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.

中文翻译：

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乐队搭配问题

为了降低电信部门的成本，已经开发了许多数学模型。随着时间的流逝，这些模型要么不再使用，要么根据新技术的发展进行修订。带通问题（BP）是2004年引入的优化问题，目的是降低通信网络中的硬件成本。但是，随着时间的流逝，光纤网络的技术进步已导致BP失去功能和可用性。应该对模型进行重大更改以使BP重新运行。在进行了这些更改之后，有必要将问题定义为新问题，而不是修订后的问题。在本文中，我们首先回顾一下BP。然后，我们讨论BP由于技术发展而变得无法使用的概念。我们引入了一个新问题，称为频带配置问题（BCP），解决了BP中的问题。我们还开发了BCP的几种数学模型。此外，我们证明了BCP是NP-hard。为了鼓励进一步的研究，我们开发了一个带搭配问题库。最后，我们提出启发式和元启发式方法来求解BCP并比较计算结果。