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TSP Cuts Which Do Not Conform to the Template Paradigm

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Computational Combinatorial Optimization

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2241))

Abstract

The first computer implementation of the Dantzig-Fulkerson-Johnson cutting-plane method for solving the traveling salesman problem, written by Martin, used subtour inequalities as well as cutting planes of Gomory's type. The practice of looking for and using cuts that match prescribed templates in conjunction with Gomory cuts was continued in computer codes of Miliotis, Land, and Fleischmann. Grötschel, Padberg, and Hong advocated a different policy, where the template paradigm is the only source of cuts; furthermore, they argued for drawing the templates exclusively from the set of linear inequalities that induce facets of the TSP polytope. These policies were adopted in the work of Crowder and Padberg, in the work of Grötschel and Holland, and in the work of Padberg and Rinaldi; their computer codes produced the most impressive computational TSP successes of the nineteen eighties. Eventually, the template paradigm became the standard frame of reference for cutting planes in the TSP. The purpose of this paper is to describe a technique for .nding cuts that disdains all understanding of the TSP polytope and bashes on regardless of all prescribed templates. Combining this technique with the traditional template approach was a crucial step in our solutions of a 13,509-city TSP instance and a 15,112-city TSP instance.

Supported by ONR Grant N00014-01-1-0058

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Author information

Authors and Affiliations

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

    David Applegate

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

    Robert Bixby

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

    Vašek Chvátal

  4. Program in Applied and Computational Mathematics, Princeton University, 08544, Princeton, NJ, USA

    William Cook

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  1. David Applegate
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  2. Robert Bixby
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  4. William Cook
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Editors and Affiliations

  1. Universität zu Köln,Institut für Informatik, Pohligstr.1, 50969, Köln, Germany

    Michael Jünger

  2. ENSIMAG - antenne de Montbonnot Laboratoire Informatique et Distribution, ZIRST, 51,avenue Jean Kuntzmann, 38330, Montbonnot Saint Martin, France

    Denis Naddef

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Applegate, D., Bixby, R., Chvátal, V., Cook, W. (2001). TSP Cuts Which Do Not Conform to the Template Paradigm. In: Jünger, M., Naddef, D. (eds) Computational Combinatorial Optimization. Lecture Notes in Computer Science, vol 2241. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45586-8_7

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  • DOI: https://doi.org/10.1007/3-540-45586-8_7

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