@misc{MasingLindnerEbert2023, author = {Masing, Berenike and Lindner, Niels and Ebert, Patricia}, title = {Forward and Line-Based Cycle Bases for Periodic Timetabling}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-89731}, year = {2023}, abstract = {The optimization of periodic timetables is an indispensable planning task in public transport. Although the periodic event scheduling problem (PESP) provides an elegant mathematical formulation of the periodic timetabling problem that led to many insights for primal heuristics, it is notoriously hard to solve to optimality. One reason is that for the standard mixed-integer linear programming formulations, linear programming relaxations are weak and the integer variables are of pure technical nature and in general do not correlate with the objective value. While the first problem has been addressed by developing several families of cutting planes, we focus on the second aspect. We discuss integral forward cycle bases as a concept to compute improved dual bounds for PESP instances. To this end, we develop the theory of forward cycle bases on general digraphs. Specifically for the application of timetabling, we devise a generic procedure to construct line-based event-activity networks, and give a simple recipe for an integral forward cycle basis on such networks. Finally, we analyze the 16 railway instances of the benchmark library PESPlib, match them to the line-based structure and use forward cycle bases to compute better dual bounds for 14 out of the 16 instances.}, language = {en} } @misc{EbertSchlechteSchwartz2025, author = {Ebert, Patricia and Schlechte, Thomas and Schwartz, Stephan}, title = {Scheduling for German Road Inspectors}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-101999}, year = {2025}, abstract = {For the yearly over 500,000 vehicle inspections of the German Federal Logistics and Mobility Office (BALM), crew rosters must be scheduled to efficiently achieve Germany's road inspection control targets. For that, we present a model to solve the respective duty scheduling and crew rostering problem in order to obtain duty rosters that comply with numerous legal regulations while maximizing the 'control success' to achieve the control targets. We formulate the Template Assignment Problem, which can be modelled as a large scale mixed-integer linear program. Here, feasible combinations of control topics are assigned to the duties using a hypergraph approach. The model is used in production by BALM, and we prove its effectiveness on a number of real-world instances.}, language = {en} } @misc{EbertMasingLindneretal.2024, author = {Ebert, Patricia and Masing, Berenike and Lindner, Niels and Gleixner, Ambros}, title = {Sorting Criteria for Line-based Periodic Timetabling Heuristics}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-97826}, year = {2024}, abstract = {It is well-known that optimal solutions are notoriously hard to find for the Periodic Event Scheduling Problem (PESP), which is the standard mathematical formulation to optimize periodic timetables in public transport. We consider a class of incremental heuristics that have been demonstrated to be effective by Lindner and Liebchen (2023), however, for only one fixed sorting strategy of lines along which a solution is constructed. Thus, in this paper, we examine a variety of sortings based on the number, weight, weighted span, and lower bound of arcs, and test for each setting various combinations of the driving, dwelling, and transfer arcs of lines. Additionally, we assess the impact on the incremental extension of the event-activity network by minimizing resp. maximizing a connectivity measure between subsets of lines. We compare our 27 sortings on the railway instances of the benchmarking library PESPlib within the ConcurrentPESP solver framework. We are able to find five new incumbent solutions, resulting in improvements of up to 2\%.}, language = {en} }