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

Abstract

New mixed integer nonlinear optimization models for the Euclidean Steiner tree problem in d-space (with \(d\ge 3\)) 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.

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Acknowledgements

We are grateful to the referee for her (or his) careful reading, insightful and precise comments. This work was partially supported by the National Council for Scientific and Technological Development - CNPq, under grant 302578/2014-5, COPPETEC Foundation, and by CAPES-MEC.

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Correspondence to Hacene Ouzia.

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Ouzia, H., Maculan, N. Mixed integer nonlinear optimization models for the Euclidean Steiner tree problem in \(\mathbb {R}^d\). J Glob Optim 83, 119–136 (2022). https://doi.org/10.1007/s10898-021-01001-6

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Keywords

  • Integer Programming
  • Euclidean Steiner tree problem
  • Steiner tree
  • Nonlinear optimization models
  • Mixed integer nonlinear optimization
  • Relaxation