Nested Column Generation decomposition for solving the Routing and Spectrum Allocation problem in Elastic Optical Networks

TL;DR

This paper introduces a nested column generation approach for the Routing and Spectrum Allocation problem in elastic optical networks, significantly improving solution accuracy and computational efficiency over previous methods.

Contribution

It develops a new mathematical model with two variable sets and applies nested column generation, achieving superior accuracy and speed compared to existing algorithms.

Findings

Achieved 1% accuracy gap versus 14.3% in previous work

Reduced running time by two orders of magnitude

Demonstrated effectiveness of nested column generation in this context

Abstract

With the continued growth of Internet traffic, and the scarcity of the optical spectrum, there is a continuous need to optimize the usage of this resource. In the process of provisioning elastic optical networks using the flexible frequency grid paradigm, telecommunication operators must deal with a combinatorial optimization problem that is NP-complete namely the Routing and Spectrum Allocation(RSA) problem. Following on our previous study, where we used Integer Linear Programming, and proposed a Column Generation algorithm based on a Lightpath decomposition, which proved to be the most efficient so far, we now consider the traditional Configuration decomposition that has been studied in other works in the past. In the process, we created an new mathematical model using two variable sets instead of a single variable set. Equally important,we independently rediscovered the Nested Column Generation technique, and we used it to propose an algorithm that led to a considerable improvement on the previous algorithms that use the same Configuration decomposition. When compared to the latest such existing study, our algorithm achieved an accuracy gap of 1% as opposed to 14.3% for the previous study, and a running time two orders of magnitude faster on average.