The Constrained-Routing and Spectrum Assignment Problem: Extended Formulation and Branch-and-Cut-and-Price Algorithm

In this paper, we study the Constrained-Routing and Spectrum Assignment (C-RSA) problem. Consider an undirected, loopless, and connected graph
${G}$
. Let
$\mathbb{S}$
be an optical spectrum of available contiguous frequency slots, and
${K}$
be a set of traffic demands. The C-RSA is to assign for each demand
${k\,\in \,K}$
a path in
${G}$
between its origin-destination nodes, and an interval of contiguous frequency slots in
$\mathbb{S}$
while respecting some technological constraints, and optimizing some linear objective function. First, we propose an extended integer linear programming formulation for the C-RSA. A column generation algorithm is developed to solve its linear relaxation. We also describe several valid inequalities for the polytope associated with this formulation, and address the related separation problems. Using these results, we derive a Branch-and-Cut-and-Price algorithm, along with computational results are presented using large-scale instances.