Chessmaps+Heuristic

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a move ordering heuristic proposed in 1999 by Kieran Greer et al., which uses a board vector of 64 square controls {dominated by White (1), Black (-1), or neutral (0)}, the **Chessmap**, along with king locations, to determine an importance vector of square areas or **sectors** by probing a neural network. Quiet moves are then sorted by the number and ranking of areas, they influence.
 * Chessmaps Heuristic**,

=Sectors= Following square sector definition with arbitrary enumeration had most promising results. code ╔════╤════╤════╦════╤════╦════╤════╤════╗ 8 ║   │    │    ║    │    ║    │    │    ║  ╟────┼─11─┼────║────┼────║────┼─ 9 ┼────╢ 7 ║    │    │    ║    7    ║    │    │    ║  ╠══════════════╣────┼────╠══════════════╣ 6 ║    │    │    ║    │    ║    │    │    ║  ╟────┼─10─┼────╠═════════╣────┼─ 8─┼────╢ 5 ║    │    │    ║    │    ║    │    │    ║  ╠══════════════╣─── 6 ───╠══════════════╣ 4 ║    │    │    ║    │    ║    │    │    ║  ╟────┼─ 2─┼────╠═════════╣────┼─ 4─┼────╢ 3 ║    │    │    ║    │    ║    │    │    ║  ╠══════════════╣────┼────╠══════════════╣ 2 ║    │    │    ║    5    ║    │    │    ║  ╟────┼─ 1─┼────║────┼────║────┼─ 3─┼────╢ 1 ║    │    │    ║    │    ║    │    │    ║  ╚════╧════╧════╩════╧════╩════╧════╧════╝     A    B    C    D    E    F    G    H code =Neural Network=

Topology
The input layer has 70 neurons, 64 for each square of the chessmap, and six for the relative king positions concerning sectors. Each of the 12 output neurons correspondents to one sector. Testing suggested that a 3-layer architecture with 16 hidden nodes being a good number.

Training
The supervised learning backpropagation algorithm on a 10000 position training set, generated from complete and randomly chosen chess games taken from master and grandmaster play, was used to train the neural network. For each position in the set, the Chessmap was calculated, and the desired output was a vector quantifying the sector influences of the move played in that position, that is for each sector whether the move increased (+1), decreased (-1) the control, or was neutral (0). All positions were considered from the White side, so when it was Black to move the position was color flipped.

Backpropagation algorithm for a 3-layer network : code format="cpp" initialize the weights in the network (often small random values) do     for each example e in the training set O = neural-net-output(network, e) // forward pass T = teacher output for e        compute error (T - O) at the output units compute delta_wh for all weights from hidden layer to output layer // backward pass compute delta_wi for all weights from input layer to hidden layer  // backward pass continued update the weights in the network until all examples classified correctly or stopping criterion satisfied return the network code =Results= Various experiments were conducted to compare the performance of the Chessmaps Heuristic with the History Heuristic on the 24 positions of the Bratko-Kopec Test. Both reduce a randomly ordered tree by about 80%, in favor to HH which can perform the search in much less time. However, along with iterative deepening, and more refined move ordering strategies concerning captures, forced and unsafe moves, the Chessmaps Heuristic got the upper hand in node reductions, specially in combination of an additional heuristic to store the last sector that caused a cutoff at each ply, quite similar to a killer slot. This sector was then retrieved and ordered first in any sector ordering, overriding the output of the neural network. The Chessmaps Heuristic is applied in Kieran Greer's chess playing program ChessMaps, written in C#.

=Résumé= In his 2012 paper //Tree Pruning for New Search Techniques in Computer Games//, Kieran Greer further outlines the Chessmaps Heuristic : and further

=See also=
 * Chunking
 * Guard Heuristic
 * History Heuristic
 * Learning
 * Neural MoveMap Heuristic
 * Neural Networks
 * Pattern Recognition

=Publications=
 * Kieran Greer (**1998**). //A Neural Network Based Search Heuristic and its Application to Computer Chess//. D.Phil. Thesis, [|University of Ulster]
 * Kieran Greer, Piyush Ojha, David A. Bell (**1999**). //A Pattern-Oriented Approach to Move Ordering: the Chessmaps Heuristic//. ICCA Journal, Vol. 22, No. 1
 * Kieran Greer (**2000**). //[|Computer chess move-ordering schemes using move influence]//. [|Artificial Intelligence], Vol. 120, No. 2
 * Levente Kocsis, Jos Uiterwijk, Eric Postma, Jaap van den Herik (**2002**). //[|The Neural MoveMap Heuristic in Chess]//. CG 2002
 * Kieran Greer (**2012**). //[|Tree Pruning for New Search Techniques in Computer Games]//. Advances in Artificial Intelligence, Vol. 2013

=External Links=
 * [|Backpropagation from Wikipedia]
 * [|Feedforward neural network from Wikipedia]
 * [|Probabilistic neural network from Wikipedia]
 * [|ChessMaps Download] by Kieran Greer

=References= =What links here?= include page="Chessmaps Heuristic" component="backlinks" limit="100"
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