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

State of the Art Overview on Automatic Railway Timetable Generation and Optimization

In railway transportation, each train needs to have a timetable that specifies which track at which time will be occupied by it. This task can be addressed by automatization techniques both in generating a timetable and in optimizing an existing one. In this paper, we give an overview on the state of the art of these techniques. We study the computation of a technically valid slot for a train that guarantees a (short) spatial and temporal way through the network. Furthermore, the construction of a cyclic timetable where trains operate e.g. every 60 minutes, and the simultaneous construction of timetables for multiple trains are considered in this paper. Finally, timetables also need to be robust against minor delays. We will review the state of the art in the literature for these aspects of railway timetabling with respect to models, solution algorithms, complexity results and applications in practice

Satisfiability and Optimization in Periodic Traffic Flow Problems

Automatically calculating periodic timetables in public railway transport systems is an NP-complete problem – namely the Periodic Event Scheduling Problem (PESP). The original model is restricted to basic periodic timetabling. Extending the model by decisional transport networks with flows induces new possibilities in the timetabling and planning process. Subsequently, the given flexibility results in a generic model extension of PESP that can be applied in subsets of the timetabling process. The successful utilization of this approach is presented for distinct chain paths, duplicated chain paths and non-connected flow graphs that represent integration of routing and timetabling, planning of periodic rail freight train paths and track allocation, respectively. Furthermore, the encoding of this generic model into a binary propositional formula is introduced and the appropriate usage of several techniques like SAT solving and MaxSAT to calculate and optimize the corresponding instances will be presented accordingly. Computational results for real-world scenarios suggest the practical impact and give promising perspectives for further scientific research

Isochronous Partitions for Region-Based Self-Triggered Control

In this work, we propose a region-based self-triggered control (STC) scheme for nonlinear systems. The state space is partitioned into a finite number of regions, each of which is associated to a uniform inter-event time. The controller, at each sampling time instant, checks to which region does the current state belong, and correspondingly decides the next sampling time instant. To derive the regions along with their corresponding inter-event times, we use approximations of isochronous manifolds, a notion firstly introduced in [1]. This work addresses some theoretical issues of [1] and proposes an effective computational approach that generates approximations of isochronous manifolds, thus enabling the region-based STC scheme. The efficiency of both our theoretical results and the proposed algorithm are demonstrated through simulation examples

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Event-triggered Control For Semi-global Stabilisation Of Systems With Actuator Saturation

This paper investigates the problem of event-triggered control for semi-global stabilisation of null controllable systems subject to actuator saturation. First, for a continuous-time system, novel event-triggered low-gain control algorithms based on Riccati equations are proposed to achieve semi-global stabilisation. The algebraic Riccati equation with a low-gain parameter is utilised to design both the event-triggering condition and the linear controller; a minimum inter-event time based on the Riccati ordinary differential equation is set a priori to exclude the Zeno behaviour. In addition, the high-low-gain techniques are utilised to extend the semi-global results to event-based global stabilisation. Furthermore, for a discrete-time system, novel low-gain and high–low-gain control algorithms are proposed to achieve event-triggered stabilisation. Numerical examples are provided to illustrate the theoretical results.postprin