A new second‐order conic optimization model for the Euclidean Steiner tree problem in Rd$\mathbb {R}^d

In this work, a new second‐order conic optimization model for the Euclidean Steiner tree problem in d‐space, where the dimension d is at least three, will be presented. Also, two strategies for eliminating isomorphic trees will be developed. Computational results highlighting the efficiency of this...

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Bibliographic Details
Published in:International transactions in operational research 2023-11, Vol.30 (6), p.3886-3903
Main Authors: Pinto, Renan Vicente, Ouzia, Hacène, Maculan, Nelson
Format: Article
Language:English
Subjects:
Euclidean geometry
Euclidean Steiner tree problem
Integer programming
Mixed integer
mixed integer nonlinear optimization
nonlinear optimization models
Nonlinear programming
Operations research
Optimization
Optimization models
second‐order conic optimization
Steiner tree
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Summary:In this work, a new second‐order conic optimization model for the Euclidean Steiner tree problem in d‐space, where the dimension d is at least three, will be presented. Also, two strategies for eliminating isomorphic trees will be developed. Computational results highlighting the efficiency of this model compared to existing models for the Euclidean Steiner tree problem will be discussed. Finally, enforcing the proposed model with any of the isomorphic tree elimination strategies permits us to compute for the first time, to the best of our knowledge, the minimum Steiner tree for the cube in R3$ \mathbb {R}^{3}$.
ISSN:0969-6016
1475-3995
DOI:10.1111/itor.13265