Almost 20 Years of Combinatorial Optimization for Railway Planning: from Lagrangian Relaxation to Column Generation

We summarize our experience in solving combinatorial optimization problems arising in railway planning, illustrating all of these problems as integer multicommodity flow ones and discussing the main features of the mathematical programming models that were successfully used in the 1990s and in recent years to solve them.

[1]  Franz Rendl,et al.  The Bundle Method for Hard Combinatorial Optimization Problems , 2001, Combinatorial Optimization.

[2]  Paolo Toth,et al.  04. Solution of the Train Platforming Problem , 2007 .

[3]  Paolo Toth,et al.  Solution of the Train Platforming Problem , 2011, Transp. Sci..

[4]  Egon Balas,et al.  A Dynamic Subgradient-Based Branch-and-Bound Procedure for Set Covering , 1992, Oper. Res..

[5]  Cynthia Barnhart,et al.  Using Branch-and-Price-and-Cut to Solve Origin-Destination Integer Multicommodity Flow Problems , 2000, Oper. Res..

[6]  Paolo Toth,et al.  Non-cyclic train timetabling and comparability graphs , 2010, Oper. Res. Lett..

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

[8]  Paolo Toth,et al.  Solving a Real-World Train Unit Assignment Problem , 2007 .

[9]  Michael R. Bussieck,et al.  Discrete optimization in public rail transport , 1997, Math. Program..

[10]  Antonio Sassano,et al.  A Lagrangian-based heuristic for large-scale set covering problems , 1998, Math. Program..

[11]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[12]  Hanif D. Sherali,et al.  Dual formulations and subgradient optimization strategies for linear programming relaxations of mixed-integer programs , 1988, Discret. Appl. Math..

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

[14]  Jacques Desrosiers,et al.  Time Constrained Routing and Scheduling , 1992 .

[15]  Marshall L. Fisher,et al.  The Lagrangian Relaxation Method for Solving Integer Programming Problems , 2004, Manag. Sci..

[16]  Martin W. P. Savelsbergh,et al.  Branch-and-Price: Column Generation for Solving Huge Integer Programs , 1998, Oper. Res..

[17]  Matteo Fischetti,et al.  Algorithms for railway crew management , 1997, Math. Program..

[18]  Matteo Fischetti,et al.  Modeling and Solving the Crew Rostering Problem , 1998, Oper. Res..

[19]  Paolo Toth,et al.  A column generation approach to train timetabling on a corridor , 2008, 4OR.

[20]  Matteo Fischetti,et al.  Modeling and Solving the Train Timetabling Problem , 2002, Oper. Res..

[21]  J. Beasley A lagrangian heuristic for set‐covering problems , 1990 .

[22]  Matteo Fischetti,et al.  A Heuristic Method for the Set Covering Problem , 1999, Oper. Res..

[23]  Leo G. Kroon,et al.  Routing trains through a railway station based on a node packing model , 2001, Eur. J. Oper. Res..

[24]  Dennis Huisman,et al.  Operations Research in passenger railway transportation , 2005 .

[25]  Paolo Toth,et al.  Chapter 3 Passenger Railway Optimization , 2007, Transportation.