D. F. Beal. A generalized quiescence search algorithm. Artificial Intelligence, 43:85--98, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....useful to assume that a null move can be played. The idea of a null move has been known for a long time [ Adelson Velskiy et al. 1975 ] and is now used in most chess programs. However, the method did not get much attention in the literature until later [ Palay, 1983; Goetsch and Cambpell, 1988; Beal, 1990 ] When searching a position to depth d, instead of making a legal move in that position a null move is made. The position is then searched to a depth less than d, most often d 1 or d 2. If the resulting score is greater than #, a cuto# is made based on the shallow search. The null move can be ....

D. F. Beal. A generalized quiescence search algorithm. Artificial Intelligence, 43:85--98, 1990.

....time. One approach is to prune unpromising lines, so that the time saved can be used to search selected lines more deeply. There exist several well established forward pruning methods for game tree search. For example, in chess the null move heuristic is very e#ective (best described by Beal [2] and Goetsch Campbell [5] while in Othello Buro s ProbCut method is the most successful [3] On the other hand, the theoretical issue surrounding forward pruning and how it a#ects decision quality has not been studied much. However, Smith and Nau [11] analyzed a model of forward pruning using ....

....As said earlier, there is a trade o# between generality and e#ectiveness, and to achieve the full pruning capability we must exploit some special characteristics of the search space. Most existing forward pruning methods are therefore domain specific. Even though methods like null move [2] and ProbCut [3] do not use explicit knowledge about their domain, they make implicit assumptions that tie them down for use in one, or at best very few, two person games. For example, the null move heuristic is very e#ective in chess, but inappropriate in Othello. Conversely, ProbCut is the ....

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D. F. Beal. A generalized quiescence search algorithm. Artificial Intelligence, 43:85--98, 1990.

....window, this narrower window can be used to prune more nodes. 5.3. Probability Based B PB The generalization of B algorithm, PB [4] makes use of a best first search strategy. Since relatively reliable bounds for a leaf position can be generated with some such technique as the null move[8], we can suppose that the expansion of a leaf node in the best first search, and back up of information from its successors will not increase the upper bound or decrease the lower bound of the possible merit values of the expanded node. This assumption is similar to the one employed by ....

D. Beal, A Generalized Quiescence Search Algorithm, Artificial Intelligence, 1988, (to appear). Also, Experiments with the null move, Advances in Computer Chess 5, Elsevier.

....important and minor features. e.g. in chess there is no point in analysing piece mobility if the player is a Queen down. This observation can be used for last ply optimizations by evaluating prominent features and using bounds on the minor features. ffl Variations of the null move heuristic (e.g. [2] [13] have been shown to be quite effective in non zugzwang games. The idea is that if a shallow search after an artificial pass move results in a fi cut it is likely that a deeper search also leads to a cut assuming that the right to move is advantageous. Therefore, skipping the deep search in ....

D.F. Beal. A generalized quiescence search algorithm. Artificial Intelligence, 43:85--98, 1990. 15

....value. In what follows, a selective extension of the fffi algorithm ProbCut will be presented which gives the common brute force approach a human touch. However, it is not the first step in this direction. Besides selective quiescence search methods, such as the null move heuristic (Beal (1990)) other algorithms have been proposed for example by McAllester (1988) Palay (1985) and Rivest (1988) which are able to search the game tree in a best first manner, but use an amount of memory roughly on the order of number of nodes searched. This is not practical for programs with a ....

Beal, D.F. (1990). A Generalized Quiescence Search Algorithm, Artificial Intelligence, Vol. 43, pp. 85--98.

....ProbCut [6] is discussed which aims at focusing the look ahead search to relevant variations and thus makes more efficient use of the allocated time. Several approaches to selective search have been studied in the past. Besides selective quiescencesearch techniques, such as the null move heuristic [3] which is quite effective in non zugzwang games, other algorithms have been proposed ( 15] 16] 17] 2] that search the game tree in best first manner, but use an amount of memory roughly on the order of number of nodes searched. Currently, this is not practical for programs with fast evaluation ....

D.F. Beal. A generalized quiescence search algorithm. Artificial Intelligence, 43:85--98, 1990.

....different search procedures that have been proposed as an improvement over the traditional full width, fixed depth, minimax search. Only those procedures that are game independent are potentially useful for a game learning program. For example, the quiescent search procedure proposed by Don Beal [12] assumes that it is illegal for a player to pass. However, for a game such as go passing is a legal move, hence a game learning program using quiescent search would perform poorly on the game of go. There have been several search procedures which attempt to achieve better play by selectively ....

D. F. Beal. A generalized quiescence search algorithm. Artificial Intelligence, 43:85--98, 1990. 93

....the real moves. To reduce the effort of searching the null move, the search depth is reduced by an additional 1 or 2 ply. This makes the null move an inexpensive heuristic for determining whether the branch is worth exploring. Null moves are discussed in numerous places throughout the literature [1, 9, 27, 37, 72]. 37 To use null moves in a game playing program, the implicit assumption is that passing is worse than doing something. This is not true in chess where a player is in check or in zugzwang. When a player is in check, the player must move to save the king from being captured. Zugzwang is a state ....

D. F. Beal. A Generalized Quiescence Search Algorithm. Artificial Intelligence, 43(1):85--98, 1990. (36)

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D. F. Beal. A generalized quiescence search algorithm. Artificial Intelligence, 43(1):85-- 98, 1990.

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