Routing and Wavelength Assignment with Protection: A Quadratic Unconstrained Binary Optimization Approach

TL;DR

This paper introduces a novel quadratic unconstrained binary optimization (QUBO) model for the routing and wavelength assignment problem with protection in optical networks, leveraging quantum-inspired technology for improved solution efficiency.

Contribution

It formulates a new QUBO model for the problem, provides conditions for model exactness, and demonstrates the effectiveness of a digital annealer over traditional methods.

Findings

Digital Annealer outperforms GUROBI in solution quality and speed.

QUBO model achieves comparable or better solutions in significantly less time.

Problem-specific heuristic is less effective than DA and exact models.

Abstract

The routing and wavelength assignment with protection is an important problem in telecommunications. Given an optical network and incoming connection requests, a commonly studied variant of the problem aims to grant maximum number of requests by assigning lightpaths at minimum network resource usage level, while ensuring the provided services remain functional in case of a single-link failure through dedicated path protection. We consider a practically relevant version where alternative lightpaths for requests are assumed to be given as a precomputed set, and show that it is NP-hard. We formulate the problem as an integer programming (IP) model, and also use it as a foundation to develop a novel quadratic unconstrained binary optimization (QUBO) model, which can be both directly solved by a state-of-the-art solver like GUROBI. We present necessary and sufficient conditions on objective function parameters to prioritize request granting objective over wavelength-link usage for both models, and a sufficient condition to ensure the exactness of the QUBO model. Moreover, we implement a problem-specific branch-and-cut algorithm for the IP model, and employ a new quantum-inspired technology, Digital Annealer (DA), for the QUBO model. We conduct computational experiments on a large suite of instances that are hard to optimally solve in order to assess the efficiency and efficacy of all of these approaches as well as a problem-specific heuristic. The results show that the emerging technology DA outperforms the considered established techniques coupled with GUROBI, in finding mostly significantly better or as good solutions in only two minutes compared to two hours of run time, whereas the problem-specific heuristic fails to be competitive.