Efficient real-time rail traffic optimization: Decomposition of rerouting, reordering, and rescheduling problems

The real-time railway traffic management problem occurs when the pre-planned timetable cannot be kept due to various disturbances; therefore, the trains must be rerouted, reordered, and rescheduled. Optimizing the real-time railway traffic management aims to resolve conflicts, minimizing the delay propagation or energy consumption. In one of our previous works, the existing mixed-integer linear programming optimization models are extended considering a safety-relevant issue of railway traffic management, the overlaps. However, solving the extended model can be time-consuming in complex control areas and traffic situations involving numerous trains. Therefore, we propose different computationally efficient multi-stage models by decomposing the problem according to the rerouting, reordering, and rescheduling sub-problems. First, a lightweight heuristic MILP model that provides a fast but sub-optimal solution is given by reformulating the train delays into pair-wise interpretation. Second, we extend the heuristic model to grant an optimal solution to the original problem faster than the existing MILP formulations. The impact of the model decomposition is investigated mathematically and experimentally in various realistic simulated traffic scenarios concerning the optimization’s objective value and computational demand. The proposed multi-stage models significantly decrease the optimization runtime of both the original and the extended railway traffic management problems.