The Constrained-Routing and Spectrum Assignment (C-RSA) problem arises in the design of 5G telecommunication optical networks. Given an undirected, loopless, and connected graph G, an optical spectrum of available contiguous frequency slots \({\mathbb {S}}\), and a set of traffic demands K, the C-RSA consists of assigning, to each traffic demand \(k\in K\), a path in G between its origin and destination, and a subset of contiguous frequency slots in \({\mathbb {S}}\) subject to certain technological constraints while optimizing some linear objective function. In this paper, we devise an exact algorithm to solve the C-RSA. We first introduce an extended integer programming formulation for the problem. Then we investigate the associated polytope and introduce several classes of valid inequalities. Based on these results, we devise a Branch-and-Cut-and-Price algorithm for the problem and present an extensive computational study. This is also be compared with a Branch-and-Cut algorithm of the state-of-the-art.

5G电信光网络的设计中出现了约束路由和频谱分配（C-RSA）问题。给定一个无向、无环且连通的图G、可用连续频隙的光谱\({\mathbb {S}}\)以及一组流量需求K，C-RSA 包括分配给每个流量需求\(k\in K\) 、 G中其起点和目的地之间的路径以及\({\mathbb {S}}\)中的连续频率间隙的子集，在优化某些线性目标函数时受到某些技术限制。在本文中，我们设计了一种精确的算法来求解 C-RSA。我们首先介绍该问题的扩展整数规划公式。然后我们研究相关的多面体并引入几类有效的不等式。基于这些结果，我们为该问题设计了一种分支切割定价算法，并进行了广泛的计算研究。这也可以与最先进的分支剪切算法进行比较。