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On the domino-parity inequalities for the STSP

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Abstract

One method which has been used very successfully for finding optimal and provably good solutions for large instances of the symmetric travelling salesman problem (STSP) is the branch and cut method. This method requires knowledge of classes of useful valid inequalities for the polytope associated with the STSP, as well as efficient separation routines for these classes of inequalities. Recently a new class of valid inequalities called the domino-parity inequalites were introduced for the STSP. An efficient separation routine is known for these constraints if certain conditions are satisfied by the point to be separated. This separation routine has never been implemented or tested. We present several performance enhancements for this separation routine, and discuss our implementation of this improved algorithm. We test our implementation and provide results which we believe demonstrate the practical usefulness of these constraints and the separation routine for the STSP within a branch and cut framework.

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Authors and Affiliations

  1. SITE, University of Ottawa, Ottawa, K1N 6N5, Canada

    Sylvia Boyd & Danielle Vella

  2. Hamilton College, Clinton, NY, USA

    Sally Cockburn

Authors
  1. Sylvia Boyd
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  2. Sally Cockburn
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  3. Danielle Vella
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Corresponding author

Correspondence to Sylvia Boyd.

Additional information

This research was partially supported by grants from the Natural Sciences and Engineering Research Council of Canada

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Boyd, S., Cockburn, S. & Vella, D. On the domino-parity inequalities for the STSP. Math. Program. 110, 501–519 (2007). https://doi.org/10.1007/s10107-006-0011-6

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  • DOI: https://doi.org/10.1007/s10107-006-0011-6

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