branches. Our numerical experiments demonstrate that the prescribed approach yields near‐optimal solutions in many cases and allows for flexibility in balancing solution quality and computational effort.

Toward Automated Knowledge Discovery in Case-Based Reasoning

Automated Case Elicitation (ACE) enables case-based reasoning (CBR) systems to automatically acquire knowledge through real-time exploration and interaction with environments. CBR is an explainable AI methodology, where decisions are based on previous encounters. ACE combined with CBR continues learning as it is being deployed, and produces specific cases that can be reviewed by humans, unlike pretrained large language models (LLMs) that learn by training offline on prior data. ACE and CBR may be useful methods to gather training data for use with generative AI, or to help them to adapt on the fly. This research explores ACE's potential by applying it to chess and conducting extensive experiments against Stockfish, the world's highest rated chess engine. An ACE agent was developed that combines random exploration with shallow alpha-beta search for novel game states. Results over 1000+ games showed the ACE player defeated Stockfish in nearly 10% of games—a notable achievement given Stockfish's extreme strength. Notably, the ACE agent required only 0.1 seconds per game compared an average of 8 minutes for Stockfish, while still gradually improving its win rate through accrued experience. Detailed analyses revealed how the relaxation of ACE's case matching criteria along with selective retention of useful cases enabled accumulation of strategic chess knowledge. The research provides valuable insights into ACE's proficiency for knowledge discovery in complex, adversarial domains. It lays groundwork for integrating ACE, an unsupervised CBR learner, with modern deep learning techniques like neural networks and large language models to combine the strengths of symbolic and subsymbolic AI. By demonstrating ACE's ability to extract strategic knowledge against world-class opponents, this work highlights its potential for impact across gaming, autonomous systems, and other complex problem-solving domains.

Chess using AI Review

This research paper explores the development of an AI chess engine leveraging the Minimax algorithm with Alpha-Beta pruning technique, implemented using Python and JavaScript programming languages. The objective is to investigate the effectiveness of these algorithms in creating a proficient and competitive chess-playing AI. The paper begins with an overview of the Minimax algorithm and its application in game theory, followed by an explanation of Alpha-Beta pruning and its role in enhancing the efficiency of the search process within the game tree. Subsequently, the implementation details of the AI chess engine in both Python and JavaScript are discussed, highlighting the design considerations, algorithmic optimizations, and programming techniques utilized. The paper also provides insights into the integration of the AI engine with a graphical user interface (GUI) for interactive gameplay experiences. Additionally, experimental results and performance evaluations are presented to assess the AI engine's strength and playing capabilities against human players or other AI opponents

A study on search techniques in the game-tree

Artificial intelligence has developed a lot in the game field and search techniques on game-trees are essential for AI-game-playing. As many techniques for searching the game-trees have been published, the time consumption of search has decreased and the accuracy of it has increased. This paper would provide a comprehensive review of existing algorithms and improvements, including their mechanisms and performances. These techniques are first divided into two sections, techniques based on Alpha-Beta pruning and techniques based on Monte-Carlo tree search. Furthermore, techniques based on Alpha-Beta pruning are further subdivided into narrow window properties and information from previous searches based on the specific aspects they focus on. Finally, this paper concludes by summarizing the performance of these techniques and identifying their suitable application scenarios, as well as suggesting potential directions for future research.

Comparison of different algorithms in Reversi AI

Minimax and alpha-beta pruning have been widely applied in AI for various strategic board games, the utilization of greedy algorithms in this context has received less attention. The Greedy algorithms aim to make locally optimal choices at each step, exploiting immediate gains. This research aims to reveal the potential benefits and limitations of applying greedy algorithms in Reversi gaming AI, specifically through a comparison with the Minimax algorithm. A series of AI versus AI matches were conducted to evaluate and compare the performance of the three different AI algorithms. The objective was to assess their gameplay strategies and decision-making abilities by measuring their average execution time and win rates. Relevant codes and experiments will be carried out in a C++ environment, and the shown codes in this article will only have pseudocode and comments. In conclusion, the findings of this study indicate that the Greedy Algorithm is not a superior alternative to the Minimax Algorithm in competitive scenarios, particularly with increased searching depth. However, greedy algorithms still have weak competitiveness with reduced computational time. For future research, concentrating on improving the performance of the Greedy Algorithm by incorporating more advanced heuristics or adaptive strategies maybe a good choice. Additionally, combining the strengths of both the Greedy Algorithm and the Minimax Algorithm could be a promising direction for further investigation.

