The Robust Traveling Salesman Problem with Interval Data

We study a version of the traveling salesman problem where travel times are specified as a range of possible values. This model reflects the difficulties to estimate travel times exactly in reality. Robustness concepts are used to drive optimization. We propose some efficient heuristic and preprocessing techniques. Computational experiments are presented.

[1]  J. F. Benders.  Partitioning procedures for solving mixed-variables programming problems , 1962 .

[2]  Roberto Montemanni,et al.  A branch and bound algorithm for the robust shortest path problem with interval data , 2004, Oper. Res. Lett..

[3]  Hande Yaman,et al.  The robust spanning tree problem with interval data , 2001, Oper. Res. Lett..

[4]  Roberto Montemanni,et al.  An exact algorithm for the robust shortest path problem with interval data , 2004, Comput. Oper. Res..

[5]  Gang Yu,et al.  On the robust shortest path problem , 1998 .

[6]  Roberto Montemanni,et al.  A Benders decomposition approach for the robust spanning tree problem with interval data , 2006, Eur. J. Oper. Res..

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

[8]  Dorit S. Hochba,et al.  Approximation Algorithms for NP-Hard Problems , 1997, SIGA.

[9]  Sanjeev Arora,et al.  Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems , 1998, JACM.

[10]  Gerhard Reinelt,et al.  A Faster Exact Separation Algorithm for Blossom Inequalities , 2004, IPCO.

[11]  A. M. Geoffrion.  Generalized Benders decomposition , 1972 .

[12]  Keld Helsgaun,et al.  An effective implementation of the Lin-Kernighan traveling salesman heuristic , 2000, Eur. J. Oper. Res..

[13]  Roberto Montemanni,et al.  The robust shortest path problem with interval data via Benders decomposition , 2005, 4OR.

[14]  André Langevin,et al.  CLASSIFICATION OF TRAVELING SALESMAN PROBLEM FORMULATIONS , 1988 .

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

[16]  Gilbert Laporte,et al.  The Vehicle Routing Problem with Stochastic Travel Times , 1992, Transp. Sci..

[17]  A Gerodimos,et al.  Robust Discrete Optimization and its Applications , 1996, J. Oper. Res. Soc..

[18]  Igor Averbakh,et al.  Interval data minmax regret network optimization problems , 2004, Discret. Appl. Math..

[19]  Roberto Montemanni,et al.  A branch and bound algorithm for the robust spanning tree problem with interval data , 2002, Eur. J. Oper. Res..

[20]  H. P. Williams,et al.  A Survey of Different Integer Programming Formulations of the Travelling Salesman Problem , 2007 .

[21]  Adam Kasperski,et al.  An approximation algorithm for interval data minmax regret combinatorial optimization problems , 2006, Inf. Process. Lett..

[22]  Toshihide Ibaraki,et al.  Implementing an efficient minimum capacity cut algorithm , 1994, Math. Program..

[23]  Panagiotis Kouvelis,et al.  Robust scheduling to hedge against processing time uncertainty in single-stage production , 1995 .

[24]  G. Reinelt.  The traveling salesman: computational solutions for TSP applications , 1994 .

[25]  Igor Averbakh,et al.  On the complexity of a class of combinatorial optimization problems with uncertainty , 2001, Math. Program..