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A multi-start local search algorithm for the Hamiltonian completion problem on undirected graphs

Author

Listed:
  • Jorik Jooken

    (KU Leuven Kulak)

  • Pieter Leyman

    (KU Leuven Kulak)

  • Patrick Causmaecker

    (KU Leuven Kulak)

Abstract

This paper proposes a local search algorithm for a specific combinatorial optimisation problem in graph theory: the Hamiltonian completion problem (HCP) on undirected graphs. In this problem, the objective is to add as few edges as possible to a given undirected graph in order to obtain a Hamiltonian graph. This problem has mainly been studied in the context of various specific kinds of undirected graphs (e.g. trees, unicyclic graphs and series-parallel graphs). The proposed algorithm, however, concentrates on solving HCP for general undirected graphs. It can be considered to belong to the category of matheuristics, because it integrates an exact linear time solution for trees into a local search algorithm for general graphs. This integration makes use of the close relation between HCP and the minimum path partition problem, which makes the algorithm equally useful for solving the latter problem. Furthermore, a benchmark set of problem instances is constructed for demonstrating the quality of the proposed algorithm. A comparison with state-of-the-art solvers indicates that the proposed algorithm is able to achieve high-quality results.

Suggested Citation

  • Jorik Jooken & Pieter Leyman & Patrick Causmaecker, 2020. "A multi-start local search algorithm for the Hamiltonian completion problem on undirected graphs," Journal of Heuristics, Springer, vol. 26(5), pages 743-769, October.
    • Handle: RePEc:spr:joheur:v:26:y:2020:i:5:d:10.1007_s10732-020-09447-9
    DOI: 10.1007/s10732-020-09447-9
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    References listed on IDEAS

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    1. Paolo Detti & Carlo Meloni & Marco Pranzo, 2007. "Local search algorithms for finding the Hamiltonian completion number of line graphs," Annals of Operations Research, Springer, vol. 156(1), pages 5-24, December.
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    Cited by:

    1. Jooken, Jorik & Leyman, Pieter & De Causmaecker, Patrick, 2022. "A new class of hard problem instances for the 0–1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 301(3), pages 841-854.

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