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Journal of Optimization
Volume 2017, Article ID 5650364, 8 pages
https://doi.org/10.1155/2017/5650364
Research Article

A Genetic Algorithm Based Approach for Solving the Minimum Dominating Set of Queens Problem

1Computer Science Department, Taibah University, Medina, Saudi Arabia
2School of Computer Sciences, Universiti Sains Malaysia, Penang, Malaysia

Correspondence should be addressed to Saad Alharbi; moc.liamg@02ibrahlas

Received 20 February 2017; Revised 24 April 2017; Accepted 3 May 2017; Published 4 June 2017

Academic Editor: Gexiang Zhang

Copyright © 2017 Saad Alharbi and Ibrahim Venkat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Burger, C. Mynhardt, and W. D. Weakley, “The domination number of the toroidal queens graph of size 3k x 3k,” Australasian Journal of Combinatorics, vol. 28, pp. 137–148, 2003. View at Google Scholar
  2. A. P. Burger and C. M. Mynhardt, “An improved upper bound for queens domination numbers,” Discrete Mathematics, vol. 266, no. 1–3, pp. 119–131, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  3. E. J. Cockayne, “Chessboard domination problems,” Annals of Discrete Mathematics, vol. 48, pp. 13–20, 1991. View at Publisher · View at Google Scholar · View at Scopus
  4. E. J. Cockayne and S. T. Hedetniemi, “On the diagonal queens domination problem,” Journal of Combinatorial Theory, Series A, vol. 42, no. 1, pp. 137–139, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  5. T. Kikuno, N. Yoshida, and Y. Kakuda, “A linear algorithm for the domination number of a series-parallel graph,” Discrete Applied Mathematics, vol. 5, no. 3, pp. 299–311, 1983. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. A. Klobučar, “Domination numbers of cardinal products P_6 × P_n,” Mathematical Communications, vol. 4, no. 2, pp. 241–250, 1999. View at Google Scholar
  7. N. Sari and D. IH Agustin, On the Domination Number of Some Graph Operations, 2016.
  8. S. S. Venkatesan and Venkatesan S., “Tight lower bounds for connected queen domination problems on the chessboard,” https://arxiv.org/abs/1608.02531.
  9. B. Doerr, A. Eremeev, C. Horoba, F. Neumann, and M. Theile, “Evolutionary algorithms and dynamic programming,” in Proceedings of the 11th annual conference on genetic and evolutionary computation, pp. 771–778, ACM, Québec, Canada, 2009.
  10. M. Mavrovouniotis, C. Li, and S. Yang, “A survey of swarm intelligence for dynamic optimization: algorithms and applications,” Swarm and Evolutionary Computation, vol. 33, pp. 1–17, 2017. View at Google Scholar
  11. D. Karaboga, B. Gorkemli, C. Ozturk, and N. Karaboga, “A comprehensive survey: artificial bee colony (ABC) algorithm and applications,” Artificial Intelligence Review, vol. 42, pp. 21–57, 2014. View at Publisher · View at Google Scholar · View at Scopus
  12. R. S. Kadadevaramath, J. C. H. Chen, B. L. Shankar, and K. Rameshkumar, “Application of particle swarm intelligence algorithms in supply chain network architecture optimization,” Expert Systems with Applications, vol. 39, no. 11, pp. 10160–10176, 2012. View at Publisher · View at Google Scholar · View at Scopus
  13. Y. Marinakis, A. Migdalas, and A. Sifaleras, “A hybrid particle swarm optimization—variable neighborhood search algorithm for constrained shortest path problems,” European Journal of Operational Research, vol. 261, no. 3, pp. 819–834, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  14. M. Akhand, S. Hossain, and S. Akter, “A comparative study of prominent particle swarm optimization based methods to solve traveling salesman problem,” International Journal of Swarm Intelligence and Evolutionary Computation, vol. 5, no. 139, p. 2, 2016. View at Google Scholar
  15. M. Srinivas and L. M. Patnaik, “Genetic algorithms: a survey,” Computer, vol. 27, no. 6, pp. 17–26, 1994. View at Publisher · View at Google Scholar · View at Scopus
