8738 eng reportzib 0 -- 2022-07-19 -- Periodic timetabling is a central aspect of both the long-term organization and the day-to-day operations of a public transportation system. The Periodic Event Scheduling Problem (PESP), the combinatorial optimization problem that forms the mathematical basis of periodic timetabling, is an extremely hard problem, for which optimal solutions are hardly ever found in practice. The most prominent solving strategies today are based on mixed-integer programming, and there is a concurrent PESP solver employing a wide range of heuristics [3]. We present tropical neighborhood search (tns), a novel PESP heuristic. The method is based on the relations between periodic timetabling and tropical geometry [4]. We implement tns into the concurrent solver, and test it on instances of the benchmarking library PESPlib. The inclusion of tns turns out to be quite beneficial to the solver: tns is able to escape local optima for the modulo network simplex algorithm, and the overall share of improvement coming from tns is substantial compared to the other methods available in the solver. Finally, we provide better primal bounds for five PESPlib instances. 1438-0064 urn:nbn:de:0297-zib-87385 10.4230/OASIcs.ATMOS.2022.3 publish appeared in 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022) Enrico Bortoletto Enrico Bortoletto Niels Lindner Berenike Masing 22-13 eng uncontrolled Periodic Timetabling eng uncontrolled Tropical Geometry eng uncontrolled Neighbourhood Search eng uncontrolled Mixed-Integer Programming Tropical geometry [See also 12K10, 14M25, 14N10, 52B20] Polyhedra and polytopes; regular figures, division of spaces [See also 51F15] Special polytopes (linear programming, centrally symmetric, etc.) Mixed integer programming Programming involving graphs or networks [See also 90C27] MODAL-Gesamt Lindner, Niels Bortoletto, Enrico Network Optimization Masing, Berenike MODAL-MobilityLab MathPlus-AA3-8 https://opus4.kobv.de/opus4-zib/files/8738/report.pdf