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A Novel Discrete Differential Evolution with Varying Variables for the Deficiency Number of Mahjong Hand

Author

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  • Xueqing Yan

    (School of Computer Science, Shaanxi Normal University, Xi’an 710062, China)

  • Yongming Li

    (School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710062, China)

Abstract

The deficiency number of one hand, i.e., the number of tiles needed to change in order to win, is an important factor in the game Mahjong, and plays a significant role in the development of artificial intelligence (AI) for Mahjong. However, it is often difficult to compute due to the large amount of possible combinations of tiles. In this paper, a novel discrete differential evolution (DE) algorithm is presented to calculate the deficiency number of the tiles. In detail, to decrease the difficulty of computing the deficiency number, some pretreatment mechanisms are first put forward to convert it into a simple combinatorial optimization problem with varying variables by changing its search space. Subsequently, by means of the superior framework of DE, a novel discrete DE algorithm is specially developed for the simplified problem through devising proper initialization, a mapping solution method, a repairing solution technique, a fitness evaluation approach, and mutation and crossover operations. Finally, several experiments are designed and conducted to evaluate the performance of the proposed algorithm by comparing it with the tree search algorithm and three other kinds of metaheuristic methods on a large number of various test cases. Experimental results indicate that the proposed algorithm is efficient and promising.

Suggested Citation

  • Xueqing Yan & Yongming Li, 2023. "A Novel Discrete Differential Evolution with Varying Variables for the Deficiency Number of Mahjong Hand," Mathematics, MDPI, vol. 11(9), pages 1-21, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2135-:d:1138303
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    References listed on IDEAS

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    1. David Silver & Julian Schrittwieser & Karen Simonyan & Ioannis Antonoglou & Aja Huang & Arthur Guez & Thomas Hubert & Lucas Baker & Matthew Lai & Adrian Bolton & Yutian Chen & Timothy Lillicrap & Fan , 2017. "Mastering the game of Go without human knowledge," Nature, Nature, vol. 550(7676), pages 354-359, October.
    2. David Silver & Aja Huang & Chris J. Maddison & Arthur Guez & Laurent Sifre & George van den Driessche & Julian Schrittwieser & Ioannis Antonoglou & Veda Panneershelvam & Marc Lanctot & Sander Dieleman, 2016. "Mastering the game of Go with deep neural networks and tree search," Nature, Nature, vol. 529(7587), pages 484-489, January.
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    Cited by:

    1. Jian Dong, 2023. "Preface to the Special Issue on “Recent Advances in Swarm Intelligence Algorithms and Their Applications”—Special Issue Book," Mathematics, MDPI, vol. 11(12), pages 1-4, June.

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