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Orthogonal Latin squares-based firefly optimization algorithm for industrial quadratic assignment tasks

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Abstract

The quadratic assignment problem (QAP) is one of the hardest combinatorial optimization tasks. It has many real-world applications such as airport gate assignment, and hospital layout problem. Designing enhanced optimization methodologies for the QAP is an active research area. In this paper, we present an integrated firefly algorithm (FA) based on mutually orthogonal Latin squares (MOLS), named as FA-MOLS, to solve the QAP. In the optimization process, the FA-MOLS employs three improvements, namely the MOLS strategy, opposition-based learning scheme, and repeated 2-exchange mutation to maintain the balance between exploitation and exploration abilities. By these improvements, it is intended to avoid the trapping in local optima and improve the convergence speed. The performance of the proposed FA-MOLS is validated on different test instances from the literature. Additionally, two real-world QAPs are simulated and investigated, the office buildings of a single company and the layout of hospital departments. The comprehensive experimental simulations and the nonparametric Wilcoxon’s test affirm that the proposed FA-MOLS can provide a highly competitive performance compared with other algorithms from the literature. Therefore, it is concluded that FA-MOLS is an efficient and reliable algorithm for solving industrial quadratic assignment tasks.

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Author information

Authors and Affiliations

  1. Department of Basic Engineering Science, Faculty of Engineering, El-Menoufia University, Shebin El-Kom, Egypt

    Rizk Masoud Rizk-Allah

  2. Department of Electronics and Computer Science, Koszalin University of Technology, 75-452, Koszalin, Poland

    Adam Slowik

  3. Faculty of Science, Helwan University, Cairo, Egypt

    Ashraf Darwish

  4. Faculty of Computers and Artificial Intelligence, Cairo University, Giza, 12613, Egypt

    Aboul Ella Hassanien

Authors
  1. Rizk Masoud Rizk-Allah
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  2. Adam Slowik
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  3. Ashraf Darwish
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  4. Aboul Ella Hassanien
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Correspondence to Aboul Ella Hassanien.

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Appendices

Appendix A: Building data

The data of the distance (Fig. 12) and flow (Fig. 13) matrices for layout of company buildings.

Fig. 12
figure 12

Distance matrix for layout of company buildings

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Fig. 13
figure 13

Flow matrix for layout of company buildings

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Appendix B: Hospital layout data

The data of the distance (Fig. 14) and flow (Fig. 15) matrices for layout of hospital departments.

Fig. 14
figure 14

Distance matrix for layout of hospital departments

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Fig. 15
figure 15

Flow matrix for layout of hospital departments

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Rizk-Allah, R.M., Slowik, A., Darwish, A. et al. Orthogonal Latin squares-based firefly optimization algorithm for industrial quadratic assignment tasks. Neural Comput & Applic 33, 16675–16696 (2021). https://doi.org/10.1007/s00521-021-06262-6

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  • DOI: https://doi.org/10.1007/s00521-021-06262-6

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