What you should know about the vehicle routing problem

In the Vehicle Routing Problem (VRP), the aim is to design a set of m minimum cost vehicle routes through n customer locations, so that each route starts and ends at a common location and some side constraints are satisfied. Common applications arise in newspaper and food delivery, and in milk collection. This article summarizes the main known results for the classical VRP in which only vehicle capacity constraints are present. The article is structured around three main headings: exact algorithms, classical heuristics, and metaheuristics. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007

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

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

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

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

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

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

[7]  George B. Dantzig,et al.  Solution of a Large-Scale Traveling-Salesman Problem , 1954, Oper. Res..

[8]  Michel Gendreau,et al.  Metaheuristics for the Vehicle Routing Problem and Its Extensions: A Categorized Bibliography , 2008 .

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

[10]  Martin W. P. Savelsbergh,et al.  10. Vehicle routing: handling edge exchanges , 2003 .

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

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

[13]  Alex Van Breedam,et al.  An analysis of the behavior of heuristics for the vehicle routing problem for a selection of problems with vehicle-relatezd, customer-related, and time-related constraints , 1994 .

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

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

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

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

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

[19]  Gregory Gutin,et al.  The traveling salesman problem , 2006, Discret. Optim..

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[39]  Paolo Toth,et al.  Exact Solution of the Vehicle Routing Problem , 1998 .

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

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

[42]  Jean-Yves Potvin,et al.  Vehicle Routing , 2009, Encyclopedia of Optimization.

[43]  James B. Orlin,et al.  New neighborhood search algorithms based on exponentially large neighborhoods , 2001 .

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

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

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

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

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

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

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

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

[52]  Bruce L. Golden,et al.  Routing Vehicles in the Real World: Applications in the Solid Waste, Beverage, Food, Dairy, and Newspaper Industries , 2002, The Vehicle Routing Problem.

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

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

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

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

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

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

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