Railway Track Allocation by Rapid Branching

The track allocation problem, also known as train routing problem or train timetabling problem, is to find a conflict-free set of train routes of maximum value in a railway network. Although it can be modeled as a standard path packing problem, instances of sizes relevant for real-world railway applications could not be solved up to now. We propose a rapid branching column generation approach that integrates the solution of the LP relaxation of a path coupling formulation of the problem with a special rounding heuristic. The approach is based on and exploits special properties of the bundle method for the approximate solution of convex piecewise linear functions. Computational results for dicult instances of the benchmark library TTPlib are reported. 1998 ACM Subject Classification G.1.6 Optimization, G.2.3 Application

[1]  Thomas Schlechte,et al.  A Library for Train Timetabling Problems , 2008 .

[2]  Dag Wedelin,et al.  An algorithm for large scale 0–1 integer programming with application to airline crew scheduling , 1995, Ann. Oper. Res..

[3]  C. Helmberg.  Semidefinite Programming for Combinatorial Optimization , 2000 .

[4]  Jonathan Eckstein,et al.  Pivot, Cut, and Dive: a heuristic for 0-1 mixed integer programming , 2007, J. Heuristics.

[5]  David Applegate,et al.  Finding Cuts in the TSP (A preliminary report) , 1995 .

[6]  Per Olov Lindberg,et al.  Railway Timetabling Using Lagrangian Relaxation , 1998, Transp. Sci..

[7]  K. Kiwiel.  Efficiency of Proximal Bundle Methods , 2000 .

[8]  Thomas Schlechte,et al.  TTPlib 2008 – A Library for Train Timetabling Problems , 2008 .

[9]  Paolo Toth,et al.  A Lagrangian heuristic algorithm for a real-world train timetabling problem , 2006, Discret. Appl. Math..

[10]  Matteo Fischetti,et al.  Algorithms for the Set Covering Problem , 2000, Ann. Oper. Res..

[11]  Jacques Desrosiers,et al.  Selected Topics in Column Generation , 2002, Oper. Res..

[12]  Ralf Borndörfer,et al.  A Bundle Method for Integrated Multi-Depot Vehicle and Duty Scheduling in Public Transit , 2008 .

[13]  Matthias Ehrgott,et al.  Railway track allocation: models and methods , 2011, OR Spectr..

[14]  Gabrio Curzio Caimi.  Train Scheduling in a Large and Highly Utilised Railway Network , 2010, OR.

[15]  Roy E. Marsten,et al.  COLDSTART -- FLEET ASSIGNMENT AT DELTA AIR LINES. , 1994 .

[16]  K. Kiwiel.  Approximations in proximal bundle methods and decomposition of convex programs , 1995 .

[17]  Christoph Helmberg,et al.  Towards Solving Very Large Scale Train Timetabling Problems by Lagrangian Relaxation , 2008, ATMOS.

[18]  Steffen Weider,et al.  Integration of Vehicle and Duty Scheduling in Public Transport , 2007 .

[19]  Ralf Borndörfer,et al.  Models for Railway Track Allocation , 2007, ATMOS.

[20]  Krzysztof C. Kiwiel,et al.  Proximity control in bundle methods for convex nondifferentiable minimization , 1990, Math. Program..

[21]  M. Grötschel,et al.  An Auctioning Approach to Railway Slot Allocation , 2006 .

[22]  Matteo Fischetti,et al.  Fast Approaches to Improve the Robustness of a Railway Timetable , 2009, Transp. Sci..