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

As consequences of disruptions in railway traffic affect passenger experience/satisfaction, appropriate dispatching decisions are necessary. The problem of optimal scheduling the order of trains is 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 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. This paper introduces QUBO and HOBO representations for dispatching 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. We consider the conditions of minimal span between trains, minimal stay on stations, track occupation, and rolling stock circulation. Furthermore, a hybrid algorithm is presented that allows obtaining better solutions compared to the ordinary approach. We demonstrate the implementation on the D-Wave Quantum Processing Unit and its hybrid solver.