Railway Timetable Optimization

In this cumulative dissertation, we study several aspects of railway timetable optimization. The first contributions cover Practical Applications of Automatic Railway Timetabling. In particular, for the problem of simultaneously scheduling all freight trains in Germany such that there are no conflicts between them, we propose a novel column generation approach. Each train can choose from an iteratively growing set of possible routes and times, so called slots. For the task of choosing maximally many slots without conflicts, we present and apply the heuristic algorithm Conflict Resolving (CR). With these two methods, we are able to schedule more than 5000 trains simultaneously, exceeding the scopes of other studies. A second practical application that we study is measuring the capacity increase in the railway network when equipping freight trains with electro-pneumatic brakes and middle buffer couplings. Methodically, we propose to explicitly construct as many slots as possible for such trains and measure the capacity as the number of constructed slots. Furthermore, we contribute to the field of Algorithms and Computability in Timetable Generation. We present two heuristic solution algorithms for the Maximum Satisfiability Problem (MaxSAT). In the literature, it has been proposed to encode different NP-complete problems that occur in railway timetabling in MaxSAT. In numerical experiments, we prove that our algorithms are competitive to state-of-the-art MaxSAT solvers. Moreover, we study the parameterized complexity status of periodic scheduling and give proofs that the problem is NP-complete for input graphs of bounded treewidth, branchwidth and carvingwidth. Finally, we propose a framework for analyzing Delay Propagation in Railway Networks. More precisely, we develop delay transmission rules based on different correlation measures that can be derived from historical operations data. What is more, we apply SHAP values from Explainable AI to the problem of discerning primary delays that occur stochastically in the operations, to secondary follow-up delays. Transmission rules that are derived from the secondary delays indicate where timetable adjustments are needed. In our last contribution in this field, we apply such adjustment rules for black-box optimization of timetables in a simulation environment

Dispatching and Rescheduling Tasks and Their Interactions with Travel Demand and the Energy Domain: Models and Algorithms

Abstract The paper aims to provide an overview of the key factors to consider when performing reliable modelling of rail services. Given our underlying belief that to build a robust simulation environment a rail service cannot be considered an isolated system, also the connected systems, which influence and, in turn, are influenced by such services, must be properly modelled. For this purpose, an extensive overview of the rail simulation and optimisation models proposed in the literature is first provided. Rail simulation models are classified according to the level of detail implemented (microscopic, mesoscopic and macroscopic), the variables involved (deterministic and stochastic) and the processing techniques adopted (synchronous and asynchronous). By contrast, within rail optimisation models, both planning (timetabling) and management (rescheduling) phases are discussed. The main issues concerning the interaction of rail services with travel demand flows and the energy domain are also described. Finally, in an attempt to provide a comprehensive framework an overview of the main metaheuristic resolution techniques used in the planning and management phases is shown

Delay Management including Capacities of Stations

The question of delay management is whether trains should wait for delayed feeder trains or should depart on time. Solutions to this problem strongly depend on the available capacity of the railway infrastructure. While the limited capacity of the tracks has been considered in delay management models, the limited capacity of the stations has been neglected so far. In this paper, we develop a model for the delay management problem that includes the stations’ capacities. This model allows to reschedule the platform assignment dynamically. Furthermore, we propose an iterative algorithm in which we first solve the delay management model with a fixed platform assignment and then improve this platform assignment in each step. We show that the latter problem can be solved in polynomial time by presenting a totally unimodular IP formulation. Finally, we present an extension of the model that balances the delay of the passengers on the one hand and the number of changes in the platform assignment on the other. All models are evaluated on real-world instances from Netherlands Railways