Solution of a Min-Max Vehicle Routing Problem

We use a branch-and-cut search to solve the Whizzkids'96 vehicle routing problem, demonstrating that the winning solution in the 1996 competition is in fact optimal. Our algorithmic framework combines the LP-based traveling salesman code of Applegate, Bixby, ChvAital, and Cook, with specialized cutting planes and a distributed search algorithm, permitting the use of a computing network located across Rice, Princeton, AT&T, and Bonn. The 1996 problem instance wasdeveloped by E. Aartsand J. K. Lenstra, and the competition was sponsored by the information technology firm CMG and the newspaper De Telegraaf.

[1]  Niklas Kohl,et al.  K-Path Cuts for the Vehicle Routing Problem with Time Windows. , 1996 .

[2]  Eugene L. Lawler,et al.  Traveling Salesman Problem , 2016 .

[3]  Jeff T. Linderoth,et al.  Solving large quadratic assignment problems on computational grids , 2002, Math. Program..

[4]  R. Bixby,et al.  On the Solution of Traveling Salesman Problems , 1998 .

[5]  Jacques Desrosiers,et al.  2-Path Cuts for the Vehicle Routing Problem with Time Windows , 1997, Transp. Sci..

[6]  G. Rinaldi,et al.  Chapter 4 The traveling salesman problem , 1995 .

[7]  Leslie E. Trotter,et al.  On the capacitated vehicle routing problem , 2003, Math. Program..

[8]  Richard M. Karp,et al.  The traveling-salesman problem and minimum spanning trees: Part II , 1971, Math. Program..

[9]  H. Goldwhite,et al.  The Manhattan Project , 1986 .

[10]  Bruce L. Golden,et al.  VEHICLE ROUTING: METHODS AND STUDIES , 1988 .

[11]  J. K. Lenstra,et al.  Whizzkids: two exercises in computational discrete optimization , 2000 .

[12]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

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

[14]  Ángel Corberán,et al.  Separating capacity constraints in the CVRP using tabu search , 1998, Eur. J. Oper. Res..

[15]  Edward W. Felten,et al.  Large-step markov chains for the TSP incorporating local search heuristics , 1992, Oper. Res. Lett..

[16]  David R. Karger,et al.  Global min-cuts in RNC, and other ramifications of a simple min-out algorithm , 1993, SODA '93.

[17]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[18]  Cynthia A. Phillips,et al.  Pico: An Object-Oriented Framework for Parallel Branch and Bound * , 2001 .

[19]  Richard M. Karp,et al.  The Traveling-Salesman Problem and Minimum Spanning Trees , 1970, Oper. Res..

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

[21]  Ulrich Blasum,et al.  Application of the Branch and Cut Method to the Vehicle Routing Problem , 2000 .

[22]  David R. Karger,et al.  An Õ(n2) algorithm for minimum cuts , 1993, STOC.

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

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

[25]  G. Nemhauser,et al.  Integer Programming , 2020 .

[26]  Gerhard Reinelt,et al.  Traveling salesman problem , 2012 .

[27]  William J. Cook,et al.  TSP Cuts Which Do Not Conform to the Template Paradigm , 2000, Computational Combinatorial Optimization.

[28]  Jean-Maurice Clochard,et al.  Using path inequalities in a branch and cut code for the symmetric traveling salesman problem , 1993, IPCO.

[29]  William R. Cook,et al.  A Parallel Cutting-Plane Algorithm for the Vehicle Routing Problem With Time Windows , 1999 .