Implementation of artificial intelligence in "ToqyzQumalaq" mobile logic game

This research paper delves into the implementation of artificial intelligence (AI) in the mobile logic game "ToqyzQumalaq," focusing on incorporating advanced algorithmic strategies to improve gameplay. The game's complexity and strategic depth present unique challenges in AI development, addressed through the integration of algorithms like Minimax, Alpha-Beta Pruning, Greedy, and Particle Swarm Optimization (PSO). The study emphasizes the creation of evaluation functions for these algorithms, ensuring AI efficiency and human-like decision-making. This aspect is vital for maintaining the strategic unpredictability essential to "ToqyzQumalaq." Extensive experimental testing against human players of various skill levels demonstrates the algorithms' effectiveness. These tests reveal the strengths and limitations of each algorithm, providing insights into their application in the game. This paper contributes to AI in gaming, highlighting the challenges and opportunities in developing AI for complex games. Its findings are relevant not only to game developers but also serve as an educational tool, showcasing the practical application of AI and algorithmic strategies.

Optimization of Alpha-Beta pruning based on heuristic algorithm

Games have become an important place for testing Artificial Intelligence (AI). Minimax and Alpha-Beta Pruning are two common and basic algorithms implemented in game AIs. However, there are still limitations of the searching time and searching depth. This paper strives to improve the game AI with a Heuristic Algorithm to optimize both the searching time and depth. The experiment consists of three AIs built with Minimax, Alpha-Beta Pruning, and Heuristic Algorithm to evident the improvement. These AIs are built to play a traditional Chinese zero-sum game, Gobang, which can be seen as an enhanced version of tic-tac-toe but more advanced. The data is collected when AIs compete with each other. Comparing the search time of three AIs, there is significant improvement of AI implemented Heuristic Algorithm; the median search time for Heuristic AI is only half of the Alpha-Beta Pruning AI, and only quarter of the Minimax AI. Moreover, because the search time decreases, the searching depth of the Heuristic AI can also be increased. With the larger searching depth, the Heuristic AI also gains a higher winning rate against the other two AIs.

Monte-Carlo tree search with Epsilon-Greedy for game of amazons

The Game of the Amazons is an abstract strategy board game. It has a high computational complexity similar to the game of Go. Due to its NP-complete nature and large branching factor of game tree, finding the optimal move given a specific game state is infeasible and it is not trivial to design a computer algorithm that is competitive to an expert in the game of amazons. One way to tackle this problem is to leverage the Monte-Carlo Tree Search by using random simulations. In this article, a computationally cheap heuristic function is proposed and use together with Monte-Carlo Tree Search algorithm with Epsilon-Greedy policy aiming to design a competitive AI for the Game of the Amazon. The effectiveness of the -greedy based Monte-Carlo algorithm is compared to the widely used MCTS with Upper Confidence Bound and other classical tree search method such as breadth-first search, depth-first search, minmax search and alpha-beta pruning.

