Artificial Intelligence A Paradigm of Human Intelligence

Transcription

1 Artificial Intelligence A Paradigm of Human Intelligence Mr. Saurabh S. Maydeo #1, Mr. Amit S. Hatekar #2 #1 Undergraduate student, Department of Information Technology, Thakur College of Engineering and Technology Kandivali East, Mumbai, Maharashtra, India #2 Asstant Professor, Department of EXTC, Thadomal Shahani Engineering College Bandra West, Mumbai, Maharashtra, India Abstract In today s world, Artificial Intelligence evolving at great speed. In 1997, s win against chess master Garry Kasparov was seen as very symbolically significant, depicting that artificial intelligence was reaching up to human intelligence [6]. Th research paper presents new approach for chess engine implementation which can be layered on top of algorithm and compares it with different exting types of Chess Engine implementation algorithms such as Minimax algorithm, Pruning and approach. All four approaches take current chess board as an input and give best as an output. Th research provides a detailed study of how all three approaches work and ir advantage, dadvantage and n compares m on bas of various parameters such as branching, space complexity, time complexity,etc. Keywords Pruning, Artificial Intelligence, Branching Factor, Chess Engine,, Minimax. I. INTRODUCTION According to far of Artificial Intelligence, John McCarthy, it science and engineering of making intelligent machines, especially intelligent computer programs. While exploiting power of computer systems, curiosity of human, lead him to wonder, Can a machine think and behave like humans do? In our day to day life for achieving something we think of all possible ways or actions to do it. n at back of our mind we assess every action and try to figure out its possible reactions. Our mind rejects all those actions which can cause some harm to achieve desire and select best possible action amongst m. A similar case re in chess game. We take into consideration all possible s of all pieces. n at back of our mind we try to figure out what will happen if we make th. We try to judge from our opponent s side too. We try to figure out if we make a certain, what will be next of our opponent? In th way we compare every and its consequences with or s and ir consequences, and play best possible selected. basic job of a chess engine to analyse given board B and return best M, I.e. F (B) = M. re 3 popular algorithms for implementing chess engine: A. Minimax Algorithm B. beta Pruning Algorithm C. Algorithm II. RELATED WORK A. Minimax Algorithm Minimax algorithm can be applied in games that are played by two players, such as tic-tac-toe, chess, checkers, etc. In chess, we can come to know from any given point, what are next available s of every piece on board. Thus, logically tee-like structure gets formed though recursion. Each node in th logical tree represents. Search trees are a way to represent searches. re are two players involved, MAX and MIN. search starts from root node. At each decion point, nodes for available s are generated, until no more decions are possible. A search tree traversed in depth-first search approach. nodes that belong to MAX player are assigned maximum value of its children. nodes for MIN player will select minimum value of its children. How good a depends on se values. Thus, MAX player selects having highest value in end, whereas MIN player selects having lowest value. At a node, MAX would pick which gives and MIN would pick node which gives lowest Minimax value (reby giving MIN highest utility). Minimax tends to be too slow for games such as chess [1]. For each turn, at any instance of time, player has many choices of pieces and ir corresponding s. Th increases branching and due to large branching deeper we go, time consuming it gets. average ISSN: Page 129

2 branching for game of chess normally 30. Th, 30 sub trees per turn are created Fig. 1 Game Tree Search and evaluation in Minimax 1. It was first algorithm that made it possible to implement decion making of artificial intelligence in chess. Dadvantages: 1. Takes huge amount of time for generating best. 2. Game tree time complexity (b n ) in chess. 3. Practically exploring entire tree not feasible since re are restrictions on space and time. 4. Branching too high, i.e. average number of children to a node 35 in chess 5. Search and evaluation of unnecessary nodes degrades overall performance and efficiency of engine. B. beta Pruning Algorithm Th algorithm overcomes drawbacks of Minimax algorithm. Minimax searches entire tree even if in some cases rest of sub tree can be ignored. Alpha beta pruning an algorithm that tries to reduce number of nodes which are explored by Minimax algorithm in its search tree. beta layered on top of Minimax algorithm. In best case, we can get same optimal solution as Minimax in O(b d/2 ) instead of O(b d ). Equivalently, we can reduce branching to b from b. [2] basic idea of alpha beta pruning of cutting or avoiding search and evaluation of sub tree which can be ignored makes it very much faster than Minimax algorithm where we have to go through all ways. Also it reduces space complexity as fewer function calls take place as we cut unnecessary parts of tree. Fig. 2 Game Tree search and evaluation in Pruning Alpha represents maximum score maximizing player assured of, minimum score minimizing player assured of. If beta alpha, it means a maximizing parent node guaranteed higher score on anor branch, or a minimizing parent node a lower score on anor branch. In such scenario, th branch can be culled and rest of th node's children can be skipped.[8] order of exploration of branches affects algorithm. sooner best s are dcovered sooner worse branches can be dcarded. In optimal case alpha-beta pruning can search to twice he depth with same amount of computation speed as Minimax.[7] 1. It reduces branching from b to square root of b. 2. As re are lesser function calls than Minimax algorithm, it has reduced space complexity 3. Th approach doesn t search and evaluate unnecessary nodes of game search tree. Dadvantages 1. Th approach doesn t suggest to maintain dictionary or look up table for starting s. 2. It slower than as it doesn t use observed strategically proven s from grandmasters game database. C. Algorithm computer chess system, developed at IBM Research during mid-1990s. chess machine defeated World Chess Master, Garry Kasparov, in a 6 game match in year re were number of s, which contributed to th AI success, such as a single-chip chess search engine, a lot of parallel computing, a strong focus on search extensions and effective use of a Grandmaster game database. blue approach can be viewed as:- ISSN: Page 130

