The Euclidean Steiner tree problem in \(\mathbb{R}^{n}\): A mathematical programming formulation

DOI10.1023/A:1018903619285zbMath0966.90064OpenAlexW32401548MaRDI QIDQ1593533

Nelson F. Maculan, Adilson Elias Xavier, Philippe Yves Paul Michelon

Publication date: 17 January 2001

Published in: Annals of Operations Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1018903619285

zbMATH Keywords

Euclidean Steiner tree problemduality in nonconvex mixed-integer programming

Mathematics Subject Classification ID

Programming involving graphs or networks (90C35) Mixed integer programming (90C11) Optimality conditions and duality in mathematical programming (90C46) Combinatorial optimization (90C27) Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49J30)

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Mixed integer nonlinear optimization models for the Euclidean Steiner tree problem in \(\mathbb{R}^d\) ⋮ A New Relaxation in Conic Form for the Euclidean Steiner Problem in ℜ ⋮ A specialized branch-and-bound algorithm for the Euclidean Steiner tree problem in \(n\)-space ⋮ On a nonconvex MINLP formulation of the Euclidean Steiner tree problem in \(n\)-space: missing proofs ⋮ A new second‐order conic optimization model for the Euclidean Steiner tree problem in Rd$\mathbb {R}^d$ ⋮ A new heuristic for the Euclidean Steiner tree problem in \(\mathbb{R}^n\) ⋮ An improved algorithm for computing Steiner minimal trees in Euclidean \(d\)-space ⋮ An overview of exact algorithms for the Euclidean Steiner tree problem inn-space ⋮ Insight into the computation of Steiner minimal trees in Euclidean space of general dimension ⋮ Iterated local search algorithms for the Euclidean Steiner tree problem inndimensions

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