Refine
Year of publication
Document Type
- ZIB-Report (52)
- In Proceedings (38)
- Article (22)
- Book chapter (3)
- Book (1)
- Doctoral Thesis (1)
- Master's Thesis (1)
- Other (1)
Language
- English (119)
Keywords
- column generation (4)
- integer programming (4)
- network aggregation (4)
- rapid branching (4)
- Railway Track Allocation (3)
- railway track allocation (3)
- Column Generation (2)
- Fahrplanung (2)
- Netzwerkaggregation (2)
- Optimization (2)
Institute
We propose a new coarse-to-fine approach to solve certain linear programs by column generation. The problems that we address contain layers corresponding to different levels of detail, i.e., coarse layers as well as fine layers. These layers are utilized to design efficient pricing rules. In a nutshell, the method shifts the pricing of a fine linear program to a coarse counterpart. In this way, major decisions are taken in the coarse layer, while minor details are tackled within the fine layer. We elucidate our methodology by an application to a complex railway rolling stock rotation problem. We provide comprehensive computational results that demonstrate the benefit of this new technique for the solution of large scale problems.
We propose a new coarse-to-fine approach to solve certain linear programs by column generation. The problems that we address contain layers corresponding to different levels of detail, i.e., coarse layers as well as fine layers. These layers are utilized to design
efficient pricing rules. In a nutshell, the method shifts the pricing of a fine linear program to a coarse counterpart. In this way, major decisions are taken in the coarse layer, while minor
details are tackled within the fine layer. We elucidate our methodology by an application to a complex railway rolling stock rotation problem. We provide comprehensive computational results that demonstrate the benefit of this new technique for the solution of large scale problems.
The airline crew scheduling problem deals with the construction of crew rotations in order to cover the flights of a given schedule at minimum cost. The problem involves complex rules for the legality and costs of individual pairings and base constraints for the availability of crews at home bases. A typical instance considers a planning horizon of one month and several thousand flights. We propose a column generation approach for solving airline crew scheduling problems that is based on a set partitioning model. We discuss algorithmic aspects such as the use of bundle techniques for the fast, approximate solution of linear programs, a pairing generator that combines Lagrangean shortest path and callback techniques, and a novel rapid branching'' IP heuristic. Computational results for a number of industrial instances are reported. Our approach has been implemented within the commercial crew scheduling system NetLine/Crew of Lufthansa Systems Berlin GmbH.
For providing railway services the company's railway rolling stock is one if not the most important ingredient. It decides about the number of passenger or cargo trips the company can offer, about the quality a passenger experiences the train ride and it is often related to the image of the company itself. Thus, it is highly desired to have the available rolling stock in the best shape possible. Moreover, in many countries, as Germany where our industrial partner DB Fernverkehr AG (DBF) is located, laws enforce regular vehicle inspections to ensure the safety of the passengers. This leads to rolling stock optimization problems with complex rules for vehicle maintenance. This problem is well studied in the literature for example see [Maróti and Kroon, 2005; Gábor Maróti and Leo G. Kroon, 2007], or [Cordeau et al., 2001] for applications including vehicle maintenance. The contribution of this paper is a new algorithmic approach to solve the Rolling Stock Rotation Problem for the ICE high speed train fleet of DBF with included vehicle maintenance. It is based on a relaxation of a mixed integer linear programming model with an iterative cut generation to enforce the feasibility of a solution of the relaxation in the solution space of the original problem. The resulting mixed integer linear programming model is based on a hypergraph approach presented in [Ralf Borndörfer et al., 2015]. The new approach is tested on real world instances modeling different scenarios for the ICE high speed train network in Germany and compared to the approaches of [Reuther, 2017] that are in operation at DB Fernverkehr AG. The approach shows a significant reduction of the run time to produce solutions with comparable or even better objective function values.
For providing railway services the company’s railway rolling stock is one if not the most important ingredient. It decides about the number of passenger or cargo trips the company can offer, about the quality a passenger experiences the train ride
and it is often related to the image of the company itself. Thus, it is highly desired to
have the available rolling stock in the best shape possible. Moreover, in many countries, as Germany where our industrial partner DB Fernverkehr AG (DBF) is located, laws enforce regular vehicle inspections to ensure the safety of the passengers. This leads to rolling stock optimization problems with complex rules for vehicle maintenance. This problem is well studied in the literature for example see Maroti and Kroon 2005, or Cordeau et. al. 2001 for applications including vehicle maintenance. The contribution of this paper is a new algorithmic approach to solve the Rolling Stock Rotation Problem for the ICE high speed train fleet of DBF with included vehicle maintenance. It is based on a relaxation of a mixed integer
linear programming model with an iterative cut generation to enforce the feasibility of a solution of the relaxation in the solution space of the original problem. The resulting mixed integer linear programming model is based on a hypergraph approach presented in Borndörfer et. al. 2015. The new approach is tested on real world instances modeling different scenarios
for the ICE high speed train network in Germany and compared to the approaches
of Reuther 2017 that are in operation at DB Fernverkehr AG. The approach shows a significant reduction of the run time to produce solutions with comparable or even better objective function values.
Two fundamental mathematical formulations for railway timetabling
are compared on a common set of sample problems, representing both
multiple track high density services in Europe and single track bidirectional
operations in North America. One formulation, ACP, enforces
against conflicts by constraining time intervals between trains,
while the other formulation, RCHF, monitors physical occupation of
controlled track segments. The results demonstrate that both ACP
and RCHF return comparable solutions in the aggregate, with some
significant differences in select instances, and a pattern of significant
differences in performance and constraint enforcement overall.
Two fundamental mathematical formulations for railway timetabling are compared on a common set of sample problems, representing both multiple track high density services in Europe and single track bidirectional operations in North America. One formulation, ACP, enforces against conflicts by constraining time intervals between trains, while the other formulation, HGF, monitors physical occupation of controlled track segments. The results demonstrate that both ACP and HGF return comparable solutions in the aggregate, with some significant differences in select instances, and a pattern of significant differences in performance and constraint enforcement overall.
We propose a model for the integrated optimization of vehicle
rotations and vehicle compositions in long distance railway passenger
transport. The main contribution of the paper is a hypergraph model
that is able to handle the challenging technical requirements as
well as very general stipulations with respect to the ``regularity''
of a schedule. The hypergraph model directly generalizes network
flow models, replacing arcs with hyperarcs. Although NP-hard in
general, the model is computationally well-behaved in practice. High
quality solutions can be produced in reasonable time using high
performance Integer Programming techniques, in particular, column
generation and rapid branching. We show that, in this way,
large-scale real world instances of our cooperation partner DB
Fernverkehr can be solved.
We propose a model for the integrated optimization of vehicle rotations and vehicle compositions in long distance railway passenger transport. The main contribution of the paper is a hypergraph model that is able to handle the challenging technical requirements as well as very general stipulations with respect to the ``regularity'' of a schedule. The hypergraph model directly generalizes network flow models, replacing arcs with hyperarcs. Although NP-hard in general, the model is computationally well-behaved in practice. High quality solutions can be produced in reasonable time using high performance Integer Programming techniques, in particular, column generation and rapid branching. We show that, in this way, large-scale real world instances of our cooperation partner DB Fernverkehr can be solved.