Abstract
This article introduces Evaluation-Function based Proof–Number Search (EF-PN) and its second-level variant EF-PN2. It is a framework for initializing the proof and disproof number of a leaf node with the help of a heuristic evaluation function. Experiments in LOA and Surakarta show that compared to PN and PN2, which use mobility to initialize the proof and disproof numbers, EF-PN and EF-PN2 take between 45% to 85% less time for solving positions. Based on these results, we may conclude that EF-PN and EF-PN2 reduce the search space considerably.
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References
Allis, L.V.: Searching for Solutions in Games and Artificial Intelligence. PhD thesis, Rijksuniversiteit Limburg, Maastricht, The Netherlands (1994)
Allis, L.V., van der Meulen, M., van den Herik, H.J.: Proof-number search. Artificial Intelligence 66(1), 91–123 (1994)
Breuker, D.M.: Memory versus Search in Games. PhD thesis, Universiteit Maastricht, Maastricht, The Netherlands (1998)
Breuker, D.M., Uiterwijk, J.W.H.M., van den Herik, H.J.: The PN2-search algorithm. In: van den Herik, H.J., Monien, B. (eds.) Advances in Computer Games 9, pp. 115–132. Maastricht University, Maastricht, The Netherlands (2001)
Kishimoto, A., Müller, M.: Search versus knowledge for solving life and death problems in Go. In: Veloso, M.M., Kambhampati, S. (eds.) AAAI 2005, pp. 1374–1379. AAAI Press / The MIT Press (2005)
Nagai, A.: A new depth-first-search algorithm for AND/OR trees. Master’s thesis, The University of Tokyo, Tokyo, Japan (1999)
Nagai, A.: Df-pn Algorithm for Searching AND/OR Trees and its Applications. PhD thesis, The University of Tokyo, Tokyo, Japan (2002)
Pawlewicz, J., Lew, Ł.: Improving Depth-First PN-Search: 1 + ε Trick. In: van den Herik, H.J., Ciancarini, P., Donkers, H.H.L.M(J.) (eds.) CG 2006. LNCS, vol. 4630, pp. 160–171. Springer, Heidelberg (2007)
Sakuta, M., Hashimoto, T., Nagashima, J., Uiterwijk, J.W.H.M., Iida, H.: Application of the killer-tree heuristic and the lamba-search method to Lines of Action. Information Sciences 154(3-4), 141–155 (2003)
Schaeffer, J.: Game over: Black to play and draw in checkers. ICGA Journal 30(4), 187–197 (2007)
Seo, M., Iida, H., Uiterwijk, J.W.H.M.: The PN*-search algorithm: Application to Tsume-Shogi. Artificial Intelligence 129(1-2), 253–277 (2001)
Winands, M.H.M.: Informed Search in Complex Games. PhD thesis, Universiteit Maastricht, Maastricht, The Netherlands (2004)
Winands, M.H.M.: SIA wins Surakarta tournament. ICGA Journal 30(3), 162 (2007)
Winands, M.H.M.: 6×6 LOA is Solved. ICGA Journal 31(3), 234–238 (2008)
Winands, M.H.M., Uiterwijk, J.W.H.M., van den Herik, H.J.: An effective two-level proof-number search algorithm. Theoretical Computer Science 313(3), 511–525 (2004)
Winands, M.H.M., van den Herik, H.J.: MIA: a world champion LOA program. In: The 11th Game Programming Workshop in Japan 2006, pp. 84–91 (2006)
Xu, C., Ma, Z.M., Tao, J., Xu, X.: Enhancements of proof number search in Connect6. In: Control and Decision Conference, pp. 4525–4529. IEEE, Los Alamitos (2009)
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Winands, M.H.M., Schadd, M.P.D. (2011). Evaluation-Function Based Proof-Number Search. In: van den Herik, H.J., Iida, H., Plaat, A. (eds) Computers and Games. CG 2010. Lecture Notes in Computer Science, vol 6515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17928-0_3
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DOI: https://doi.org/10.1007/978-3-642-17928-0_3
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