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Harmony search based memetic algorithms for solving sudoku

Author

Listed:
  • Assif Assad

    (Indian Institute of Technology Roorkee)

  • Kusum Deep

    (Indian Institute of Technology Roorkee)

Abstract

The development of hybrid procedures for optimization focuses on enhancing the strength and compensating for the weakness of two or more complementary approaches. The goal is to intelligently combine the key elements of the competing methodologies to create a superior solution procedure. The objective of this paper is to explore the hybridization between Harmony Search and Hill Climbing algorithm by utilizing the exploration power of the former and exploitation power of the latter in the context of solving Sudoku which is a well-known hard combinatorial optimization problem. We call this hybrid algorithm Harmony Search Hill Climber (HSHC). In order to extend the exploration capabilities of HSHC it is further modified to create three different algorithms namely Retrievable Harmony Search Hill Climber (RHSHC), Global Best Retrievable Harmony Search Hill Climber (GB-RHSHC) and Random Best Retrievable Harmony Search Hill Climber (RB-RHSHC). Comparing the four algorithms proposed in this paper RHSHC outperforms its three variations in terms of effectiveness. Experimental results demonstrate that RHSHC perform significantly better than standard Harmony Search algorithm and standard Hill climber algorithm. On comparing RHSHC with the genetic algorithm it has been concluded that former outperforms latter both in terms of effectiveness and efficiency particularly for Hard and Expert level puzzles. Comparing RHSHC and hybrid AC3-tabu search algorithm it has been concluded that RHSHC is very competent to hybrid AC3-tabu search algorithm.

Suggested Citation

  • Assif Assad & Kusum Deep, 2018. "Harmony search based memetic algorithms for solving sudoku," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(4), pages 741-754, August.
    • Handle: RePEc:spr:ijsaem:v:9:y:2018:i:4:d:10.1007_s13198-017-0620-x
    DOI: 10.1007/s13198-017-0620-x
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    References listed on IDEAS

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    1. Harish Sharma & Jagdish Chand Bansal & K. V. Arya & Xin-She Yang, 2016. "Lévy flight artificial bee colony algorithm," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(11), pages 2652-2670, August.
    2. Weyland, Dennis, 2015. "A critical analysis of the harmony search algorithm—How not to solve sudoku," Operations Research Perspectives, Elsevier, vol. 2(C), pages 97-105.
    3. Mohammed Al-Betar & Ahamad Khader, 2012. "A harmony search algorithm for university course timetabling," Annals of Operations Research, Springer, vol. 194(1), pages 3-31, April.
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