TY - CHAP A1 - Löbel, Fabian A1 - Lindner, Niels ED - Sauer, Jonas ED - Schmidt, Marie T1 - A Geometric Approach to Integrated Periodic Timetabling and Passenger Routing T2 - 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025) N2 - We offer a geometric perspective on the problem of integrated periodic timetabling and passenger routing in public transport. Inside the space of periodic tensions, we single out those regions, where the same set of paths provides shortest passenger routes. This results in a polyhedral subdivision, which we combine with the known decomposition by polytropes. On each maximal region of the common refinement, the integrated problem is solvable in polynomial time. We transform these insights into a new geometry-driven primal heuristic, integrated tropical neighborhood search (ITNS). Computationally, we compare implementations of ITNS and the integrated (restricted) modulo network simplex algorithm on the TimPassLib benchmark set, and contribute better solutions in terms of total travel time for all but one of the twenty-five instances for which a proven optimal solution is not yet known. KW - Periodic Timetabling KW - Passenger Routing KW - Polyhedral Complexes Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0030-drops-247580 SN - 978-3-95977-404-8 SN - 2190-6807 VL - 137 SP - 2:1 EP - 2:19 PB - Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik CY - Dagstuhl, Germany ER -