Efficient Mixed Integer Linear Programming Approaches to Dynamic Path Restoration

TL;DR

The paper tackles dynamic restoration after a single link failure in elastic optical networks (flex-grid RSA) and provides MILP formulations for the generalized RSA problem and its maximum-subset variant to obtain ground-truth solutions. A trimming procedure removes useless colors and triples, and a max-flow–style MILP uses variables $x^{d,l}_{c}$ over directed links with color-contiguity and non-overlap constraints to ensure feasible, non-intersecting paths when possible. The key contribution is the trimming-based reduction of MILP size (to $O(|U|)$) and substantial speedups on real network topologies (NSFNET, USNET) with a mix of modulation schemes, enabling efficient ground-truth computation to evaluate heuristics. The work also compares indexing strategies with prior RSA models, demonstrating practical gains by avoiding path enumeration and leveraging activation-based constraints for contiguity, with broad applicability to restoration and spectrum assignment in flex-grid networks.

Abstract

We consider the problem of single link failure in an elastic optical network, (also known as flex-grid WDM network). The task is to reroute optical connections that go through the broken link using free capacity of other links of the network. Nowadays, dynamic restoration gains popularity, in which the possiblity of rerouting is only inspected after a link failure is detected. Since the problem of recovery is NP-hard, heuristic algorithms are used to either find such routes, or suggest that the routes do not exist. In order to understand the quality of these heuristics, often mixed integer linear programming is used to obtain exact positive and negative answers. We present a detailed such model that checks whether restoration is possible without the use of additional regenerators. This means, that the new light paths need to satisfy a length constraint. As preprossing we apply a trimming procedure that takes advantage of this length constraint, and significantly speeds up the evaluation of these models. Our model is more general, and besides solving the problem of link restoration, also solves the full problem of wavelength and spectrum assignment.