Alpha-beta Pruning Algorithm Research Articles

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.

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.

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.

APPLYING ALPHA-BETA ALGORITHM IN A CHESS ENGINE

Minimax Algorithm, is a solution to reduce the burden on hardware in chess engine. However, a more in-depth method is needed to further increase the search algorithm. One of those solutions is called Alpha-Beta Pruning algorithm. The idea is to eliminate the unnecessary nodes in the search tree.

A GA based method for search-space reduction of chess game-tree

In this study, a GA (Genetic Algorithm) basesented to reduce the chess game tree space. GA is exploited in some studies and by chess engines in order to: 1) tune the weights of the chess evaluation function or 2) to solve particular problems in chess like finding mate in number of moves. Applying GA for reducing the search space of the chess game tree is a new idea being proposed in this study. A GA-based chess engine is designed and implemented where only the branches of the game tree produced by GA are traversed. Improvements in the basic GA to reduce the problem of GA tactic are evident here. To evaluate the efficiency of this new proposed chess engine, it is matched against an engine where the Alpha-Beta pruning and Min-Max algorithm are applied.

The Analysis of Alpha Beta Pruning and MTD(f) Algorithm to Determine the Best Algorithm to be Implemented at Connect Four Prototype

Connect Four is a two-player game which the players take turns dropping discs into a grid to connect 4 of one’s own discs next to each other vertically, horizontally, or diagonally. At Connect Four, Computer requires artificial intelligence (AI) in order to play properly like human. There are many AI algorithms that can be implemented to Connect Four, but the suitable algorithms are unknown. The suitable algorithm means optimal in choosing move and its execution time is not slow at search depth which is deep enough. In this research, analysis and comparison between standard alpha beta (AB) Pruning and MTD(f) will be carried out at the prototype of Connect Four in terms of optimality (win percentage) and speed (execution time and the number of leaf nodes). Experiments are carried out by running computer versus computer mode with 12 different conditions, i.e. varied search depth (5 through 10) and who moves first. The percentage achieved by MTD(f) based on experiments is win 45,83%, lose 37,5% and draw 16,67%. In the experiments with search depth 8, MTD(f) execution time is 35, 19% faster and evaluate 56,27% fewer leaf nodes than AB Pruning. The results of this research are MTD(f) is as optimal as AB Pruning at Connect Four prototype, but MTD(f) on average is faster and evaluates fewer leaf nodes than AB Pruning. The execution time of MTD(f) is not slow and much faster than AB Pruning at search depth which is deep enough.

The Analysis of Alpha Beta Pruning and MTD(f) Algorithm to Determine the Best Algorithm to be Implemented at Connect Four Prototype

Connect Four is a two-player game which the players take turns dropping discs into a grid to connect 4 of one’s own discs next to each other vertically, horizontally, or diagonally. At Connect Four, Computer requires artificial intelligence (AI) in order to play properly like human. There are many AI algorithms that can be implemented to Connect Four, but the suitable algorithms are unknown. The suitable algorithm means optimal in choosing move and its execution time is not slow at search depth which is deep enough. In this research, analysis and comparison between standard alpha beta (AB) Pruning and MTD(f) will be carried out at the prototype of Connect Four in terms of optimality (win percentage) and speed (execution time and the number of leaf nodes). Experiments are carried out by running computer versus computer mode with 12 different conditions, i.e. varied search depth (5 through 10) and who moves first. The percentage achieved by MTD(f) based on experiments is win 45,83%, lose 37,5% and draw 16,67%. In the experiments with search depth 8, MTD(f) execution time is 35, 19% faster and evaluate 56,27% fewer leaf nodes than AB Pruning. The results of this research are MTD(f) is as optimal as AB Pruning at Connect Four prototype, but MTD(f) on average is faster and evaluates fewer leaf nodes than AB Pruning. The execution time of MTD(f) is not slow and much faster than AB Pruning at search depth which is deep enough.

The Analysis of Alpha Beta Pruning and MTD(f) Algorithm to Determine the Best Algorithm to be Implemented at Connect Four Prototype

Connect Four is a two-player game which the players take turns dropping discs into a grid to connect 4 of one’s own discs next to each other vertically, horizontally, or diagonally. At Connect Four, Computer requires artificial intelligence (AI) in order to play properly like human. There are many AI algorithms that can be implemented to Connect Four, but the suitable algorithms are unknown. The suitable algorithm means optimal in choosing move and its execution time is not slow at search depth which is deep enough. In this research, analysis and comparison between standard alpha beta (AB) Pruning and MTD(f) will be carried out at the prototype of Connect Four in terms of optimality (win percentage) and speed (execution time and the number of leaf nodes). Experiments are carried out by running computer versus computer mode with 12 different conditions, i.e. varied search depth (5 through 10) and who moves first. The percentage achieved by MTD(f) based on experiments is win 45,83%, lose 37,5% and draw 16,67%. In the experiments with search depth 8, MTD(f) execution time is 35, 19% faster and evaluate 56,27% fewer leaf nodes than AB Pruning. The results of this research are MTD(f) is as optimal as AB Pruning at Connect Four prototype, but MTD(f) on average is faster and evaluates fewer leaf nodes than AB Pruning. The execution time of MTD(f) is not slow and much faster than AB Pruning at search depth which is deep enough.

IMPLEMENTASI ALGORITMA NEGASCOUT PADA PERMAINAN NINE MEN’S MORRIS

Application development nowadays many are using technology/knowledge of Artificial Intelligence study. This research tries to make an intelligence agent that can play Nine Men’s Morris game using Negascout algorithm. The purpose of this research are to compare the effectiveness of Negascout algorithm in exploring the best move along with time that required, compared with Alpha-Beta Pruning algorithm. The result from this research are Negascout algorithm explores fewer nodes and require less time in the search of the best move compared with Alpha-Beta Pruning algorithm.

A quantitative analysis of the alpha-beta pruning algorithm

Since the early 70s the question of efficiency of the alpha-beta pruning algorithm has been of interest to those who have been working on game-playing programs. In this paper, we present a quantitative study of the algorithm deriving estimates for its efficiency based on the scoring scheme suggested by Newborn [ 7].

The solution for the branching factor of the alpha-beta pruning algorithm and its optimality

article Free Access Share on The solution for the branching factor of the alpha-beta pruning algorithm and its optimality Author: Judea Pearl Univ. of Califorina, Los Angeles, CA Univ. of Califorina, Los Angeles, CAView Profile Authors Info & Claims Communications of the ACMVolume 25Issue 8Aug 1982 pp 559–564https://doi.org/10.1145/358589.358616Published:01 August 1982Publication History 79citation1,782DownloadsMetricsTotal Citations79Total Downloads1,782Last 12 Months225Last 6 weeks29 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

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.