Fifty Years of Vehicle Routing

The Vehicle Routing Problem (VRP) was introduced 50 years ago by Dantzig and Ramser under the title “The Truck Dispatching Problem.” The study of the VRP has given rise to major developments in the fields of exact algorithms and heuristics. In particular, highly sophisticated exact mathematical programming decomposition algorithms and powerful metaheuristics for the VRP have been put forward in recent years. The purpose of this article is to provide a brief account of this development.

[1]  Gilbert Laporte,et al.  An exact algorithm for the asymmetrical capacitated vehicle routing problem , 1986, Networks.

[2]  George B. Dantzig,et al.  The Truck Dispatching Problem , 1959 .

[3]  Thomas L. Magnanti,et al.  Implementing vehicle routing algorithms , 1977, Networks.

[4]  Gilbert Laporte,et al.  A Tabu Search Heuristic for the Vehicle Routing Problem , 1991 .

[5]  Paolo Toth,et al.  Branch-And-Bound Algorithms for the Capacitated VRP , 2002, The Vehicle Routing Problem.

[6]  E. Balas,et al.  Set Partitioning: A survey , 1976 .

[7]  James B. Orlin,et al.  Creating very large scale neighborhoods out of smaller ones by compounding moves , 2006, J. Heuristics.

[8]  Marshall L. Fisher,et al.  A generalized assignment heuristic for vehicle routing , 1981, Networks.

[9]  Richard F. Hartl,et al.  D-Ants: Savings Based Ants divide and conquer the vehicle routing problem , 2004, Comput. Oper. Res..

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

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

[12]  Michel Gendreau,et al.  Metaheuristics for the Capacitated VRP , 2002, The Vehicle Routing Problem.

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

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

[15]  Gilbert Laporte,et al.  An Improved Petal Heuristic for the Vehicle Routeing Problem , 1996 .

[16]  Paolo Toth,et al.  Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations , 1981, Math. Program..

[17]  Harvey M. Salkin,et al.  A set-partitioning-based exact algorithm for the vehicle routing problem , 1989, Networks.

[18]  Nicos Christofides,et al.  An Algorithm for the Vehicle-dispatching Problem , 1969 .

[19]  Billy E. Gillett,et al.  A Heuristic Algorithm for the Vehicle-Dispatch Problem , 1974, Oper. Res..

[20]  Paul M. Thompson,et al.  Cyclic Transfer Algorithm for Multivehicle Routing and Scheduling Problems , 1993, Oper. Res..

[21]  P. Toth,et al.  Some New Branching and Bounding Criteria for the Asymmetric Travelling Salesman Problem , 1980 .

[22]  Barrie M. Baker,et al.  Extensions to the generalised assignment heuristic for vehicle routing , 1999, Eur. J. Oper. Res..

[23]  Michel Gendreau,et al.  A guide to vehicle routing heuristics , 2002, J. Oper. Res. Soc..

[24]  Christos D. Tarantilis,et al.  Solving the vehicle routing problem with adaptive memory programming methodology , 2005, Comput. Oper. Res..

[25]  Nicos Christofides,et al.  Distribution management : mathematical modelling and practical analysis , 1971 .

[26]  Adam N. Letchford,et al.  A new branch-and-cut algorithm for the capacitated vehicle routing problem , 2004, Math. Program..

[27]  Nicos Christofides,et al.  The vehicle routing problem , 1976, Revue française d'automatique, informatique, recherche opérationnelle. Recherche opérationnelle.

[28]  David M. Ryan,et al.  An Integer Programming Approach to the Vehicle Scheduling Problem , 1976 .

[29]  Nicos Christofides,et al.  An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts , 2008, Math. Program..

[30]  Christian Prins,et al.  A GRASP × Evolutionary Local Search Hybrid for the Vehicle Routing Problem , 2009, Bio-inspired Algorithms for the Vehicle Routing Problem.

[31]  Marvin D. Nelson,et al.  Implementation techniques for the vehicle routing problem , 1985, Comput. Oper. Res..

[32]  Ulrich Derigs,et al.  Applying the attribute based hill climber heuristic to the vehicle routing problem , 2007, Eur. J. Oper. Res..

[33]  William J. Cook,et al.  Solution of a Large-Scale Traveling-Salesman Problem , 1954, 50 Years of Integer Programming.

[34]  G. Laporte,et al.  A tabu search heuristic for periodic and multi-depot vehicle routing problems , 1997, Networks.

[35]  Bezalel Gavish,et al.  Parallel Savings Based Heuristics for the Delivery Problem , 1991, Oper. Res..

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

[37]  Gilbert Laporte,et al.  A concise guide to the Traveling Salesman Problem , 2010, J. Oper. Res. Soc..

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

[39]  Paolo Toth,et al.  The Granular Tabu Search and Its Application to the Vehicle-Routing Problem , 2003, INFORMS J. Comput..

[40]  Michel Gendreau,et al.  New Heuristics for the Vehicle Routing Problem , 2005 .

[41]  Olli Bräysy,et al.  Active guided evolution strategies for large-scale vehicle routing problems with time windows , 2005, Comput. Oper. Res..

