TY - GEN A1 - Schenker, Sebastian A1 - Borndörfer, Ralf A1 - Skutella, Martin T1 - A novel partitioning of the set of non-dominated points N2 - We consider a novel partitioning of the set of non-dominated points for general multi-objective integer programs with $k$ objectives. The set of non-dominated points is partitioned into a set of non-dominated points whose efficient solutions are also efficient for some restricted subproblem with one less objective; the second partition comprises the non-dominated points whose efficient solutions are inefficient for any of the restricted subproblems. We show that the first partition has the nice property that it yields finite rectangular boxes in which the points of the second partition are located. T3 - ZIB-Report - 16-55 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61286 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Karbstein, Marika T1 - Metric Inequalities for Routings on Direct Connections with Application in Line Planning N2 - We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the feasibility condition for arc capacities in ordinary multi-commodity flows. The concept allows to solve large-scale real-world line planning problems in public transport including a novel passenger routing model that favors direct connections over connections with transfers. T3 - ZIB-Report - 15-07 KW - combinatorial optimization KW - integer programming KW - line planning KW - transfers KW - direct connection KW - metric inequalities Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53507 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - Timetabling and Passenger Routing in Public Transport T2 - Appeard in: Proceedings of Conference on Advanced Systems in Public Transport 2015 (CASPT2015) N2 - The task of timetabling is to schedule the trips in a public transport system by determining periodic arrival and departure times at every station. The goal is to provide a service that is both attractive for passengers and can be operated economically. To date, timetable optimization is generally done with respect to fixed passenger routes, i.e., it is assumed that passengers do not respond to changes in the timetable. This is unrealistic and ignores potentially valuable degrees of freedom. We investigate in this paper periodic timetabling models with integrated passenger routing. We propose several models that differ in the allowed passenger paths and the objectives. We compare these models theoretically and report on computations on real-world instances for the city of Wuppertal. T3 - ZIB-Report - 15-31 KW - Passenger routing KW - Periodic timetabling KW - Public transport Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-55305 SN - 1438-0064 ER - TY - GEN A1 - Heismann, Olga A1 - Borndörfer, Ralf T1 - A Generalization of Odd Set Inequalities for the Set Packing Problem N2 - The set packing problem, sometimes also called the stable set problem, is a well-known NP-hard problem in combinatorial optimization with a wide range of applications and an interesting polyhedral structure, that has been the subject of intensive study. We contribute to this field by showing how, employing cliques, odd set inequalities for the matching problem can be generalized to valid inequalities for the set packing polytope with a clear combinatorial meaning. T3 - ZIB-Report - 14-28 KW - set packing KW - matching KW - hypergraph KW - inequality KW - facet Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-51010 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Karbstein, Marika T1 - Metric Inequalities for Routings on Direct Connections N2 - We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We show that the concept of metric inequalities to characterize capacities that support a multi-commodity flow can be generalized to deal with direct connections. T3 - ZIB-Report - 14-04 KW - metric inequalities KW - direct connection KW - multi-commodity flow problem Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-44219 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Dittbrenner, Bastian A1 - Langenhan, Andreas A1 - Seidl, Stephan A1 - Weider, Steffen T1 - Integrierte Dienst- und Dienstreihenfolgeplanung zur Erhöhung der Fahrerzufriedenheit N2 - Wir stellen einen mathematischen Optimierungsansatz zur integrierten Dienst- und Dienstreihenfolgeplanung im öffentlichen Nahverkehr vor, mit dem sich bei konstanten Personalkosten die Fahrerzufriedenheit deutlich steigern lässt. T3 - ZIB-Report - 14-02 KW - duty scheduling KW - duty rostering KW - integrated scheduling KW - Benders' decomposition Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-50270 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - A Configuration Model for the Line Planning Problem N2 - We propose a novel extended formulation for the line planning problem in public transport. It is based on a new concept of frequency configurations that account for all possible options to provide a required transportation capacity on an infrastructure edge. We show that this model yields a strong LP relaxation. It implies, in particular, general classes of facet defining inequalities for the standard model. T3 - ZIB-Report - 13-40 KW - combinatorial optimization KW - polyhedral combinatorics KW - line planning Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-41903 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Heismann, Olga T1 - Minimum Cost Hyperassignments with Applications to ICE/IC Rotation Planning N2 - Vehicle rotation planning is a fundamental problem in rail transport. It decides how the railcars, locomotives, and carriages are operated in order to implement the trips of the timetable. One important planning requirement is operational regularity, i.e., using the rolling stock in the same way on every day of operation. We propose to take regularity into account by modeling the vehicle rotation planning problem as a minimum cost hyperassignment problem (HAP). Hyperassignments are generalizations of assignments from directed graphs to directed hypergraphs. Finding a minimum cost hyperassignment is NP-hard. Most instances arising from regular vehicle rotation planning, however, can be solved well in practice. We show that, in particular, clique inequalities strengthen the canonical LP relaxation substantially. T3 - ZIB-Report - 11-46 KW - hyperassignments KW - vehicle rotation planning Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14564 UR - http://link.springer.com/chapter/10.1007%2F978-3-642-29210-1_10 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Langenhan, Andreas A1 - Löbel, Andreas A1 - Schulz, Christof A1 - Weider, Steffen T1 - Duty Scheduling Templates N2 - We propose duty templates as a novel concept to produce similar duty schedules for similar days of operation in public transit. Duty templates can conveniently handle various types of similarity requirements, and they can be implemented with ease using standard algorithmic techniques. They have produced good results in practice. T3 - ZIB-Report - 12-09 KW - duty scheduling KW - duty templates Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14699 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Löbel, Andreas A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - Rapid Branching N2 - We propose rapid branching (RB) as a general branch-and-bound heuristic for solving large scale optimization problems in traffic and transport. The key idea is to combine a special branching rule and a greedy node selection strategy in order to produce solutions of controlled quality rapidly and efficiently. We report on three successful applications of the method for integrated vehicle and crew scheduling, railway track allocation, and railway vehicle rotation planning. T3 - ZIB-Report - 12-10 KW - large scale optimization KW - rapid branching KW - column generation Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14728 SN - 1438-0064 ER -