License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CP.2021.30
URN: urn:nbn:de:0030-drops-153212
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15321/
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Isoart, Nicolas ; Régin, Jean-Charles

A k-Opt Based Constraint for the TSP

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LIPIcs-CP-2021-30.pdf (0.7 MB)

Abstract

The LKH algorithm based on k-opt is an extremely efficient algorithm solving the TSP. Given a non-optimal tour in a graph, the idea of k-opt is to iteratively swap k edges of this tour in order to find a shorter tour. However, the optimality of a tour cannot be proved with this method. In that case, exact solving methods such as CP can be used. The CP model is based on a graph variable with mandatory and optional edges. Through branch-and-bound and filtering algorithms, the set of mandatory edges will be modified. In this paper, we introduce a new constraint to the CP model named mandatory Hamiltonian path constraint searching for k-opt in the mandatory Hamiltonian paths. Experiments have shown that the mandatory Hamiltonian path constraint allows us to gain on average a factor of 3 on the solving time. In addition, we have been able to solve some instances that remain unsolved with the state of the art CP solver with a 1 week time out.

BibTeX - Entry

@InProceedings{isoart_et_al:LIPIcs.CP.2021.30,
  author =	{Isoart, Nicolas and R\'{e}gin, Jean-Charles},
  title =	{{A k-Opt Based Constraint for the TSP}},
  booktitle =	{27th International Conference on Principles and Practice of Constraint Programming (CP 2021)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-211-2},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{210},
  editor =	{Michel, Laurent D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15321},
  URN =		{urn:nbn:de:0030-drops-153212},
  doi =		{10.4230/LIPIcs.CP.2021.30},
  annote =	{Keywords: TSP, k-opt, 1-tree, Constraint}
}

Keywords: TSP, k-opt, 1-tree, Constraint
Collection: 27th International Conference on Principles and Practice of Constraint Programming (CP 2021)
Issue Date: 2021
Date of publication: 15.10.2021

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