Quadratic and Higher-Order Unconstrained Binary Optimization of Railway Rescheduling for Quantum Computing

TL;DR

This paper presents novel QUBO and HOBO formulations for railway rescheduling problems, enabling quantum annealing solutions that consider complex track and station conditions, with a hybrid quantum-classical approach demonstrated on D-Wave hardware.

Contribution

Introduces a new HOBO formulation for railway rescheduling, extending quantum optimization methods to multi-track and station scenarios.

Findings

Successful implementation on D-Wave quantum hardware

Effective encoding of complex railway constraints in QUBO/HOBO

Hybrid quantum-classical approach improves rescheduling solutions

Abstract

As consequences of disruptions in railway traffic affect passenger experience/satisfaction, appropriate rerouting and/or rescheduling is necessary. These problems are known to be NP-hard, given the numerous restrictions of traffic nature. With the recent advances in quantum technologies, quantum annealing has become an alternative method to solve such optimization problems. To use quantum annealing, the problem needs to be encoded in QUBO (quadratic unconstrained binary optimization) or HOBO (higher-order binary optimization) formulation that can be recast as a QUBO. This paper introduces QUBO and HOBO representations for rescheduling problems of railway traffic management; the latter is a new approach up to our knowledge. This new approach takes into account not only the single-track lines but also the double- and multi-track lines, as well as stations composed of tracks and switches. We consider the conditions of minimal headway between trains, minimal stay on stations, track occupation, and rolling stock circulation. Furthermore, a hybrid quantum-classical procedure is presented that includes rerouting. We demonstrate the proof of concept implementation on the D-Wave Quantum Processing Unit and D-Wave hybrid solver.