Abstract
Sliding tile puzzle or n-puzzle is a standard problem for solving a game by a tree search algorithm such as A*, involving heuristics. A typical example of such a puzzle is 15-puzzle that consists of a square frame containing 4 × 4 numbered square tiles, one of which is missing. The goal is to position the tiles in correct order by sliding moves of the tiles, which use the empty space. The problem is NP-complete and for puzzles involving a greater number of tiles, the search space is too big for standard tree search algorithms. This type of puzzles is therefore quite often used for analysis and testing of heuristics. This paper aims to obtain a better characterization of popular heuristics used for this kind of problems by analysis of the transition graph of admissible moves. Our analysis shows, that both Manhattan distance and Tiles out of place heuristics work properly only near the goal, otherwise the information they provide is next to useless for a single move, IDA* with these heuristics works mainly due to reduction of branching of the search tree, for more consecutive moves.
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Acknowledgements
The work was in part supported by the grant APVV-17-0116 Algorithm of collective intelligence: Interdisciplinary study of swarming behaviour in bats, and the grant VEGA 1/0145/18 Optimization of network security by computational intelligence.
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Dirgová Luptáková, I., Pospíchal, J. (2021). Transition Graph Analysis of Sliding Tile Puzzle Heuristics. In: Matoušek, R., Kůdela, J. (eds) Recent Advances in Soft Computing and Cybernetics. Studies in Fuzziness and Soft Computing, vol 403. Springer, Cham. https://doi.org/10.1007/978-3-030-61659-5_13
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