Column Generation Heuristic for a Rich Arc Routing Problem

In this paper we address a real world optimisation problem, the Rail Track Inspection Scheduling Problem (RTISP). This problem consists of scheduling network inspection tasks. The objective is to minimise total deadhead distance. A mixed integer formulation of the problem is presented. A column generation based algorithm is proposed to solve this rich arc routing problem. Its performance is analysed by benchmarking a real world dataset from the French national railway company (SNCF). The efficiency of the algorithm is compared to an enhanced greedy algorithm. Its ability to schedule one year of inspection tasks on a sparse graph with thousand nodes, arcs and edges is assessed.

[1]  Nathalie Perrier,et al.  A survey of models and algorithms for winter road maintenance. Part II: system design for snow disposal , 2006, Comput. Oper. Res..

[2]  Ellis L. Johnson,et al.  Solving the Capacitated Arc Routing Problem with Time Windows using Column Generation , 2009 .

[3]  Michel Gendreau,et al.  Arc Routing Problems, Part II: The Rural Postman Problem , 1995, Oper. Res..

[4]  M. BelenguerJ.,et al.  The Capacitated Arc Routing Problem , 1998 .

[5]  Nicolas Jozefowiez,et al.  The vehicle routing problem: Latest advances and new challenges , 2007 .

[6]  Hartmut Noltemeier,et al.  Geometric Modelling , 1998, Computing Supplement.

[7]  André Langevin,et al.  Vehicle Routing for Urban Snow Plowing Operations , 2006, Transp. Sci..

[8]  Stefan Irnich Solution of real-world postman problems , 2008, Eur. J. Oper. Res..

[9]  Bruce L. Golden,et al.  Capacitated arc routing problems , 1981, Networks.

[10]  M. Dror Arc Routing : Theory, Solutions and Applications , 2000 .

[11]  A. Mas-Colell,et al.  Microeconomic Theory , 1995 .

[12]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[13]  G. Brunnett Geometric Modelling , 1995, Computing Supplement.

[14]  Gilbert Laporte,et al.  The capacitated arc routing problem with intermediate facilities , 2001, Networks.

[15]  Gilbert Laporte,et al.  Arc Routing Problems, Part I: The Chinese Postman Problem , 1995, Oper. Res..

[16]  André Langevin,et al.  A survey of models and algorithms for winter road maintenance. Part IV: Vehicle routing and fleet sizing for plowing and snow disposal , 2005, Comput. Oper. Res..

[17]  A. Schrijver,et al.  The Traveling Salesman Problem , 2011 .

[18]  Vasek Chvátal,et al.  A Greedy Heuristic for the Set-Covering Problem , 1979, Math. Oper. Res..

[19]  Nacima Labadie,et al.  GRASP with Path Relinking for the Capacitated Arc Routing Problem with Time Windows , 2009, EvoWorkshops.

[20]  J. Davenport Editor , 1960 .

[21]  André Langevin,et al.  A survey of models and algorithms for winter road maintenance. Part III: Vehicle routing and depot location for spreading , 2005, Comput. Oper. Res..

[22]  Michel Gendreau,et al.  An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems , 2004, Networks.

[23]  Michel Gendreau,et al.  ARC ROUTING PROBLEMS. , 1994 .

[24]  Byung-In Kim,et al.  Waste collection vehicle routing problem with time windows using multi-objective genetic algorithms , 2007 .

[25]  André Langevin,et al.  A survey of models and algorithms for winter road maintenance. Part I: system design for spreading and plowing , 2006, Comput. Oper. Res..

[26]  André Langevin,et al.  The capacitated arc routing problem with refill points , 2007, Oper. Res. Lett..

[27]  William J. Cook,et al.  The Traveling Salesman Problem: A Computational Study , 2007 .

[28]  Jacques F. Benders,et al.  Partitioning procedures for solving mixed-variables programming problems , 2005, Comput. Manag. Sci..