[42]  Fred W. Glover,et al.  Future paths for integer programming and links to artificial intelligence , 1986, Comput. Oper. Res..

[43]  Yuichi Nagata,et al.  Edge assembly-based memetic algorithm for the capacitated vehicle routing problem , 2009 .

[44]  Roberto Baldacci,et al.  An Exact Algorithm for the Capacitated Vehicle Routing Problem Based on a Two-Commodity Network Flow Formulation , 2004, Oper. Res..

[45]  Giovanni Rinaldi,et al.  Branch-And-Cut Algorithms for the Capacitated VRP , 2001, The Vehicle Routing Problem.

[46]  Gilbert Laporte,et al.  Optimal Routing under Capacity and Distance Restrictions , 1985, Oper. Res..

[47]  Éric D. Taillard,et al.  Parallel iterative search methods for vehicle routing problems , 1993, Networks.

[48]  Paolo Toth,et al.  State-space relaxation procedures for the computation of bounds to routing problems , 1981, Networks.

[49]  David L. Applegate,et al.  The traveling salesman problem , 2006 .

[50]  Christos D. Tarantilis,et al.  BoneRoute: An Adaptive Memory-Based Method for Effective Fleet Management , 2002, Ann. Oper. Res..

[51]  William J. Cook,et al.  The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics) , 2007 .

[52]  John Holt,et al.  A Repeated Matching Heuristic for the Vehicle Routeing Problem , 1994 .

[53]  G. Laporte,et al.  Exact Algorithms for the Vehicle Routing Problem , 1987 .

[54]  James P. Kelly,et al.  The Impact of Metaheuristics on Solving the Vehicle Routing Problem: Algorithms, Problem Sets, and Computational Results , 1998 .

[55]  M. Padberg,et al.  Solving airline crew scheduling problems by branch-and-cut , 1993 .

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

[57]  Paul Shaw,et al.  Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems , 1998, CP.

[58]  Olli Bräysy,et al.  Active-guided evolution strategies for large-scale capacitated vehicle routing problems , 2007, Comput. Oper. Res..

[59]  Yves Rochat,et al.  Probabilistic diversification and intensification in local search for vehicle routing , 1995, J. Heuristics.

[60]  Paolo Toth,et al.  Models, relaxations and exact approaches for the capacitated vehicle routing problem , 2002, Discret. Appl. Math..

[61]  Marshall L. Fisher,et al.  Chapter 1 Vehicle routing , 1995 .

[62]  Bruce L. Golden,et al.  Very large-scale vehicle routing: new test problems, algorithms, and results , 2005, Comput. Oper. Res..

[63]  Gilbert Laporte,et al.  Classical Heuristics for the Capacitated VRP , 2002, The Vehicle Routing Problem.

[64]  H. Paessens,et al.  The savings algorithm for the vehicle routing problem , 1988 .

[65]  Adam N. Letchford,et al.  Multistars, partial multistars and the capacitated vehicle routing problem , 2002, Math. Program..

[66]  Pablo Moscato,et al.  A Gentle Introduction to Memetic Algorithms , 2003, Handbook of Metaheuristics.

[67]  G. Laporte,et al.  A branch and bound algorithm for the capacitated vehicle routing problem , 1983 .

[68]  Renato F. Werneck,et al.  Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem , 2006, Math. Program..

[69]  Michel Gendreau,et al.  An efficient variable neighborhood search heuristic for very large scale vehicle routing problems , 2007, Comput. Oper. Res..

[70]  Yuichi Nagata,et al.  Edge Assembly Crossover for the Capacitated Vehicle Routing Problem , 2007, EvoCOP.

[71]  Gilbert Laporte,et al.  What you should know about the vehicle routing problem , 2007 .

[72]  M. R. Rao,et al.  Allocation of Transportation Units to Alternative Trips - A Column Generation Scheme with Out-of-Kilter Subproblems , 1968, Oper. Res..

[73]  Nicos Christofides,et al.  A new exact algorithm for the vehicle routing problem based onq-paths andk-shortest paths relaxations , 1995, Ann. Oper. Res..

[74]  Gilbert Laporte,et al.  A unified tabu search heuristic for vehicle routing problems with time windows , 2001, J. Oper. Res. Soc..

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

[76]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[77]  David Pisinger,et al.  A unified heuristic for a large class of Vehicle Routing Problems with Backhauls , 2006, Eur. J. Oper. Res..

[78]  Fred Glover,et al.  Extensions of the Petal Method for Vehicle Routeing , 1993 .

[79]  Christian Prins,et al.  A simple and effective evolutionary algorithm for the vehicle routing problem , 2004, Comput. Oper. Res..

[80]  Stephen C. Graves,et al.  The Travelling Salesman Problem and Related Problems , 1978 .

[81]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[82]  M. Balinski,et al.  On an Integer Program for a Delivery Problem , 1964 .

[83]  Marshall L. Fisher,et al.  Optimal Solution of Vehicle Routing Problems Using Minimum K-Trees , 1994, Oper. Res..

[84]  G. Dueck New optimization heuristics , 1993 .

[85]  David Pisinger,et al.  A general heuristic for vehicle routing problems , 2007, Comput. Oper. Res..