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Solving Steiner Tree Problems in Graphs with Lagrangian Relaxation

Author

Listed:
  • Laura Bahiense

    (Universidade Federal do Rio de Janeiro, COPPE-Sistemas e Computação)

  • Francisco Barahona

    (IBM T. J. Watson Research Center)

  • Oscar Porto

    (Rua Marquês de São Vicente 225, Predio Cardeal Leme, Sala 401)

Abstract

This paper presents an algorithm to obtain near optimal solutions for the Steiner tree problem in graphs. It is based on a Lagrangian relaxation of a multi-commodity flow formulation of the problem. An extension of the subgradient algorithm, the volume algorithm, has been used to obtain lower bounds and to estimate primal solutions. It was possible to solve several difficult instances from the literature to proven optimality without branching. Computational results are reported for problems drawn from the SteinLib library.

Suggested Citation

  • Laura Bahiense & Francisco Barahona & Oscar Porto, 2003. "Solving Steiner Tree Problems in Graphs with Lagrangian Relaxation," Journal of Combinatorial Optimization, Springer, vol. 7(3), pages 259-282, September.
    • Handle: RePEc:spr:jcomop:v:7:y:2003:i:3:d:10.1023_a:1027368621279
    DOI: 10.1023/A:1027368621279
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    References listed on IDEAS

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    1. T. L. Magnanti & R. T. Wong, 1984. "Network Design and Transportation Planning: Models and Algorithms," Transportation Science, INFORMS, vol. 18(1), pages 1-55, February.
    2. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    3. Sunil Chopra & Edgar R. Gorres & M. R. Rao, 1992. "Solving the Steiner Tree Problem on a Graph Using Branch and Cut," INFORMS Journal on Computing, INFORMS, vol. 4(3), pages 320-335, August.
    4. Kaj Holmberg & Johan Hellstrand, 1998. "Solving the Uncapacitated Network Design Problem by a Lagrangean Heuristic and Branch-and-Bound," Operations Research, INFORMS, vol. 46(2), pages 247-259, April.
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    Cited by:

    1. Igor Litvinchev & Socorro Rangel & Jania Saucedo, 2010. "A Lagrangian bound for many-to-many assignment problems," Journal of Combinatorial Optimization, Springer, vol. 19(3), pages 241-257, April.

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    Keywords

    Steiner trees; Lagrangian relaxation;

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