The development of computer-based algorithms based on gobang game

Gobang is a worldwide two-player strategy board game, which is popular especially in the Asian region. Recently, the science and technology has been developing fast and artificial intelligence was applied in numerous fields like the board game. Gobang, a strategy game with moderate difficulty, is a suitable example for people to test algorithms and solve board game problems. As a result, many related algorithms were appearing with different advantages and disadvantages. In this work, these already existed algorithms, game tree, minimax search, alpha-beta pruning, genetic algorithm and monte carlo tree search, were discussed and compared. The results and comparison showed that game tree and minimax search had a large number of nodes to calculate to reach a suitable search depth, about 1.00E+12 and 1.29E+14 respectively, which meant they need a long calculating time, while the alpha-beta pruning need to calculate about 2.2E+07 nodes and genetic algorithm only need to calculate about 1.00E+04 nodes, which cost 0.6 seconds for every move. Plus, the monte carlo tree search could reach nearly 100% win rate through self-play, which making gobang algorithm become more refined. Additionally, these algorithms had already made gobang AI powerful with fast move and high win rate, so they also had been applied in many different fields to develop and spread gobang.

Application of Different Artificial Intelligence Methods on Reversi

Using different algorithms in artificial intelligence to perform adversarial agent games. The most popular adversarial game that could be implemented using artificial intelligence algorithms is chess games. The algorithm this research used includes minimax with improvement and deep reinforcement learning. The goal for this research is to compute the popular game Reversi in different artificial intelligence methods successfully. Moreover, the research seeks for improvements in the heuristic part of minimax algorithm and the combination of deep reinforcement learning with Monte Carlo Tree with Neural Network. This paper uses Reversi as an example to analyze different algorithms, including Minimax, Monte Carlo Tree, and Neural Networks. As a result, both algorithms work successfully. The alpha-beta pruning minimax algorithm with improvement in heuristic function and fixed depth cut-off significantly increase the winning probability and time cost of our artificial intelligence agent. The deep reinforcement learning successfully combined MCTS with neural network to train two agents to complete Reversi with great winning probability.

Design and Realization of Surakarta Chess Game Program

At present, the research on Surakarta game is relatively less than other games. Aiming at this situation, a Surakarta chess game program is designed. This program implements basic algorithms such as board representation, move generation, game evaluation, and game tree search. The evaluation of the chess game takes into account the number of pieces, moving range, attacking range, attacking power of pieces, board value, arc value, etc. The game tree search algorithm uses the Alpha-Beta pruning algorithm. The whole program is fully functional and has a strong game level, which provides reference significance and reference value for related research. The program won the second prize at the national level in the computer game competition for college students in China, and the second prize at the provincial level in the computer game competition for college students in Liaoning Province, which verified the feasibility of the game program algorithm.

Try Dam: Digital Checkers Game Application Based on Machine Learning

A traditional game like checker or dam is often played by people in the past during their free time. Despite their leisurely and compelling activities, the games stimulate the cognitive, social and emotional well-being of players, to plan the right strategy to win the game. However, moving along with the difference in time, traditional games that used to be often played by all sections of society are increasingly being marginalized by the younger generation. Due to the development of technology, the younger generation appears to be more inclined to play mobile games than traditional ones. The proposed solution to this problem is to create a traditional game in digital form; and this paper aims to develop a digital checkers game application using machine learning and to test the functionality and effectiveness of the game. The development of this digital checkers game applies agile model, combined with game design strategy. The Alpha-Beta Pruning algorithm will be used to produce a computer capable of playing checkers. Based on the game competition result, the player's winning rate decreases along with the chosen difficulty level. Once the difficulty level increase, players need to demonstrate their mastery to play against computer. The computer has gained increased information to defeat the opponent using various strategies using "alpha-beta pruning" technique. This digital checkers game is expected to increase awareness and passion among generation young towards the local traditional games. Expected game play experience from the application include entertainment and easy access especially using smart telephone device.

