Basic and Hybrid Imperialist Competitive Algorithms for Solving the n-Queens Problem

Ellips Masehian, Nasrin Mohabbati-Kalejahi, Hossein Akbaripour

2012

Abstract

The n-queens problem is a classical combinatorial optimization problem which has been proved to be NP-hard. The goal is to place n non-attacking queens on an n×n chessboard. In this paper, the Imperialist Com-petitive Algorithm (ICA), which is a recent evolutionary metaheuristic method, has been applied for solving the n-queens problem. As another variation, the ICA was combined with a local search method, resulting the Hybrid ICA (HICA). Extensive experimental results showed that the proposed HICA outperformed the basic ICA in terms of average runtimes and average number of fitness function evaluations. The developed algorithms were also compared to the Cooperative PSO (CPSO) algorithm, which is currently the best algo-rithm in the literature for finding the first valid solution to the n-queens problem, and the results showed that the HICA dominates the CPSO by evaluating the fitness function fewer times.

References

  1. Abramson, B., and Yung, M., (1989). Divide and conquer under global constraints: A solution to the n-queens problem. Journal of Parallel and Distributed Computing, 6(3), 649-662.
  2. Amooshahi, A., Joudaki, M., Imani, M., and N. Mazhari., (2011). Presenting a new method based on cooperative PSO to solve permutation problems: A case study of nqueen problem. 3rd Int. Conference on Electronics Computer Technology (ICECT), 4, 218-222.
  3. Atashpaz-Gargari, E. and Lucas, C., (2007). Imperialist competitive algorithm: An algorithm for optimization inspired by imperialistic competition. IEEE congress on evolutionary computation, 4661-4667.
  4. Bell, J. and Stevens, B., (2009).A survey of known results and research areas for n-queens. Discrete Mathematics, 309, 1-31.
  5. Bezzel, M., (1848).Proposal of 8-queens problem, Berliner Schachzeitung, 3, 363.
  6. Campos, V., Laguna, M. and Mart, R., (2005). Contextindependent scatter search and tabu search for permutation problems. INFORMS J. Computing, 17, 111-122.
  7. Dirakkhunakon, S. and Suansook, Y., (2009). Simulated Annealing with iterative improvement. International Conference on Signal Processing Systems, 302-306.
  8. Draa, A., Meshoul, S., Talbi, H., and Batouche, M., (2010).A Quantum-Inspired Differential Evolution Algorithm for Solving the n-Queens Problem. The International Arab Journal of Information Technology, 7(1), 21-27.
  9. Draa, A., Talbi H., and Batouche, M., (2005). A Quantum Inspired Genetic Algorithm for Solving the N-Queens Problem, Proceedings of the 7th International Symposium on Programming and Systems, 145-152.
  10. Erbas, C., Sarkeshik, S. and Tanik, M. M., (1992). Different perspectives of the n-queens problem. Proceedings of the 1992 ACM Annual Conference on Communications, ACM Press, 99-108.
  11. Homaifar, A., Turner, J., and Ali, S., (1992). The nQueens Problem and Genetic Algorithms. Proceedings IEEE Southeast Conference, 1, 262-267.
  12. Jagota, A., (1993). Optimization by reduction to maximum clique. IEEE International Conference on Neural Networks, 3, 1526-1531.
  13. Kennedy, J. and Eberhart, R. C., (1995). Particle swarm optimization. Proceedings of IEEE Int'l. Conf. on Neural Networks, IV, 1942-1948.
  14. Khan, S., Bilal, M., Sharif, M., Sajid, M. and Baig, R., (2009). Solution of n-Queen Problem Using ACO.IEEE 13th International Multi-Topic Conference, 1-5.
  15. Kilani, Y., (2010). Comparing the performance of the genetic and local search algorithms for solving the satisfiability problems. Applied Soft Computing, 10, 198-207.
  16. Kosters, W., (2012). n-Queens Bibliography. Retrieved May 4, 2012, from http://www.liacs.nl/kosters/ nqueens/.
  17. Lionnet, F. J. E., (1869). Question 963, Nouvelles Annales de Mathématiques, 28, 560.
  18. Martinjak, I. and Golub, M., (2007). Comparison of Heuristic Algorithms for the N-Queen Problem. Proceedings of the ITI 2007 29th International. Conference on Information Technology Interfaces, 25-28.
  19. Minton, S., M. D. Johnston, A. Philips and P. Laird, (1990). Solving Large-Scale Constraint-Satisfaction and Scheduling Problems Using a Heuristic Repair Method. Proceedings of 8th National Conference on Artificial Intelligence, Boston, Massachusetts, AIAA Press.
  20. Nazari-Shirkouhi, S., Eivazy, H., Ghodsi, R., Rezaie, K. and Atashpaz-Gargari, E., (2010). Solving the integrated product mix-outsourcing problem using the Imperialist Competitive Algorithm. Expert Systems with Applications, 37, 7615-7626.
  21. Pauls, E., (1874). Das Maximalproblem der Damen auf dem Schachbrete, II, Deutsche Schachzeitung.Organ fur das Gesammte Schachleben, 29(9), 257-267.
  22. Rivin, I. and Zabih, R., (1992). A Dynamic Programming Solution to the n-Queens Problem. Information Processing Letters, 41, 253-256.
  23. Russell, S. J. and Norvig, P., (1995).Artificial Intelligence A Modern Approach. Prentice-Hall Inc., NJ.
  24. San Segundo, P., (2011). New decision rules for exact search in n-Queens. Journal of Global Optimization, 51, 497-514.
  25. Sloane, N. J. A., (2012). The online encyclopedia of integer sequences.retrieved from http://oeis.org/A000170.
  26. Sosic, R. and Gu, J., (1994). Efficient local search with conflict minimization.IEEE Transactions on Knowledge and Data Engineering, (6E), 661-668.
  27. Tambouratzis, T., (1997). A Simulated Annealing Artificial Neural Network Implementation of the n-Queens Problem. Int. J. of Intelligent Systems, 12, 739-752.
  28. Yang, X-S., (2010). Nature-inspired metaheuristic algorithms: Luniver Press.
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Paper Citation


in Harvard Style

Masehian E., Mohabbati-Kalejahi N. and Akbaripour H. (2012). Basic and Hybrid Imperialist Competitive Algorithms for Solving the n-Queens Problem . In Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2012) ISBN 978-989-8565-33-4, pages 87-95. DOI: 10.5220/0004160900870095


in Bibtex Style

@conference{ecta12,
author={Ellips Masehian and Nasrin Mohabbati-Kalejahi and Hossein Akbaripour},
title={Basic and Hybrid Imperialist Competitive Algorithms for Solving the n-Queens Problem},
booktitle={Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2012)},
year={2012},
pages={87-95},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004160900870095},
isbn={978-989-8565-33-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2012)
TI - Basic and Hybrid Imperialist Competitive Algorithms for Solving the n-Queens Problem
SN - 978-989-8565-33-4
AU - Masehian E.
AU - Mohabbati-Kalejahi N.
AU - Akbaripour H.
PY - 2012
SP - 87
EP - 95
DO - 10.5220/0004160900870095