A variable neighborhood search for the capacitated arc routing problem with intermediate facilities

Abstract The capacitated arc routing problem (CARP) focuses on servicing edges of an undirected network graph. A wide spectrum of applications like mail delivery, waste collection or street maintenance outlines the relevance of this problem. A realistic variant of the CARP arises from the need of intermediate facilities (IFs) to load up or unload the service vehicle and from tour length restrictions. The proposed Variable Neighborhood Search (VNS) is a simple and robust solution technique which tackles the basic problem as well as its extensions. The VNS shows excellent results on four different benchmark sets. Particularly, for all 120 instances the best known solution could be found and in 71 cases a new best solution was achieved.

[1]  José-Manuel Belenguer,et al.  A cutting plane algorithm for the capacitated arc routing problem , 2003, Comput. Oper. Res..

[2]  G. Ulusoy The fleet size and mix problem for capacitated arc routing , 1985 .

[3]  Nenad Mladenović,et al.  An Introduction to Variable Neighborhood Search , 1997 .

[4]  Paolo Toth,et al.  The Vehicle Routing Problem , 2002, SIAM monographs on discrete mathematics and applications.

[5]  Roberto Baldacci,et al.  Exact methods based on node-routing formulations for undirected arc-routing problems , 2006 .

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

[7]  Michel Gendreau,et al.  A Tabu Search Heuristic for the Vehicle Routing Problem with Soft Time Windows , 1997, Transp. Sci..

[8]  Silvano Martello,et al.  Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization , 2012 .

[9]  Roberto Baldacci,et al.  Exact methods based on node routing formulations for arc routing problems , 2004 .

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

[11]  Philippe Lacomme,et al.  Evolutionary algorithms for periodic arc routing problems , 2005, Eur. J. Oper. Res..

[12]  Peter Greistorfer,et al.  A Tabu Scatter Search Metaheuristic for the Arc Routing Problem , 2002 .

[13]  Richard F. Hartl,et al.  Scheduling periodic customer visits for a traveling salesperson , 2007, Eur. J. Oper. Res..

[14]  Roberto Musmanno,et al.  Tabu Search Heuristics for the Arc Routing Problem with Intermediate Facilities under Capacity and Length Restrictions , 2004, J. Math. Model. Algorithms.

[15]  José-Manuel Belenguer,et al.  Lower and upper bounds for the mixed capacitated arc routing problem , 2006, Comput. Oper. Res..

[16]  Luc Muyldermans,et al.  A guided local search heuristic for the capacitated arc routing problem , 2003, Eur. J. Oper. Res..

[17]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[18]  José-Manuel Belenguer,et al.  The Capacitated Arc Routing Problem: Valid Inequalities and Facets , 1998, Comput. Optim. Appl..

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

[20]  Stefan Voß,et al.  Multiple center capacitated arc routing problems: A tabu search algorithm using capacitated trees , 2000, Eur. J. Oper. Res..

[21]  Lawrence Bodin,et al.  Capacitated Arc Routing Problem with Vehicle-Site Dependencies: The Philadelphia Experience , 2001, The Vehicle Routing Problem.

[22]  Philippe Lacomme,et al.  Competitive Memetic Algorithms for Arc Routing Problems , 2004, Ann. Oper. Res..

[23]  Zhengyu Zhu,et al.  A Genetic Algorithm for the Capacitated Arc Routing Problem , 2007, 2007 IEEE International Conference on Automation and Logistics.

[24]  Richard W. Eglese,et al.  Routeing Winter Gritting Vehicles , 1994, Discret. Appl. Math..

[25]  Richard W. Eglese,et al.  A deterministic tabu search algorithm for the capacitated arc routing problem , 2008, Comput. Oper. Res..

[26]  Feng Chu,et al.  A Scatter Search for the periodic capacitated arc routing problem , 2006, Eur. J. Oper. Res..

[27]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[28]  George L. Nemhauser,et al.  Handbooks in operations research and management science , 1989 .

[29]  Gerhard W. Dueck,et al.  Threshold accepting: a general purpose optimization algorithm appearing superior to simulated anneal , 1990 .

[30]  Bruce L. Golden,et al.  Chapter 5 Arc routing methods and applications , 1995 .

[31]  Richard F. Hartl,et al.  A Variable Neighborhood Search for the Multi Depot Vehicle Routing Problem with Time Windows , 2004, J. Heuristics.

[32]  Philippe Lacomme,et al.  Evolutionary Algorithms for Stochastic Arc Routing Problems , 2004, EvoWorkshops.

[33]  Gilbert Laporte,et al.  A Tabu Search Heuristic for the Capacitated Arc Routing Problem , 2000, Oper. Res..

[34]  Sanne Wøhlk New lower bound for the Capacitated Arc Routing Problem , 2006, Comput. Oper. Res..

[35]  Olli Bräysy,et al.  A Reactive Variable Neighborhood Search for the Vehicle-Routing Problem with Time Windows , 2003, INFORMS J. Comput..

[36]  Alain Hertz,et al.  A Variable Neighborhood Descent Algorithm for the Undirected Capacitated Arc Routing Problem , 2001, Transp. Sci..

[37]  Philippe Lacomme,et al.  A Genetic Algorithm for the Capacitated Arc Routing Problem and Its Extensions , 2001, EvoWorkshops.

[38]  S. C. Wirasinghe,et al.  An approximate procedure for determining the number, capacities and locations of solid waste transfer-stations in an urban region , 1983 .

[39]  Daniele Vigo,et al.  Exact solution of mixed CARP instances , 2006 .

[40]  Pierre Hansen,et al.  Variable neighborhood search: Principles and applications , 1998, Eur. J. Oper. Res..