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    The band collocation problem
    (Springer, 2020) Kutucu, Hakan; Gursoy, Arif; Kurt, Mehmet; Nuriyev, Urfat
    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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    A Heuristic Algorithm for the Band Collocation Problem
    (Ieee, 2016) Gursoy, Arif; Kurt, Mehmet; Kutucu, Hakan; Nuriyev, Urfat
    In this paper we present a heuristic algorithm for the The Band Collocation Problem (BCP) which may have some applications in the field of telecommunication. First, we give the definition the BCP. Second, we explain how we create the problem instances with known optimal solutions as a library. Third, we propose the heuristic algorithm. Then, we analysis and interpret the results of the proposed algorithm on the problem instances with known optimal solutions. Finally, we suggest new ideas about the BCP and its solution approaches.
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    New heuristics and meta-heuristics for the Bandpass problem
    (Elsevier - Division Reed Elsevier India Pvt Ltd, 2017) Gursoy, Arif; Kurt, Mehmet; Kutucu, Hakan; Nuriyev, Urfat
    The Bandpass problem (BP), modelled by Babayev et al., is a combinatorial optimization problem arising in optical communication networks using wavelength division multiplexing technology. The BP aims to design an optimal packing of information flows on different wavelengths into groups to obtain the highest available cost reduction. In this paper, we propose new methods to solve the BP. Firstly, we present two new heuristic algorithms which generate better solutions than the algorithm introduced by Babayev et al. for almost all of the problem instances of the BP library. Secondly, we present a new meta-heuristic algorithm using three different crossover and five different mutation operators. Totally, fifteen implementations have been created and tested using two different outputs which are obtained by our proposed heuristics as the initial population. The experimental results show that the proposed meta-heuristic algorithm improves the solutions. (C) 2017 Karabuk University. Publishing services by Elsevier B.V.
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    ON THE COMPLEXITY OF THE BANDPASS PROBLEM
    (Inst Applied Mathematics, 2023) Kurt, Mehmet; Kutucu, Hakan; Gursoy, Arif; Nuriyev, Urfat
    In this paper, we prove that the Bandpass Problem is NP-hard by restriction from the Bandpass Problem to the Satisfiability Problem. Furthermore, we define the 1-Bandpass De-cision Problem, and show that there is a one-to-one correspondence between the k-Satisfiability Decision Problem and the 1-Bandpass Decision Problem.