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Application of New Hybrid Harmony Search Algorithms Based on Cellular Automata Theory for Solving Magic Square Problems

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Proceedings of Fourth International Conference on Soft Computing for Problem Solving

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 335))

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Abstract

Magic square construction is a complex and hard permutation problem of recreational combinatorics with a long history. The complexity level enhances rapidly when the number of magic squares increases with the order of magic square. This paper proposes two hybrid metaheuristic algorithms, so-called cellular harmony search (CHS) and smallest-small-world cellular harmony search (SSWCHS) for solving magic square problems. The inspiration of the CHS is based on the cellular automata (CA) formation, while the SSWCHS is inspired by the structure of smallest-small-world network (SSWN) and CA using the concept of HS. Numerical optimization results obtained are compared with different optimizers in terms of statistical results and number of found feasible solutions. Computational results show that the proposed hybrid optimizers are computationally effective and highly efficient for tackling magic square problems.

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Acknowledgments

This work was supported by the National Research Foundation of Korean (NRF) grant funded by the Korean government (MSIP) (NRF-2013R1A2A1A01013886).

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Authors and Affiliations

  1. School of Civil, Environmental and Architectural Engineering, Korea University, Seoul, 136-713, Republic of Korea

    Do Guen Yoo, Ali Sadollah, Joong Hoon Kim & Ho Min Lee

Authors
  1. Do Guen Yoo
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  2. Ali Sadollah
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  3. Joong Hoon Kim
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  4. Ho Min Lee
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Corresponding author

Correspondence to Do Guen Yoo .

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Editors and Affiliations

  1. Mathematics, National Institute of Technology Silchar, Silchar, Assam, India

    Kedar Nath Das

  2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India

    Kusum Deep

  3. Department of Paper Technology, Indian Institute of Technology Roorkee, Roorkee, India

    Millie Pant

  4. Department of Mathematics, South Asian University, New Delhi, India

    Jagdish Chand Bansal

  5. Department of Computer Science, Liverpool Hope University, Liverpool, United Kingdom

    Atulya Nagar

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Guen Yoo, D., Sadollah, A., Kim, J.H., Lee, H.M. (2015). Application of New Hybrid Harmony Search Algorithms Based on Cellular Automata Theory for Solving Magic Square Problems. In: Das, K., Deep, K., Pant, M., Bansal, J., Nagar, A. (eds) Proceedings of Fourth International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 335. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2217-0_21

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  • DOI: https://doi.org/10.1007/978-81-322-2217-0_21

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  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-2216-3

  • Online ISBN: 978-81-322-2217-0

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