  16. D. E. Goldberg and J. H. Holland, “Genetic algorithms and machine learning,” Machine Learning, vol. 3, no. 2-3, pp. 95–99, 1998. View at Publisher · View at Google Scholar
  17. A. Barolli, M. Takizawa, F. Xhafa, and L. Barolli, “Application of genetic algorithms for QoS routing in mobile ad-hoc networks: A survey,” in Proceedings of the 5th International Conference on Broadband Wireless Computing, Communication and Applications (BWCCA '10), pp. 250–259, Fukuoka, Japan, November 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. B. M. Varghese and R. J. S. Raj, “A survey on variants of genetic algorithm for scheduling workflow of tasks,” in Proceedings of the 2nd International Conference on Science Technology Engineering and Management (ICONSTEM '16), 2016.
  19. A. Abu-Srhan and E. Al Daoud, “A hybrid algorithm using a genetic algorithm and cuckoo search algorithm to solve the traveling salesman problem and its application to multiple sequence alignment,” International Journal of Advanced Science and Technology, vol. 61, pp. 29–38, 2013. View at Google Scholar
  20. A. M. Allakany, T. M. Mahmoud, K. Okamura, and M. R. Girgis, “Multiple constraints QoS multicast routing optimization algorithm based on Genetic Tabu Search Algorithm,” Advances in Computer Science, vol. 4, no. 3, 2015. View at Google Scholar
  21. D. T. Pham, T. T. B. Huynh, and T. L. Bui, “A survey on hybridizing genetic algorithm with dynamic programming for solving the traveling salesman problem,” in Proceedings of the International Conference on Soft Computing and Pattern Recognition (SoCPaR '13), pp. 66–71, Hanoi, Vietnam, December 2013. View at Publisher · View at Google Scholar · View at Scopus
  22. I. Rivin, I. Vardi, and P. Zimmermann, “The n-queens problem,” The American Mathematical Monthly, vol. 101, no. 7, pp. 629–639, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  23. A. Bruen and R. Dixon, “The n-queens problem,” Discrete Mathematics, vol. 12, no. 4, pp. 393–395, 1975. View at Publisher · View at Google Scholar · View at MathSciNet
  24. C. Letavec and J. Ruggiero, “The n-queens problem,” INFORMS Transactions on Education, vol. 2, no. 3, pp. 101–103, 2002. View at Google Scholar
  25. R. Sosic and J. Gu, “3,000,000 Queens in less than one minute,” ACM SIGART Bulletin, vol. 2, no. 2, pp. 22–24, 1991. View at Google Scholar
  26. M. R. Engelhardt, “A group-based search for solutions of the n-queens problem,” Discrete Mathematics, vol. 307, no. 21, pp. 2535–2551, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  27. Z. Szaniszlo, M. Tomova, and C. Wyels, “The N-queens problem on a symmetric Toeplitz matrix,” Discrete Mathematics, vol. 309, no. 4, pp. 969–974, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  28. J. Bell and B. Stevens, “A survey of known results and research areas for n-queens,” Discrete Mathematics, vol. 309, no. 1, pp. 1–31, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  29. R. Sosič and J. Gu, “Efficient local search with conflict minimization: a case study of the n-queens problem,” IEEE Transactions on Knowledge and Data Engineering, vol. 6, no. 5, pp. 661–668, 1994. View at Publisher · View at Google Scholar · View at Scopus
  30. T. Kwok and K. A. Smith, “Experimental analysis of chaotic neural network models for combinatorial optimization under a unifying framework,” Neural Networks, vol. 13, no. 7, pp. 731–744, 2000. View at Publisher · View at Google Scholar · View at Scopus
  31. N. Funabiki, Y. Takenaka, and S. Nishikawa, “A maximum neural network approach for N-queens problems,” Biological Cybernetics, vol. 76, no. 4, pp. 251–255, 1997. View at Publisher · View at Google Scholar · View at Scopus
