Solving rescheduling problems in heterogeneous urban railway networks using hybrid quantum-classical approach

TL;DR

The paper tackles real-time railway rescheduling in heterogeneous urban networks by formulating an ILP that captures train sequencing, retiming, and shunting under a two-block signaling regime. It evaluates a hybrid quantum-classical approach using D-Wave's Leap CQM solver against IBM CPLEX on a real Polish network and synthetic line variants, expressing the problem with decision variables such as $t^{(\text{out})}(j,s)$ and $t^{(\text{in})}(j,s')$ and a secondary-delays objective $f(t)=\sum_j w_j (t^{(\text{out})}(j,s^*)-\upsilon(j,s^*))$ under constraints including $t^{(\text{in})}(j,s')= t^{(\text{out})}(j,s)+ \tau^{(\text{pass})}(j,s\rightarrow s')$ and headway conditions. The results show that CQM can produce feasible, close-to-optimal solutions within seconds and, for harder instances, can outperform exact CPLEX in computational time, though not always in objective value. The work demonstrates quantum readiness for medium-scale railway dispatching and discusses limitations, such as suboptimality in some cases and the need for improving $d_{\max}$ selection and hardware capabilities. Overall, the study suggests that hybrid quantum-classical approaches are a viable component of future real-time railway optimization, with potential gains as quantum hardware and custom hybrid algorithms evolve.

Abstract

We address the applicability of a hybrid quantum-classical heuristics for practical railway rescheduling management problems. We build an integer linear programming model and solve it with D-Wave's quantum-classical hybrid solver (CQM) as well as with CPLEX, for comparison. The proposed approach is demonstrated on a real-life heterogeneous urban network in Poland, including both single- and multi-track segments. All the requirements posed by the operator of the network are included in the model. The computational results demonstrate the readiness for application and the benefits of quantum-classical hybrid solvers in a realistic railway scenario: they yield acceptable solutions on time, which is a critical requirement in a rescheduling situation. In particular, CQM as a probabilistic heuristic solver provides a number of feasible, close-to-optimal solutions the dispatcher can choose from.

Figures (6)

• Figure 1: Edges and nodes on the example railway network. Interlocking areas of stations in green.
• Figure 2: The part of the Polish railway network which is the subject of our considerations. It is located in the central part of the Metropolis. The displayed non-decision stations such as ZZ or RCB become decision stations in certain problem instances, e.g. due to an assumed closure of one of the tracks between ZZ and RCB.
• Figure 3: Synthetic experiments $line1$, $line2$, $line3$. Comparison of the performance of classical solver (CPLEX) with that of the hybrid CQM. All the displayed solutions are feasible. Total computational time (middle panel) and QPU times (lower panel) were provided by the D-Wave output. Panel a) - $line1$, results of both solvers were similar in terms of the objective, but the CPLEX computation was faster. Panel b) - $line2$ namely the double-track line with closures and dense traffic, has appeared to be most challenging for both the classical solvers (in terms of computational time) and the quantum solver (in terms of objective). In this example, there are instances where the current CQM D-Wave hybrid solver provides feasible, though not optimal solutions of similar quality to those that CPLEX provides when its computational time is limited to be similar to that of CQM. When CPLEX is required to solve the problem to optimality, it can be slower than CQM. Increasing the value of the t_min parameter does, in most cases, improve the quality of the solution at the cost of computational time. Panel c) - $line3$ all the displayed solutions are feasible. The results of both solvers were similar in terms of the objective, but CPLEX computation was faster.
• Figure 4: Real-life experiments. Statistics of CPLEX (left, read) and CQM (right, blue) solutions (Table \ref{['tab::results_of_CPLEX_CQM']}) for selected networks in Table \ref{['tab::cases']}. The statistics were calculated over trains in the classical cases, and over trains and realizations in the CQM cases. Vertical lines are ranges, while horizontal lines are $0.25$ and $0.75$ percentiles.
• Figure 5: Real-life experiments. Dependence on the t_min parameter for network $7$ a) and network $9$ b), see Table \ref{['tab::cases']}. All solutions were feasible. For higher t_min we expect smaller objective values but higher total computational time. For each parameter value, there were $5$ realizations of the experiment performed. Interestingly, a linear (negatively sloped) relation between the objective and the logarithm of ${\tt t\_min}$ can be observed, suggesting power law scaling.