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Journal of Optical Communications and Networking

Routing and wavelength assignment problems in optical networks—comparing formulations for solution by quantum annealing

Ethan Davies, Darren Banfield, Ben Weaver, Catherine White, Nigel Walker

Published Nov 14, 2025• 3 citations
Publisher

Abstract

We develop four different quadratic unconstrained binary optimization formulations of routing problems relevant to the optical transport layers in telecommunications networks. Our formulations handle joint routing and wavelength assignment, unicast, multicast trees, and shared risk avoidance. We show that this approach is viable, even for multicast, and we test and compare the effectiveness of each formulation at solving these problems using the DWave hybrid solver. We describe expedients we applied to ensure valid solutions, along with challenges of the QUBO approach.

DOI
10.1364/jocn.553657

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We develop four different quadratic unconstrained binary optimization formulations of routing problems relevant to the optical transport layers in telecommunications networks. Our formulations handle joint routing and wavelength assignment, unicast, multicast trees, and shared risk avoidance. We show that this approach is viable, even for multicast, and we test and compare the effectiveness of each formulation at solving these problems using the DWave hybrid solver. We describe expedients we applied to ensure valid solutions, along with challenges of the QUBO approach.
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Vehicle Routing Problem is a well-known optimization issue, which has many extensions resulting from practical appliances. The problem is NP-hard, therefore it may be impossible to find an optimal solution for big instances, with traditional computation methods. Recent development of quantum technology, may be a response for this challenge, which however requires a different formulation of the model. The problem is then modeled using Quadratic Unconstrained Binary Optimization (QUBO) equations. Such model can be run using quantum annealers (QA), designed specifically for optimization purposes. This paper is a systematic survey of Vehicle Routing Problem models that are formulated using QUBO, to be solved on quantum computers. The main goal of the paper is to check research gaps in this subject, compare and explain different approaches of modeling various problem extensions with QUBO. The results obtained in reviewed papers will be presented and analyzed. Moreover, the theoretical basis for quantum computation will be presented, with focus on D-Wave company solutions.