  32. J. Mandziuk and B. Macuk, “A neural network designed to solve the N-queens problem,” Biological Cybernetics, vol. 66, no. 4, pp. 375–379, 1992. View at Publisher · View at Google Scholar · View at Scopus
  33. Z. Wang, D. Huang, J. Tan, T. Liu, K. Zhao, and L. Li, “A parallel algorithm for solving the n-queens problem based on inspired computational model,” BioSystems, vol. 131, pp. 22–29, 2015. View at Publisher · View at Google Scholar · View at Scopus
  34. A. Maroosi and R. C. Muniyandi, “Accelerated execution of P systems with active membranes to solve the N-queens problem,” Theoretical Computer Science, vol. 551, pp. 39–54, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  35. R. Maazallahi, A. Niknafs, and P. Arabkhedri, “A polynomial-time dna computing solution for the n-queens problem,” Procedia—Social and Behavioral Sciences, vol. 83, pp. 622–628, 2013. View at Google Scholar
  36. A. Draa, S. Meshoul, H. Talbi, and M. Batouche, “A quantum-inspired differential evolution algorithm for solving the N-queens problem,” Neural Networks, vol. 1, p. 12, 2011. View at Google Scholar
  37. B. Keswani, Implementation of n-Queens Puzzle Using Meta-Heuristic Algorithm (Cuckoo Search) [Dissertation], Suresh Gyan Vihar University, 2013.
  38. A. A. Shaikh, A. Shah, K. Ali, and A. H. S. Bukhari, “Particle swarm optimization for N-queens problem,” Journal of Advanced Computer Science & Technology, vol. 1, no. 2, pp. 57–63, 2012. View at Google Scholar
  39. J. E. A. Heris and M. A. Oskoei, “Modified genetic algorithm for solving n-queens problem,” in Proceedings of the Iranian Conference on Intelligent Systems (ICIS '14), Bam, Iran, February 2014. View at Publisher · View at Google Scholar · View at Scopus
  40. S. Khan, M. Bilal, M. Sharif, M. Sajid, and R. Baig, “Solution of n-Queen problem using ACO,” in Proceedings of the IEEE 13th International Multitopic Conference (INMIC '09), pp. 1–5, IEEE, Islamabad, Pakistan, December 2009. View at Publisher · View at Google Scholar · View at Scopus
  41. N. Vaughan, “Swapping algorithm and meta-heuristic solutions for combinatorial optimization n-queens problem,” in Proceedings of the Science and Information Conference (SAI '15), pp. 102–104, London, UK, July 2015. View at Publisher · View at Google Scholar · View at Scopus
  42. E. Masehian, H. Akbaripour, and N. Mohabbati-Kalejahi, “Landscape analysis and efficient metaheuristics for solving the n-queens problem,” Computational Optimization and Applications, vol. 56, no. 3, pp. 735–764, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  43. A. P. Burger and C. M. Mynhardt, “An upper bound for the minimum number of queens covering the n×n chessboard,” Discrete Applied Mathematics, vol. 121, no. 1–3, pp. 51–60, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  44. W. D. Weakley, “Upper bounds for domination numbers of the queen's graph,” Discrete Mathematics, vol. 242, no. 1–3, pp. 229–243, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  45. P. Gibbons and J. Webb, “Some new results for the queens domination problem,” Australasian Journal of Combinatorics, vol. 15, pp. 145–160, 1997. View at Google Scholar
  46. S. Bozóki, P. Gál, I. Marosi, and W. D. Weakley, “Domination of the rectangular queen's graph,” https://arxiv.org/abs/1606.02060.
  47. H. Fernau, “Minimum dominating set of queens: a trivial programming exercise?” Discrete Applied Mathematics, vol. 158, no. 4, pp. 308–318, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  48. N. Mohabbati-Kalejahi, H. Akbaripour, and E. Masehian, “Basic and hybrid imperialist competitive algorithms for solving the non-attacking and non-dominating n-queens problems,” in Computational Intelligence: International Joint Conference, IJCCI 2012 Barcelona, Spain, October 5–7, 2012 Revised Selected Papers, K. Madani, A. D. Correia, A. Rosa, and J. Filipe, Eds., pp. 79–96, Springer, 2015. View at Google Scholar