Computationally Efficient Dynamic Traffic Optimization of Railway Systems

In this paper, we investigate dynamic traffic optimization in railway systems, i.e., the behavior of these systems through time when their movements are dictated by solutions to optimization models with finite horizons. As interactions between trains are not considered beyond the limits of finite horizons, the danger of leading the system into a deadlock arises. In this paper we present new procedures to establish finite prediction horizons that are formally guaranteed to operate the system in a way that is compatible with the physical constraints of the network while avoiding deadlocking and minimizing computations. The key to this result is the notion of
recursive feasibility
. This paper introduces conditions sufficient to attain it. We then discuss several important ramifications of recursive feasibility that enable efficient computations. We examine the possibility of decomposing the underlying optimization models into smaller models with shorter horizons, or into models that only consider subsets of all trains. We also discuss warm starting and anytime approaches. We finally perform numerical experiments verifying these results on models that include a real-world railway system used for freight transport. On harder instances, some of our approaches outperform solving the same models as monolithic MILPs by more than two order of magnitude in terms of median computation times, while also achieving better worst–case optimality gaps.