In this work, we consider a practical railway dispatching problem: delay and conflict management on a single-track railway line. We examine the issue of train dispatching consequences caused by the arrival of an already delayed train to the segment being considered. This problem is computationally hard and often needs to be solved timely. Here, we introduce a quadratic unconstrained binary optimization (QUBO) model of the problem in question, compatible with the emerging quantum annealing technology. The model's instances can be executed on present-day quantum annealers. As a proof-of-concept, we solve selected real-life problems from the Polish railway network using D-Wave quantum annealers. As a reference, we also provide solutions calculated with classical methods, including those relevant to the community (linear integer programming) and a sophisticated algorithm based on tensor networks for solving QUBO problems.
In this work, we consider a practical railway dispatching problem: delay and conflict management on a single-track railway line. We examine the issue of train dispatching consequences caused by the arrival of an already delayed train to the segment being considered. This problem is computationally hard and often needs to be solved timely. Here, we introduce a quadratic unconstrained binary optimization (QUBO) model of the problem in question, compatible with the emerging quantum annealing technology. The model's instances can be executed on present-day quantum annealers. As a proof-of-concept, we solve selected real-life problems from the Polish railway network using D-Wave quantum annealers. As a reference, we also provide solutions calculated with classical methods, including those relevant to the community (linear integer programming) and a sophisticated algorithm based on tensor networks for solving QUBO problems.
We are in the noisy intermediate-scale quantum (NISQ) devices' era, in which quantum hardware has become available for application in real-world problems. However, demonstrations of the usefulness of such NISQ devices are still rare. In this work, we consider a practical railway dispatching problem: delay and conflict management on single-track railway lines. We examine the train dispatching consequences of the arrival of an already delayed train to a given network segment. This problem is computationally hard and needs to be solved almost in real time. We introduce a quadratic unconstrained binary optimization (QUBO) model of this problem, which is compatible with the emerging quantum annealing technology. The model's instances can be executed on present-day quantum annealers. As a proof-of-concept, we solve selected real-life problems from the Polish railway network using D-Wave quantum annealers. As a reference, we also provide solutions calculated with classical methods, including the conventional solution of a linear integer version of the model as well as the solution of the QUBO model using a tensor network-based algorithm. Our preliminary results illustrate the degree of difficulty of real-life railway instances for the current quantum annealing technology. Moreover, our analysis shows that the new generation of quantum annealers (the advantage system) does not perform well on those instances, either.
The consequences of disruptions in railway traffic are the primary cause of passengers' dissatisfaction. Hence, appropriate dispatching decisions are necessary (e.g., by assigning the order of trains), given the numerous restrictions of traffic nature. The latter is perceived as an NP-hard problem. This paper outlines QUBO (quadratic unconstrained binary optimization) and HOBO (higher-order binary optimization) representations for dispatching problems of railway traffic management. Specifically, we consider minimal span between trains, minimal stay on stations, station/track occupation, and rolling stock circulation. The main result is the hybrid algorithm to deal with disturbances in rail traffic on single-, double- and multi-track lines; the demonstrative model illustrates the issue briefly. This algorithm can solve railway dispatching problems using the quantum annealer or any other QUBO-based optimization device.
Abstract As consequences of disruptions in railway traffic affect passenger experience and 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 quadratic unconstrained binary optimization (QUBO) or higher-order binary optimization (HOBO) 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.
In this thesis, we focus on the problem of validating and benchmarking quantum annealers. To this end, we propose two algorithms for solving real-world problems and test how they perform on the current generation of quantum annealers. The first algorithm allows for solving the dynamics of quantum systems (or, in fact, any dynamical systems). The second of the proposed algorithms is suitable for solving a particular family of railway dispatching problems. We assess the performance of those algorithms on the current generation of D-Wave quantum annealers with the assistance of two novel, classical strategies for solving an Ising model also presented in the thesis. The first, tensor network-based approach is a heuristic algorithm tailored for solving instances defined on Chimera-like graphs, thus making it ideal for providing a baseline with which the results from physical annealers can be compared. The other presented approach is a massively parallel implementation of the exhaustive (brute-force) search through the whole solution space. Although the brute-force approach is limited to moderate instance sizes, it has the advantage of being able to compute the low energy spectrum and certify the solutions. Our results suggest that present-day quantum annealers are able to solve a subset of the aforementioned problems. In particular, we show that the D-Wave annealers are capable of capturing the dynamics of a simple quantum system in a specific regime of parameters, and can be used to obtain good-quality solutions for instances of railway conflict management problems. Finally, our findings indicate that the current generation of D-Wave annealers is far from perfect. We discuss problem instances for which the annealers failed to find a good or even feasible solution. We also provide, where possible, a plausible explanation of why some of the presented problems might be hard for the annealers.
This study examines the coordinated optimization of departure sequencing and section-track allocation in railway short-term concentrated departure scenarios. A quadratic unconstrained binary optimization (QUBO) model is formulated to represent departure-position assignment and section-track selection within a unified binary framework. Because the quality of a dispatching scheme depends on time-dependent operational interactions that cannot be fully captured by a static combinatorial model, a simulation-based evaluation layer is introduced to assess section occupation, intermediate-station waiting, platform-capacity pressure, running-time fluctuations, and delay propagation. Within this layered framework, conventional heuristics, quantum-inspired algorithms, and hybrid algorithms are compared on the same decision structure. The results show that the QUBO model can generate feasible candidate schemes after decoding, while the simulation layer clearly differentiates the operational performance of the competing algorithms under both normal and disturbed conditions. In the tested scenarios, QPSO-QAOA performs best under normal conditions, and the quantum-enhanced methods reduce comprehensive cost by 4.28\%--26.26\% and total delay by 4.37\%--24.25\% on average under dynamic conditions relative to their conventional counterparts. These findings suggest that the integration of QUBO-based modeling and simulation-based evaluation provides a useful methodological framework for railway short-term concentrated departure scheduling, although validation with real operational data remains necessary.
Abstract Timetable scheduling is a combinatorial optimization problem that presents formidable challenges for classical computers. This paper introduces a pioneering methodology for addressing the high-speed train timetabling problem through quantum computing. Initially, a comprehensive binary integer programming model, grounded in the space–time network, is proposed (M1). To manage the intricacy of model M1, a knapsack problem reformulation is employed to establish a simplified binary integer programming model (M2). Both M1 and M2 are subsequently converted into quadratic unconstrained binary optimization (QUBO) models to harness the potential of quantum computing. Several techniques, including the Gurobi solver, simulated annealing, and the coherent Ising machine (CIM) quantum simulator, are deployed to solve the model across four distinct scenarios of varying complexity. The findings indicate that CIM quantum simulator outperforms the simulated annealing method in terms of solution quality for medium-scale problems.