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A novel hybrid genetic algorithm-based firefly mating algorithm for solving Sudoku

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Abstract

Sudoku is an NP-complete-based mathematical puzzle, which has enormous applications in the domains of steganography, visual cryptography, DNA computing, and so on. Therefore, solving Sudoku effectively can bring revolution in various fields. Several heuristics are there to solve this interesting structure. One of the heuristics, genetic algorithm, is used by many researchers to solve Sudoku successfully, but they face various problems. Genetic algorithm has so many lacunas, and to overcome these, we have hybridised it in a novel way. In this paper, we have developed a hybrid genetic algorithm-based firefly mating algorithm, which can solve Sudoku instances with a greater success rate for easy, medium, and hard difficulty level puzzles. Our proposed method has controlled “getting stuck in local optima”, considering a smaller population and lesser generation.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Haldia Institute of Technology, Haldia, Purba Medinipur, West Bengal, 721657, India

    Sunanda Jana

  2. Department of Computer Science and Engineering, University of Calcutta, JD-2, Sector-III, Salt Lake, Kolkata, West Bengal, 700106, India

    Anamika Dey & Rajat Kumar Pal

  3. Department of Information Technology, North-Eastern Hill University, Umshing Mawkynroh, Shillong, Meghalaya, 793022, India

    Arnab Kumar Maji

Authors
  1. Sunanda Jana
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  2. Anamika Dey
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  3. Arnab Kumar Maji
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  4. Rajat Kumar Pal
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Correspondence to Arnab Kumar Maji.

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Appendix

Appendix

In this paper, all experimental results have been computed based on only three sets of Sudoku instances of type Easy, Medium, and Hard, and for each such set, particularly, we have utilised 50 specific Sudoku instances that were selected randomly. Out of these 150 instances in total, only 12 instances of each of easy, medium, and hard have been included below as example Sudoku instances.

1.1 Sample easy Sudoku instances

figure b

1.2 Sample medium Sudoku instances

figure c

1.3 Sample hard Sudoku instances

figure d

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Jana, S., Dey, A., Maji, A.K. et al. A novel hybrid genetic algorithm-based firefly mating algorithm for solving Sudoku. Innovations Syst Softw Eng 17, 261–275 (2021). https://doi.org/10.1007/s11334-021-00397-4

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  • DOI: https://doi.org/10.1007/s11334-021-00397-4

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