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All Colors Shortest Path problem on trees

Author

Listed:
  • Mehmet Berkehan Akçay

    (Izmir University of Economics)

  • Hüseyin Akcan

    (Izmir University of Economics)

  • Cem Evrendilek

    (Izmir University of Economics)

Abstract

Given an edge weighted tree T(V, E), rooted at a designated base vertex $$r \in V$$ r ∈ V , and a color from a set of colors $$C=\{1,\ldots ,k\}$$ C = { 1 , … , k } assigned to every vertex $$v \in V$$ v ∈ V , All Colors Shortest Path problem on trees (ACSP-t) seeks the shortest, possibly non-simple, path starting from r in T such that at least one node from every distinct color in C is visited. We show that ACSP-t is NP-hard, and also prove that it does not have a constant factor approximation. We give an integer linear programming formulation of ACSP-t. Based on a linear programming relaxation of this formulation, an iterative rounding heuristic is proposed. The paper also explores genetic algorithm and tabu search to develop alternative heuristic solutions for ACSP-t. The performance of all the proposed heuristics are evaluated experimentally for a wide range of trees that are generated parametrically.

Suggested Citation

  • Mehmet Berkehan Akçay & Hüseyin Akcan & Cem Evrendilek, 2018. "All Colors Shortest Path problem on trees," Journal of Heuristics, Springer, vol. 24(4), pages 617-644, August.
    • Handle: RePEc:spr:joheur:v:24:y:2018:i:4:d:10.1007_s10732-018-9370-4
    DOI: 10.1007/s10732-018-9370-4
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    References listed on IDEAS

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    1. Pop, Petrică C. & Matei, Oliviu & Sabo, Cosmin & Petrovan, Adrian, 2018. "A two-level solution approach for solving the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 265(2), pages 478-487.
    2. Öncan, Temel & Cordeau, Jean-François & Laporte, Gilbert, 2008. "A tabu search heuristic for the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 191(2), pages 306-319, December.
    3. Pop, Petrica C. & Kern, W. & Still, G., 2006. "A new relaxation method for the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 170(3), pages 900-908, May.
    4. Dror, M. & Haouari, M. & Chaouachi, J., 2000. "Generalized spanning trees," European Journal of Operational Research, Elsevier, vol. 120(3), pages 583-592, February.
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    Cited by:

    1. F. Carrabs & R. Cerulli & R. Pentangelo & A. Raiconi, 2018. "A two-level metaheuristic for the all colors shortest path problem," Computational Optimization and Applications, Springer, vol. 71(2), pages 525-551, November.

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