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Adaptation of a Branching Algorithm to Solve the Multi-Objective Hamiltonian Cycle Problem

In: Operations Research Proceedings 2019

Author

Listed:
  • Maialen Murua

    (TECNALIA)

  • Diego Galar

    (TECNALIA
    Luleå University of Technology)

  • Roberto Santana

    (University of the Basque Country (UPV/EHU))

Abstract

The Hamiltonian cycle problem (HCP) consists of finding a cycle of length N in an N-vertices graph. In this investigation, a graph G is considered with an associated set of matrices, in which each cell in the matrix corresponds to the weight of an arc. Thus, a multi-objective variant of the HCP is addressed and a Pareto set of solutions that minimizes the weights of the arcs for each objective is computed. To solve the HCP problem, the Branch-and-Fix algorithm is employed, a specific branching algorithm that uses the embedding of the problem in a particular stochastic process. To address the multi-objective HCP, the Branch-and-Fix algorithm is extended by computing different Hamiltonian cycles and fathoming the branches of the tree at earlier stages. The introduced anytime algorithm can produce a valid solution at any time of the execution, improving the quality of the Pareto Set as time increases.

Suggested Citation

  • Maialen Murua & Diego Galar & Roberto Santana, 2020. "Adaptation of a Branching Algorithm to Solve the Multi-Objective Hamiltonian Cycle Problem," Operations Research Proceedings, in: Janis S. Neufeld & Udo Buscher & Rainer Lasch & Dominik Möst & Jörn Schönberger (ed.), Operations Research Proceedings 2019, pages 231-237, Springer.
    • Handle: RePEc:spr:oprchp:978-3-030-48439-2_28
    DOI: 10.1007/978-3-030-48439-2_28
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