Solving large-scale time capacitated arc routing problems: from real-time heuristics to metaheuristics

This paper discusses the Time Capacitated Arc Routing Problem (TCARP) and introduces a heuristic and a metaheuristic algorithm for solving large-size instances of it. The TCARP is a realistic extension of the Capacitated Arc Routing Problem in which edge-servicing and edge-traversing costs, as well as vehicle capacities, are all time-based—i.e., given in time units. Accordingly, the TCARP goal is to minimise the total time employed in servicing the required edges, for which other edges might need to be traversed too. According to the numerical experiments carried out, the proposed heuristic is able to provide real-time results of high quality even for the largest instances considered. Likewise, the proposed metaheuristic outperforms other existing approaches, both in quality as well as in computing times.

[1]  Wen Lea Pearn,et al.  New lower bounds for the Capacitated Arc Routing Problem , 1988, Networks.

[2]  J. Potvin,et al.  A dynamic capacitated arc routing problem with time-dependent service costs , 2011 .

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

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

[5]  Johan W. Joubert,et al.  Applying min–max k postmen problems to the routing of security guards , 2012, J. Oper. Res. Soc..

[6]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[7]  M. Cândida Mourão,et al.  An updated annotated bibliography on arc routing problems , 2017, Networks.

[8]  Wen Lea Pearn,et al.  Augment-insert algorithms for the capacitated arc routing problem , 1991, Comput. Oper. Res..

[9]  Paulo Morelato França,et al.  GRASP with evolutionary path-relinking for the capacitated arc routing problem , 2013, Comput. Oper. Res..

[10]  Adam N. Letchford,et al.  Polyhedral Theory for Arc Routing Problems , 2000 .

[11]  Bruce L. Golden,et al.  The vehicle routing problem : latest advances and new challenges , 2008 .

[12]  Angel A. Juan,et al.  Using iterated local search for solving the flow-shop problem: Parallelization, parametrization, and randomization issues , 2014, Int. Trans. Oper. Res..

[13]  Moshe Dror,et al.  Routing electric meter readers , 1979, Comput. Oper. Res..

[14]  Angel A. Juan,et al.  SR-1: A simulation-based algorithm for the Capacitated Vehicle Routing Problem , 2008, 2008 Winter Simulation Conference.

[15]  Marcus Poggi de Aragão,et al.  Solving capacitated arc routing problems using a transformation to the CVRP , 2006, Comput. Oper. Res..

[16]  Kathryn A. Dowsland,et al.  Simulated Annealing , 1989, Encyclopedia of GIS.

[17]  Lawrence Bodin,et al.  Networks and vehicle routing for municipal waste collection , 1974, Networks.

[18]  Shanling Li,et al.  Multi-job Cutting Stock Problem with Due Dates and Release Dates , 1996 .

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

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

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

[22]  Wen Lea Pearn,et al.  Transforming arc routing into node routing problems , 1987, Comput. Oper. Res..

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

[24]  Gokhan Kirlik,et al.  Capacitated arc routing problem with deadheading demands , 2012, Comput. Oper. Res..

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

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

[27]  Angel A. Juan,et al.  Biased randomization of heuristics using skewed probability distributions: A survey and some applications , 2017, Comput. Ind. Eng..

[28]  Zhibin Jiang,et al.  A memetic algorithm with iterated local search for the capacitated arc routing problem , 2013 .

[29]  Fred W. Glover,et al.  A hybrid metaheuristic approach for the capacitated arc routing problem , 2016, Eur. J. Oper. Res..

[30]  Barry B. Barrios,et al.  MIRHA: multi-start biased randomization of heuristics with adaptive local search for solving non-smooth routing problems , 2013 .

[31]  Wen Lea Pearn,et al.  Approximate solutions for the capacitated arc routing problem , 1989, Comput. Oper. Res..

[32]  Angel A. Juan,et al.  Rich Vehicle Routing Problem , 2014, ACM Comput. Surv..

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

[34]  Stefan Irnich,et al.  In-Depth Analysis of Pricing Problem Relaxations for the Capacitated Arc-Routing Problem , 2015, Transp. Sci..

[35]  Gilbert Laporte,et al.  An Exact Algorithm for the Capacitated Arc Routing Problem with Deadheading Demand , 2013, Oper. Res..

[36]  Ángel Corberán,et al.  Recent results on Arc Routing Problems: An annotated bibliography , 2010 .

[37]  Sanne Wøhlk.  A Decade of Capacitated Arc Routing , 2008 .

[38]  Thibaut Vidal,et al.  Node, Edge, Arc Routing and Turn Penalties: Multiple Problems - One Neighborhood Extension , 2017, Oper. Res..

[39]  Kenneth Sörensen,et al.  Solving the mobile mapping van problem: A hybrid metaheuristic for capacitated arc routing with soft time windows , 2010, Comput. Oper. Res..

[40]  Ryuichi Hirabayashi,et al.  NODE DUPLICATION LOWER BOUNDS FOR THE CAPACITATED ARC ROUTING PROBLEM , 1992 .

[41]  Richard W. Eglese,et al.  A constraint programming approach to the Chinese postman problem with time windows , 2006, Comput. Oper. Res..

[42]  Yaxiong Lin,et al.  A new algorithm for the directed chinese postman problem , 1988, Comput. Oper. Res..

[43]  Yaghout Nourani,et al.  A comparison of simulated annealing cooling strategies , 1998 .

[44]  Bruce L. Golden,et al.  Computational experiments with algorithms for a class of routing problems , 1983, Comput. Oper. Res..

[45]  Richard W. Eglese,et al.  An Interactive Algorithm for Vehicle Routeing for Winter — Gritting , 1996 .

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

[47]  Sanne Wøhlk,et al.  Contributions to Arc Routing , 2005 .

[48]  Martin Trépanier,et al.  Road network monitoring: algorithms and a case study , 2006, Comput. Oper. Res..

[49]  Ángel Corberán,et al.  The Capacitated Arc Routing Problem: Lower bounds , 1992, Networks.

[50]  Jh van Vuuren,et al.  Network service scheduling and routing , 2004 .

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

[52]  Angel A. Juan,et al.  Development and assessment of the SHARP and RandSHARP algorithms for the arc routing problem , 2012, AI Commun..

[53]  Javier Faulin,et al.  Using parallel & distributed computing for real-time solving of vehicle routing problems with stochastic demands , 2011, Annals of Operations Research.

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

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

[56]  Sanne Wøhlk.  An Approximation Algorithm for the Capacitated Arc Routing Problem , 2008 .

[57]  Adam N. Letchford,et al.  Exploiting sparsity in pricing routines for the capacitated arc routing problem , 2009, Comput. Oper. Res..

[58]  Christian Prins.  Chapter 7: The Capacitated Arc Routing Problem: Heuristics , 2013 .

[59]  G. Clarke,et al.  Scheduling of Vehicles from a Central Depot to a Number of Delivery Points , 1964 .

[60]  Alain Hertz,et al.  Recent Trends in Arc Routing , 2005 .

[61]  Peter B. Keenan,et al.  Arc routing for rural Irish networks , 1996 .

[62]  Gilbert Laporte,et al.  Arc Routing: Problems, Methods, and Applications , 2015 .

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

[64]  Geir Hasle.  Routing Applications in Newspaper Delivery , 2012 .

[65]  Craig A. Knoblock,et al.  A Survey of Digital Map Processing Techniques , 2014, ACM Comput. Surv..

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