TY - GEN A1 - Lindner, Niels A1 - Liebchen, Christian T1 - Determining all integer vertices of the PESP polytope by flipping arcs N2 - We investigate polyhedral aspects of the Periodic Event Scheduling Problem (PESP), the mathematical basis for periodic timetabling problems in public transport. Flipping the orientation of arcs, we obtain a new class of valid inequalities, the flip inequalities, comprising both the known cycle and change-cycle inequalities. For a point of the LP relaxation, a violated flip inequality can be found in pseudo-polynomial time, and even in linear time for a spanning tree solution. Our main result is that the integer vertices of the polytope described by the flip inequalities are exactly the vertices of the PESP polytope, i.e., the convex hull of all feasible periodic slacks with corresponding modulo parameters. Moreover, we show that this flip polytope equals the PESP polytope in some special cases. On the computational side, we devise several heuristic approaches concerning the separation of cutting planes from flip inequalities. These produce better dual bounds for the smallest and largest instance of the benchmarking library PESPlib. T3 - ZIB-Report - 20-19 KW - Periodic Event Scheduling Problem KW - Periodic Timetabling KW - Mixed Integer Programming Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78793 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Liebchen, Christian T1 - Timetable Merging for the Periodic Event Scheduling Problem N2 - We propose a new mixed integer programming based heuristic for computing new benchmark primal solutions for instances of the PESPlib. The PESPlib is a collection of instances for the Periodic Event Scheduling Problem (PESP), comprising periodic timetabling problems inspired by real-world railway timetabling settings, and attracting several international research teams during the last years. We describe two strategies to merge a set of good periodic timetables. These make use of the instance structure and minimum weight cycle bases, finally leading to restricted mixed integer programming formulations with tighter variable bounds. Implementing this timetable merging approach in a concurrent solver, we improve the objective values of the best known solutions for the smallest and largest PESPlib instances by 1.7 and 4.3 percent, respectively. T3 - ZIB-Report - 21-06 KW - Periodic Event Scheduling Problem KW - Periodic Timetabling KW - Railway Timetabling KW - PESPlib KW - Benchmark Solutions KW - Mixed Integer Programming Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81587 SN - 1438-0064 ER - TY - CHAP A1 - Lindner, Niels A1 - Liebchen, Christian ED - Huisman, Dennis ED - Zaroliagis, Christos D. T1 - Determining all integer vertices of the PESP polytope by flipping arcs T2 - 20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020) N2 - We investigate polyhedral aspects of the Periodic Event Scheduling Problem (PESP), the mathematical basis for periodic timetabling problems in public transport. Flipping the orientation of arcs, we obtain a new class of valid inequalities, the flip inequalities, comprising both the known cycle and change-cycle inequalities. For a point of the LP relaxation, a violated flip inequality can be found in pseudo-polynomial time, and even in linear time for a spanning tree solution. Our main result is that the integer vertices of the polytope described by the flip inequalities are exactly the vertices of the PESP polytope, i.e., the convex hull of all feasible periodic slacks with corresponding modulo parameters. Moreover, we show that this flip polytope equals the PESP polytope in some special cases. On the computational side, we devise several heuristic approaches concerning the separation of cutting planes from flip inequalities. We finally present better dual bounds for the smallest and largest instance of the benchmarking library PESPlib. Y1 - 2020 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2020.5 VL - 85 SP - 5:1 EP - 5:18 PB - Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik CY - Dagstuhl, Germany ER -