3 Minimax + + Progressive ening + Parallel Computing + Opening Book + End-Game Strategies + Uneven Tree. In -, layered on top of Minimax with concept of progressive deepening. When we use depth-first search, even if nearest nodes of root node on right sub tree having checkmate condition, n also it will be evaluated after full evaluation of left sub tree. Thus, parallel computing speeds up decion making process in such cases. Th parallel computing can be implemented by means of multithreading [5]. Just like human chess masters, - system also uses some strategically-proven opening s without evaluating whole board on starting of game. se opening s are stored in database, which can be called as opening book[4]. Similarly, it also maintains strategically-proven endgame s and uses m for ending game in less time. Along with opening book and end-game book, it also uses extended book. se books or databases compre of strategically-proven s from Grandmasters games. Using pruning that layered on Minimax, th system already guarantees of avoiding unnecessary s by cutting sub trees, which are not required for evaluation, but still if we specify depth of search as say 8, n that maximum limit for search and say in some cases opponent defeating after 8 th deepness level. To handle th, - system made capable of deciding where to search furr and on which depth to stop. Th makes game search tree uneven. 1. re are lesser function calls than Minimax algorithm, it has reduced space complexity. 2. As th system maintains opening s book it faster than simple and Minimax approach. 3. Parallel computing reduces time complexity in some check mate situations. first. Th approach avoids search and evaluation of whole game tree and saves time. Normally, while playing chess, whenever any human plays certain s, if he finds that th successful; he tries to remember that for playing it for next time. Though human being has a limitation of not being able to memorize huge number of s, whereas in computerized chess game system, th limitation can be dealt with. Computerized chess game will be played with billions of players. We can make a centralized database, which can analyse play and record successful and timesaving s, and it can maintain rating of success of all se s. Thus, along with Grandmasters games, chess engine can also use its own database of successful s in next game. Initially chess engine searches for current situation of board in database. If similar situation found, n having highest rating evaluated. After evaluation, if chess engine also finds it successful n it increments its rating in database and plays that. If similar situation not present in database, chess engine finds best through deep blue approach and stores current situation and successful with its initial rating into database. Since many engines can interact with server, higher rating of in particular situation, higher probability of it being successful. Th because when engine finds current situation in database, it evaluates s stored corresponding to it and increments rating if it finds particular successful. Thus th approach can save a lot of time. Since it has capability to determine wher searching furr needed or not (uneven tree), it increases performance. D. Proposed Work Th approach can be layered on top of approach. As we know, deep-blue system uses opening book, end-game book and extended book, which contains strategically-proven best s based on observations of Grandmasters games. If rating of specific in similar situation high, n more emphas given on evaluating that ISSN: Page 131

4 Fig.3 Flowchart for recording and using observations made by computer chess engine. E. Comparon Paramet Minimax er Branchin g Factor Speed of searching best Run time Memory requirem ent Strategic s Database effective branching equal to mean branching, i.e. equal to b. Very slow (Hence impractica l to implement ) Too large, since many function calls take place due to inability to avoid searching unnecessa ry nodes. present branch ing reduce d to about square root of averag e branch ing, i.e. b Moder ate than Minim ax present branc hing reduc ed to about squar e root of avera ge branc hing, i.e. b Fast It uses datab ase for s such as openi ng book, exten ded book Propose d Algorit hm branchin g reduced to about square root of average branchin g, i.e. b Faster than It creates & uses database s of strategic s generate d by its own observat ion ISSN: Page 132

5 Paramet er Ability to avoid search and evaluatio n of unnecess ary nodes Parallel computin g Ability to learn from self observati on Minimax Unable. It capabl e. implement ed. imple mented in pure approa ch. It capab le. Imple mente d by ways like multit hreadi ng unable unable unabl e Propose d Algorit hm It capable Implem ented by ways like multithr eading It capable Table1 comparon between Minimax, beta Pruning, and Proposed algorithm [8]Chrtopher F. Joerg1 and Bradley C. Kuszmaul2, Massively Parallel Chess, MIT Laboratory for Computer Science NE43-247, 545 Technology Square Cambridge, MA III. CONCLUSION In th paper, different approaches for chess engine implementation are dcussed and compared. After analysing working of all four approaches, blue seemed to be better than Minimax and Pruning algorithms and proposed approach seemed to be best choice among all four algorithms if it layered on top of. REFERENCES, [1] Wikipedia Minimax, available: dated :- 1 sept 2016 [2] D. E. Knuth and R. W. Moore. An analys of alpha-beta pruning. Artificial Intelligence, 6(4): , [4]IBM,, available : :- 27 aug 2016 [5] Brian Greskamp, Parallelizing a Simple Chess Program, available : [6]Wikipedia, versus Garry Kasparov, available: versus_garry_kasparov dated:- 22 aug 2016 [7]S. H. Fuller, J. G. Gaschnig and J. J. Gillogly, ANALYSIS OF THE ALPHA-BETA PRUNING ALGORITHM, Department of Computer Science Carnegie-Mellon University Pittsburgh, Pennsylvania July, 1973 ISSN: Page 133