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The band collocation problem

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Abstract

In order to reduce costs in the telecommunication sector, many mathematical models have been developed. Over time, these models either fall out out of use or are revised according to new technological developments. The Bandpass Problem (BP) is an optimization problem introduced in 2004 to reduce hardware costs in communication networks. However, over time, technological advances in fiber-optic networks have caused the BP to lose functionality and usability. Major changes should be made to the model to make the BP functional again. It is necessary to define the problem after having made these changes as a new problem, not as a revised problem. In this paper, we first review the BP. We then discuss the notion that the BP has become unusable due to technological developments. We introduce a new problem called the Band Collocation Problem (BCP), which fixes the issues in the BP. We also develop several mathematical models of the BCP. Furthermore, we prove that the BCP is NP-hard. In order to encourage further research, we develop a Library of Band Collocation Problems. Finally, we present heuristic and meta-heuristic methods to solve the BCP and compare the computational results.

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Acknowledgements

The authors are grateful to the anonymous referees for their constructive comments and valuable suggestions which have helped us very much to improve the quality of the paper.

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Authors and Affiliations

  1. Department of Computer Engineering, Karabuk University, Karabuk, Turkey

    Hakan Kutucu

  2. Department of Mathematics, Ege University, Izmir, Turkey

    Arif Gursoy & Urfat Nuriyev

  3. Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

    Mehmet Kurt

  4. Institute of Control Systems of Azerbaijan National Academy of Sciences, Baku, Azerbaijan

    Urfat Nuriyev

Authors
  1. Hakan Kutucu
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  2. Arif Gursoy
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  3. Mehmet Kurt
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  4. Urfat Nuriyev
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Correspondence to Arif Gursoy.

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Kutucu, H., Gursoy, A., Kurt, M. et al. The band collocation problem. J Comb Optim 40, 454–481 (2020). https://doi.org/10.1007/s10878-020-00576-2

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