Crop Yield Prediction by Integrating Et-DP Dimensionality Reduction and ABP-XGBOOST Technique

In the Indian economy, one of the most significant sectors is agriculture, which is the primary source of livelihood. In precision agriculture, the major intention is to ameliorate Crop Yield (CY) production along with quality by mitigating operational costs along with environmental pollution. To attain precision agriculture, Crop Yield Prediction (CYP) is highly significant. However, CYs become unpredictable owing to their reliance on huge dimension features like soil, climate, pesticides, diseases, et cetera. Therefore, for CYP, a Feature Selection (FS)-centric Machine Learning (ML) methodology is desired to provide precision agriculture along with mitigate the computational time. An Ensemble Threshold-centric Data Perturbation (DP) FS (ET-DPFS) dimensionality reduction centered Alpha-Beta Pruning centered Extreme Gradient Boosting (ABP-XGBOOST) CYP methodology is developed here. In this model, highly pertinent candidate features, which contain higher relevance regarding the class, lower redundancy amongst the features being selected, along with stay strong against noisy data, are selected. In the proposed work, firstly, by dealing with Nan values, missing values, outliers, categorical features, along with date-time variables, an exploratory evaluation is conducted over the data. After that, by utilizing the Analysis of Variance (ANOVA) test, the redundant features are taken away. Then, by employing the ET-DPFS, the relevant features are selected. ‘’3’ base learner FS methodologies like Median Absolute Deviation-centric LASSO (MAD-LASSO), Coefficient Vector-centric Mayfly Optimization (CV-MO), and HE weight initialization-centered Relief (HEwint-Relief) are included in this ET-DPFS. Lastly, by deploying the ABP-XGBOOST, the features being selected are trained along with verified. Experiential evaluation displays that the proposed methodology is highly reliable than the prevailing methodologies by achieving precise prediction with lower Values for Mean Square Error (MSE), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE).

Analysis of Game Tree Search Algorithms Using Minimax Algorithm and Alpha-Beta Pruning

An important topic of research in computer systems is the optimization of finding the optimum course of action based on different variables, such as the environment's state, the system's goal, etc. The building of the entire state search space, also known as the minimax algorithm, can result from any search algorithm's attempt to find the best feasible solution from among all known possibilities. The recursive backtracking algorithm known as Minimax is used to select the next action in a game of strategy for two players. The algorithm works well because it anticipates that your adversary will play well as well. However, as the tree's depth increases, we observe that minimax frequently investigates repetitive and unlikely situations. We'll also take a look at the minimax extension known as alpha-beta pruning, which prohibits us from considering states that won't be chosen. We will also examine a number of established techniques for resolving two-player games, such as adversarial search and other machine learning-based techniques.

Tree Search Algorithms For Chinese Chess

Computer Games are an important aspect of Artificial Intelligence (AI) which has produced many representative algorithms of optimal strategies. Therefore, many AI researchers have applied game theory to various board games in an attempt to find the essence of games and grasp the core of AI behaviour. AlphaGo is a very famous and typical chess-playing program that uses Monte Carlo tree search (MCTS) to estimate the value of each node in the search tree and optimize the possible results. Chinese chess is one of the traditional chess versions with its typical strategy. However, due to its late start and high complexity, there are many more technical problems to be solved. In this paper, we recommend two commonly used search frameworks for Chinese chess: the minimax algorithm and the alpha-beta pruning algorithm. On this basis, to deal with the complex and changeable situation, the Chinese chess algorithm based on Monte Carlo tree search and appropriate neural network evaluation function is studied.

Peningkatan Kemenangan Non-Playable Character dalam Permainan Triple Triad Menggunakan Alpha-Beta Pruning

Non-Playable Character (NPC) is one of the essential elements in video games. Generally, NPCs provide challenges for players in completing missions in the game, where NPCs mean acting as enemies. The role of the enemy causes the victory rate to be one of the main goals of artificial intelligence applied to NPCs. The challenges that these NPCs provide are significant to keep players going. NPCs must be able to provide a balanced challenge like humans to have an experience that is as enjoyable as when playing with other people. The problem is the low win rate achieved by NPCs so that players can feel bored. The alpha-beta pruning algorithm is one of the decision-making algorithms that is often applied to games that require more than or equal two players. Therefore, this algorithm is suitable for applying to the object of research, namely the Triple Triad game. The Triple Triad game is a board game played by two players. The Triple Triad game was first introduced as a mini-game in the Final Fantasy VIII game. This game is a combination of card games and board games. In this study, the alpha-beta pruning algorithm was proven to increase the win rate of NPCs. It is indicated by comparing the win rate of NPCs who choose a random step, which is 17.5%, with an NPC that has applied the alpha-beta pruning algorithm, which is 55%. Therefore, there is a significant increase in the win rate. Keywords: Alpha-beta pruning; artificial intelligence; card; game; Non-Playable Character.

