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Implementing the Dantzig-Fulkerson-Johnson algorithm for large traveling salesman problems

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Abstract.

 Dantzig, Fulkerson, and Johnson (1954) introduced the cutting-plane method as a means of attacking the traveling salesman problem; this method has been applied to broad classes of problems in combinatorial optimization and integer programming. In this paper we discuss an implementation of Dantzig et al.'s method that is suitable for TSP instances having 1,000,000 or more cities. Our aim is to use the study of the TSP as a step towards understanding the applicability and limits of the general cutting-plane method in large-scale applications.

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Authors and Affiliations

  1. Algorithms and Optimization Department, AT&T Labs – Research, Florham Park, NJ 07932, USA, , , , , , US

    David Applegate

  2. Computational and Applied Mathematics, Rice University, Houston, TX 77005, USA, , , , , , US

    Robert Bixby

  3. Department of Computer Science, Rutgers University, Piscataway, NJ 08854, USA, , , , , , US

    Vašek Chvátal

  4. Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA, , , , , , US

    William Cook

Authors
  1. David Applegate
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  2. Robert Bixby
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  3. Vašek Chvátal
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  4. William Cook
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Additional information

Received: December 6, 2002 / Accepted: April 24, 2003 Published online: May 28, 2003

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ID="*" Supported by ONR Grant N00014-03-1-0040

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Applegate, D., Bixby, R., Chvátal, V. et al. Implementing the Dantzig-Fulkerson-Johnson algorithm for large traveling salesman problems. Math. Program., Ser. B 97, 91–153 (2003). https://doi.org/10.1007/s10107-003-0440-4

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  • DOI: https://doi.org/10.1007/s10107-003-0440-4

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