Iterated local search algorithms for the Euclidean Steiner tree problem in <i>n</i> dimensions

Forte, Vinicius Leal do; Montenegro, Flávio; Brito, José André de Moura; Maculan, Nelson

doi:10.1111/itor.12168

Cited by 8 publications

(5 citation statements)

References 19 publications

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“…Smith shows that for any initial position defined for the Steiner points, this method converges to the only optimal coordinates of the Steiner points. The studies by Fampa and Anstreicher [Fampa and Anstreicher 2008] and Forte et al [Forte et al 2015] also use this method to reposition Steiner points. For more details on this iterative procedure, see Smith [Smith 1992].…”

Section: Methodsmentioning

confidence: 99%

Hybrid Greedy Genetic Algorithm for the Euclidean Steiner Tree Problem

Oliveira

Sanches

Osti

2019

Anais Do XVI Encontro Nacional De Inteligência Artificial E Computacional (ENIAC 2019)

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This paper presents a genetic algorithm for the Euclidean Steiner tree problem. This is an optimization problem whose objective is to obtain a minimum length tree to interconnect a set of fixed points, and for this purpose to be achieved, new auxiliary points, called Steiner points, can be added. The proposed heuristic uses a genetic algorithm to manipulate spanning trees, which are then transformed into Steiner trees by inserting and repositioning the Steiner points. Greedy genetic operators and evolutionary strategies are tested. Results of numerical experiments for benchmark library problem (OR-Library) are presented and discussed.This paper presents a genetic algorithm for the Euclidean Steiner tree problem. This is an optimization problem whose objective is to obtain a minimum length tree to interconnect a set of fixed points, and for this purpose to be achieved, new auxiliary points, called Steiner points, can be added. The proposed heuristic uses a genetic algorithm to manipulate spanning trees, which are then transformed into Steiner trees by inserting and repositioning the Steiner points. Greedy genetic operators and evolutionary strategies are tested. Results of numerical experiments for benchmark library problem (OR-Library) are presented and discussed.

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Section: Methodsmentioning

confidence: 99%

Hybrid Greedy Genetic Algorithm for the Euclidean Steiner Tree Problem

Oliveira

Sanches

Osti

2019

Anais Do XVI Encontro Nacional De Inteligência Artificial E Computacional (ENIAC 2019)

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“…Finally, for more recent heuristic approaches, one can refer to Do Forte et al. (2015), Lorenzen and Winter (2016), Whittle et al. (2020), Pinto and Maculan (2022), Montenegro et al (2002), and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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

Ouzia

Pinto

Maculan

2023

Int Trans Operational Res

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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 double-struckR3$ \mathbb {R}^{3}$.

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“…[11]). Finding efficient algorithms to compute an approximate solution is still an active research fieldin graph theory (see for instance [9] and references therein). We also refer to [13] for the study in a general metric space setting.…”

Section: Introductionmentioning

confidence: 99%

Numerical approximation of the Steiner problem in dimension $2$ and $3$

Bonnivard¹,

Bretin²,

Lemenant³

2019

Math. Comp.

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The aim of this work is to present some numerical computations of solutions of the Steiner Problem, based on the recent phase field approximations proposed in [12] and analyzed in [5, 4]. Our strategy consists in improving the regularity of the associated phase field solution by use of higherorder derivatives in the Cahn-Hilliard functional as in [6]. We justify the convergence of this slightly modified version of the functional, together with other technics that we employ to improve the numerical experiments. In particular, we are able to consider a large number of points in dimension 2. We finally present and justify an approximation method that is efficient in dimension 3, which is one of the major novelties of the paper.

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Iterated local search algorithms for the Euclidean Steiner tree problem in n dimensions

Cited by 8 publications

References 19 publications

Hybrid Greedy Genetic Algorithm for the Euclidean Steiner Tree Problem

Hybrid Greedy Genetic Algorithm for the Euclidean Steiner Tree Problem

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

Numerical approximation of the Steiner problem in dimension $2$ and $3$

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