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Quantum Information Processing

High-speed train timetable optimization based on space–time network model and quantum simulator

Hui-Zhang Xu, Junhua Chen, Xingchen Zhang, Te-Er Lu, Tianze Gao, Kai Wen, Yin Ma

Published Nov 22, 2023• 9 citations
Publisher

Abstract

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.

DOI
10.1007/s11128-023-04170-3

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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.
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Flexible job-shop scheduling problems (FJSPs) represent one of the most complex combinatorial optimization challenges. Modern production systems and control processes demand rapid decision-making in scheduling. To address this challenge, we propose a quantum computing approach for solving FJSPs. We propose a quadratic unconstrained binary optimization (QUBO) model to minimize the makespan of FJSPs, with the scheduling scheme encoded in the ground state of the Hamiltonian operator. The model is solved using a coherent Ising machine (CIM). Numerical experiments are conducted to evaluate and validate the performance and effectiveness of the CIM. The results demonstrate that quantum computing holds significant potential for solving FJSPs more efficiently than traditional computational methods.
Public transport systems play a crucial role in the development of large cities. Bus network design to optimize passenger flow coverage in a global metropolis is a challenging task. As an essential part of bus travel planning, considering the bus transfer factor in the existing extremely complex and extensive public bus network usually leads to a optimization problem characterized by high-dimensionality and non-linearity. While classical computers struggle to deal with this kind of problems, quantum computers shed new light into this field. The coherent Ising machine (CIM), a specialized optical quantum computer using a photonic dissipative architecture, has shown its remarkable computational power in combinatorial optimization problems. We construct the classical model and the quadratic unconstrained binary optimization (QUBO) model of the bus route optimization problem, and solve it using a classical computer and CIM, respectively. Our experimental results demonstrate the significant acceleration capability of CIM over classical computers in finding the optimal or near-optimal solutions, albeit subject to the hardware limitations of the 100-qubit CIM.
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