An N-Puzzle Solver Using Tissue P System with Evolutional Symport/Antiport Rules and Cell Division

  • Resmi RamachandranPillaiEmail author
  • Michael Arock
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1048)


An N-puzzle is a sliding blocks game that takes place on a grid with tiles each numbered from 1 to N. Many strategies like branch and bound and iterative deepening are exist in the literature to find the solution of the puzzle. But, here, a different membrane computing algorithm also called P systems, motivated from the structure and working of the living cell has been used to obtain the solution. A variation of P system, called tissue P system with evolutional symport/antiport (TPSESA) rules, is used to solve the puzzle. It has been proved that the power of computation of TPSESA rules with membrane division is universal Turing computable. In this paper, a concept of dynamic membrane division is also considered so that it completely simulates the behavior of a living cell. On the basis of experiments performed on a sample of different instances, the proposed algorithm is very efficient and reliable. As far as the author is concerned, this is the first time, an N-Puzzle problem is solved using the framework of membrane computing.


Membrane computing Symport/antiport Active membranes 


  1. 1.
    Paun, G.: Introduction to Membrane. Computing (2006). Scholar
  2. 2.
    Maroosi, A., Muniyandi, R.C.: Accelerated execution of P system with active membranes to solve the N-queens problem. Theor. Comput. Sci. 551, 39–54 (2014)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Alhazov, A., Pan, L., Paun, G.: Trading polarizations for labels in P systems with active membranes. IJISCE 3 (2010)Google Scholar
  4. 4.
    Alhazov, A., Freund, R.: Polarization less P systems with one active membrane. In: International Conference on Membrane Computing. Springer, Berlin (2015)CrossRefGoogle Scholar
  5. 5.
    Xiang, L., Xue, J.: Solving job shop scheduling problems by P system with active membranes. In: 7th International Conference on Intelligent Human-Machine Systems and Cybernetics. 978-1-4799-8646-0/15 $ 31.00. IEEE (2015)Google Scholar
  6. 6.
    Song, B., Zhang, C., Pan, L.: Tissue -like P systems with evolutional symport/antiport rules. Elsevier 378, 177–193 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Bhasin, H., Singla, N.: Modified genetic algorithms based solution to subset sum problem. IJARAI 1 (2012)Google Scholar
  8. 8.
    Hayes, R.: The Sam Loyd 15-Puzzle. Dublin, Trinity College Dublin, Department of Computer Science, TCD-CS-2001-24, p. 28 (2001)Google Scholar
  9. 9.
    Bauer, B.: The Manhattan Pair Distance Heuristic for the 15 Puzzle. Paderborn, Germany (1994)Google Scholar
  10. 10.
    Calabro, C.: Solving the 15-Puzzle (2005).
  11. 11.
    Pizlo, Z., Li, Z.: Solving combinatorial problems: The 15-puzzle. Mem. Cogn. 33(6), 1069 (2005)CrossRefGoogle Scholar
  12. 12.
    Felner, A., Adler, A.: Solving the 24 puzzle with instance dependent pattern databases. In: Proceedings of the Sixth International Symposium on Abstraction, Reformulation and Approximation (SARA05), pp. 248–260 (2005)Google Scholar
  13. 13.
    Felner, A., Korf, R.E., Hanan, S.: Additive Pattern Database Heuristics. J. Artif. Intell. Res. (JAIR) 22, 279–318 (2004)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Drogoul, A., Dubreuil, C.: A distributed approach to N-puzzle solving. In: Proceedings of the Distributed Artificial Intelligence, pp. 95–108 (1993)Google Scholar
  15. 15.
    Bhasin, H., Singla, N.: Genetic based algorithm for N-Puzzle problem. Int. J. Comput. Appl. (0975-8887), 51(22) (2012)Google Scholar

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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.National Institute of TechnologyTiruchirappalliIndia

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