Tic Tac Toe by Minimax Alpha-Beta Pruning Using Arduino

Abstract: Heuristic algorithms are put to the test in games. Because they incorporate an unexpected opponent, two-person games are more challenging than a basic puzzle. In a two-player game, you must presume that your opponent has the same information as you and can use it just as well. As a result, you must presume that your opponent will make the best available move at each level of the game. The minimax method is built on this foundation. The players in minimax are referred to as MAX (the player) and MIN (the player) (the opponent). Both aim to get the most out of their actions. The player, MAX, is attempting to maximise her score. And MIN is the opponent attempting to reduce MAX's score to the bare minimum. It is impossible to stretch the graph to its leaf nodes in most games.The number of layers in the state space is increased to n. The heuristic evaluation function assigns a value to each leaf node in this subgraph. The values are then passed back to the root node. The heuristic value of the best state that can be attained from that node is represented by the value propagated back. The process of alpha-beta pruning is used to reduce the amount of computation and searching required during minimax. Minimax is a two-pass search, with the first pass assigning heuristic values to nodes at the lowest depth and the second pass propagating those values up the tree. The depth-first approach is used in alpha-beta search. A MAX node's initial or temporary value is called an alpha value.Because MAX nodes receive the highest value from their descendants, an alpha value can never fall; it can only rise. A beta value is a value linked with a MIN node that is initial or transitory. A beta value can never increase; it can only go down because MIN nodes are assigned the lowest value among their progeny. Assume alpha = 6 for a MAX node. Then any branches originating from a MIN descendant with a beta value less than or equal to 6 won't be included in the search. So, if you know that the MAX node has an alpha of 6 and that one of its MIN children has a beta of less than or equal to 6, you don't need to look any farther down the MIN node. This is called Alpha Beta Pruning. Keywords: component, formatting, style, styling, insert (key words)

Deep Learning and the Game of Checkers

In this paper we present an approach which given only a set of rules is able to learn to play the game of Checkers. We utilize neural networks and reinforced learning combined with Monte Carlo Tree Search and alpha-beta pruning. Any human influence or knowledge is removed by generating needed data, for training neural network, using self-play. After a certain number of finished games, we initialize the training and transfer better neural network version to next iteration. We compare different obtained versions of neural networks and their progress in playing the game of Checkers. Every new version of neural network represented a better player.

Alpha-Beta Pruning for Games with Simultaneous Moves

Alpha-Beta pruning is one of the most powerful and fundamental MiniMax search improvements. It was designed for sequential two-player zero-sum perfect information games. In this paper we introduce an Alpha-Beta-like sound pruning method for the more general class of “stacked matrix games” that allow for simultaneous moves by both players. This is accomplished by maintaining upper and lower bounds for achievable payoffs in states with simultaneous actions and dominated action pruning based on the feasibility of certain linear programs. Empirical data shows considerable savings in terms of expanded nodes compared to naive depth-first move computation without pruning.

Solving Dots-And-Boxes

Dots-And-Boxes is a well-known and widely-played combinatorial game. While the rules of play are very simple, the state space for even very small games is extremely large, and finding the outcome under optimal play is correspondingly hard. In this paper we introduce a Dots-And-Boxes solver which is significantly faster than the current state-of-the-art: over an order-of-magnitude faster on several large problems. Our approach uses Alpha-Beta search and applies a number of techniques---both problem-specific and general---that reduce the search space to a manageable size. Using these techniques, we have determined for the first time that Dots-And-Boxes on a board of 4 x 5 boxes is a tie given optimal play; this is the largest game solved to date.