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arXiv:2107.03234 · Quantum Information Processing

Quadratic and higher-order unconstrained binary optimization of railway rescheduling for quantum computing

Krzysztof Domino, Akash Kundu, Özlem Salehi, Krzysztof Krawiec

Published Sep 29, 2022• 26 citations
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Abstract

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.

DOI
10.1007/s11128-022-03670-y

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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.
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.
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.
In this research paper, we employ D-Wave’s quantum annealer to address the NP-hard problem of optimizing new metro station locations while considering both points of interest and existing stations. By formulating the problem as Quadratic Unconstrained Binary Optimization (QUBO) and Binary Quadratic Model (BQM), our approach harnesses the power of quantum computing to yield superior solutions compared to classical methods. This research has the potential to revolutionize urban transportation planning by efficiently balancing accessibility to points of interest and minimizing congestion around existing stations, offering a compelling solution to a complex urban development challenge. Notably, we emphasize the NP-hard nature of this problem, underlining its computational complexity and the significance of our quantum computing approach.
Quantum Annealing is an alternative type of computation in which problems are encoded in quantum Hamiltonians (energy functions) and quantum dynamics is used to find solutions (ground states of minimal energy). Quantum computers such as the D-Wave systems are indeed implementing those ideas in hardware, as well as "quantum-inspired" devices based on classical electronics such as Fujitsu’s Digital Annealing Unit. All those systems use the same modeling language: Quadratic Unconstrained Binary Optimization (QUBO). However, QUBO is a low-level language and for modeling combinatorial problems such as constraint satisfaction and constrained optimization problems, we need to introduce higher-level abstractions in order to define complex constraints.
We study daily rolling stock circulation planning for electric multiple units (EMUs) on a regional passenger network, focusing on services where identical EMUs may be coupled in pairs on selected routes. Motivated by the operational needs of the regional operator Silesian Railways in Poland, we formulate an acyclic mixed-integer linear program on a one-day horizon that incorporates depot balance constraints, demand-driven seat and bicycle capacity limits, and simple crew availability constraints. Using a graph/hyper-graph representation of train movements, we first solve an ILP formulation. We then derive a Quadratic Unconstrained Binary Optimization (QUBO) reformulation and evaluate its solution by quantum annealing on D-Wave Advantage systems and by the classical quantum-inspired VeloxQ solver. In computational experiments on real-world instances from the Silesian network, with up to 404 train trips and 11 EMU types, the ILP approach yields high-quality daily circulation plans within at most about 40 minutes. The quantum and quantum-inspired solvers are restricted to substantially smaller sub-instances due to the large number of terms in the QUBO and embedding limitations in the case of quantum hardware. These results quantify the present frontier of QUBO-based methods for rolling stock circulation. They can be helpful in designing a hybrid classical-quantum approach.