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Mixed integer nonlinear optimization models for the Euclidean Steiner tree problem in $$\mathbb {R}^d$$ R d

Author

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  • Hacene Ouzia

    (Sorbonne Universite, CNRS, LIP-6)

  • Nelson Maculan

    (Universidade Federal do Rio de Janeiro, COPPE & IM)

Abstract

New mixed integer nonlinear optimization models for the Euclidean Steiner tree problem in d-space (with $$d\ge 3$$ d ≥ 3 ) will be presented in this work. All models feature a nonsmooth objective function but the continuous relaxations of their set of feasible solutions are convex. From these models, four convex mixed integer linear and nonlinear relaxations will be considered. Each relaxation has the same set of feasible solutions as the set of feasible solutions of the model from which it is derived. Finally, preliminary computational results highlighting the main features of the presented relaxations will be discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:83:y:2022:i:1:d:10.1007_s10898-021-01001-6
    DOI: 10.1007/s10898-021-01001-6
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    References listed on IDEAS

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    1. Courtney Stanton & J. MacGregor Smith, 2004. "Steiner Trees and 3-D Macromolecular Conformation," INFORMS Journal on Computing, INFORMS, vol. 16(4), pages 470-485, November.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

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