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Artificial Bee Colony Algorithm for Solving the Knight’s Tour Problem

  • Anan Banharnsakun
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 866)

Abstract

The knight’s tour problem is one of the most interesting classic chessboard puzzles, in which the objective is to construct a sequence of admissible moves made by a chess knight from square to square in such a way that it lands upon every square of a chessboard exactly once. In this work, we consider the knight’s tour problem as an optimization problem and propose the artificial bee colony (ABC) algorithm, one of the most popular biologically inspired methods, as an alternative approach to its solution. In other words, we aim to present an algorithm for finding the longest possible sequence of moves of a chess knight based on solutions generated by the ABC method. Experimental results obtained by our method demonstrate that the proposed approach works well for constructing a sequence of admissible moves of a chess knight and outperforms other existing algorithms.

Keywords

Artificial Bee Colony Knight’s Tour Problem Optimization Computational Intelligence Combinatorial Problem 

References

  1. 1.
    Watkins, J.J.: Across the board: the mathematics of chessboard problems. Princeton University Press (2004)Google Scholar
  2. 2.
    Ball, W.W.R., Coxeter, H.S.M.: Mathematical Recreations And Essays, 13th edn. Dover, New York (1987)Google Scholar
  3. 3.
    Borrell, R.A.: Brute force approach to solving the knight’s tour problem using Prolog. In: Proceedings of the 2009 International Conference on Artificial Intelligence (ICAI 2009), vol. 2, pp. 600–604 (2009)Google Scholar
  4. 4.
    Lin, S.S., Wei, C.L.: Optimal algorithms for constructing knight’s tours on arbitrary n × m chessboards. Discret. Appl. Math. 146(3), 219–232 (2005)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Paris, L.: Heuristic strategies for the knight tour problem. In: Proceedings of the International Conference on Artificial Intelligence (IC-AI 2004), pp. 1121–1125 (2004)Google Scholar
  6. 6.
    Takefuji, Y., Lee, K.C.: Neural network computing for knight’s tour problems. Neurocomputing 4(5), 249–254 (1992)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Yang, X.S., Cui, Z., Xiao, R., Gandomi, A.H., Karamanoglu, M.: Swarm Intelligence And Bio-Inspired Computation: Theory And Applications. Newnes, Massachusetts (2013)CrossRefGoogle Scholar
  8. 8.
    Goldberg, D.E.: Genetic Algorithms. Pearson Education, India (2006)Google Scholar
  9. 9.
    Dorigo, M., Birattari, M., Stutzle, T.: Ant colony optimization. IEEE Comput. Intell. Mag. 1(4), 28–39 (2006)CrossRefGoogle Scholar
  10. 10.
    Poli, R., Kennedy, J., Blackwell, T.: Part. Swarm Optim. Swarm Intell. 1(1), 33–57 (2007)CrossRefGoogle Scholar
  11. 11.
    Yang, X.S.: Firefly algorithm, stochastic test functions and design optimisation. Int. J. Bio-Inspired Comput. 2(2), 78–84 (2010)CrossRefGoogle Scholar
  12. 12.
    Gordon, V.S., Slocum, T.J.: The knight’s tour - evolutionary vs. depth-first search. In: Proceedings of the 2004 IEEE Congress on Evolutionary Computation (CEC 2004), vol. 2, pp. 1435–1440 (2004)Google Scholar
  13. 13.
    Hingston, P., Kendall, G.: Enumerating knight’s tours using an ant colony algorithm. In: Proceedings of the 2005 IEEE Congress on Evolutionary Computation (CEC 2005), vol. 2, pp. 1003–1010 (2005)Google Scholar
  14. 14.
    Leonard, B.J., Engelbrecht, A.P.: Angle modulated particle swarm variants. In: Proceedings of the International Conference on Swarm Intelligence (ANTS 2014), pp. 38–49 (2014)Google Scholar
  15. 15.
    Ismail, M.M, et al.: Solving knight’s tour problem using firefly algorithm. In: Proceedings of the 3rd International Conference on Engineering and ICT (ICEI 2012), pp. 5–8 (2012)Google Scholar
  16. 16.
    Karaboga, D., Gorkemli, B., Ozturk, C., Karaboga, N.: A comprehensive survey: artificial bee colony (ABC) algorithm and applications. Artif. Intell. Rev. 42(1), 21–57 (2014)CrossRefGoogle Scholar
  17. 17.
    Karaboga, D., Basturk, B.: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J. Glob. Optim. 39(3), 459–471 (2007)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Banharnsakun, A., Tanathong, S.: Object detection based on template matching through use of best-so-far ABC. Computational Intelligence and Neuroscience 2014, article no. 7 (2014)Google Scholar
  19. 19.
    Banharnsakun, A.: A MapReduce-based artificial bee colony for large-scale data clustering. Pattern Recognit. Lett. 93, 78–84 (2017)CrossRefGoogle Scholar
  20. 20.
    Banharnsakun, A.: Hybrid ABC-ANN for pavement surface distress detection and classification. Int. J. Mach. Learn. Cybern. 8(2), 699–710 (2017)CrossRefGoogle Scholar
  21. 21.
    Banharnsakun, A.: Feature point matching based on ABC-NCC algorithm. Evol. Syst. 9(1), 71–80 (2018)CrossRefGoogle Scholar
  22. 22.
    Banharnsakun, A.: Artificial bee colony approach for enhancing LSB based image steganography. Multimed. Tools Appl. 77(20), 27491–27504 (2018)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Computational Intelligence Research Laboratory (CIRLab), Computer Engineering Department, Faculty of Engineering at SrirachaKasetsart University Sriracha CampusChonburiThailand

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