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The Euclidean Steiner tree problem in R n : A mathematical programming formulation

Author

Listed:
  • Nelson Maculan
  • Philippe Michelon
  • Adilson Xavier

Abstract

A nonconvex mixed-integer programming formulation for the Euclidean Steiner Tree Problem (ESTP) in R n is presented. After obtaining separability between integer and continuous variables in the objective function, a Lagrange dual program is proposed. To solve this dual problem (and obtaining a lower bound for ESTP) we use subgradient techniques. In order to evaluate a subgradient at each iteration we have to solve three optimization problems, two in polynomial time, and one is a special convex nondifferentiable programming problem. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • Nelson Maculan & Philippe Michelon & Adilson Xavier, 2000. "The Euclidean Steiner tree problem in R n : A mathematical programming formulation," Annals of Operations Research, Springer, vol. 96(1), pages 209-220, November.
    • Handle: RePEc:spr:annopr:v:96:y:2000:i:1:p:209-220:10.1023/a:1018903619285
    DOI: 10.1023/A:1018903619285
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    Cited by:

    1. Renan Vicente Pinto & Nelson Maculan, 2023. "A new heuristic for the Euclidean Steiner Tree Problem in $${\mathbb {R}}^n$$ R n," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 391-413, July.
    2. Marcia Fampa & Jon Lee & Wendel Melo, 2016. "A specialized branch-and-bound algorithm for the Euclidean Steiner tree problem in n-space," Computational Optimization and Applications, Springer, vol. 65(1), pages 47-71, September.
    3. Hacene Ouzia & Nelson Maculan, 2022. "Mixed integer nonlinear optimization models for the Euclidean Steiner tree problem in $$\mathbb {R}^d$$ R d," Journal of Global Optimization, Springer, vol. 83(1), pages 119-136, May.

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