A k-Opt Based Constraint for the TSP

Authors Nicolas Isoart, Jean-Charles Régin

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Nicolas Isoart
  • Université Côte d'Azur, Nice, France
Jean-Charles Régin
  • Université Côte d'Azur, Nice, France

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Nicolas Isoart and Jean-Charles Régin. A k-Opt Based Constraint for the TSP. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • TSP
  • k-opt
  • 1-tree
  • Constraint


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