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An algorithmic framework for the exact solution of tree-star problems

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An algorithmic framework for the exact solution of tree-star problems. / Leitner, Markus; Ljubic, Ivana; Salazar-Gonzalez, Juan Jose; Sinnl, Markus.

In: European Journal of Operational Research, Vol. 261, No. 1, 16.08.2017, p. 54-66.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Leitner, M, Ljubic, I, Salazar-Gonzalez, JJ & Sinnl, M 2017, 'An algorithmic framework for the exact solution of tree-star problems', European Journal of Operational Research, vol. 261, no. 1, pp. 54-66. https://doi.org/10.1016/j.ejor.2017.02.011

APA

Leitner, M., Ljubic, I., Salazar-Gonzalez, J. J., & Sinnl, M. (2017). An algorithmic framework for the exact solution of tree-star problems. European Journal of Operational Research, 261(1), 54-66. https://doi.org/10.1016/j.ejor.2017.02.011

Vancouver

Leitner M, Ljubic I, Salazar-Gonzalez JJ, Sinnl M. An algorithmic framework for the exact solution of tree-star problems. European Journal of Operational Research. 2017 Aug 16;261(1):54-66. https://doi.org/10.1016/j.ejor.2017.02.011

Author

Leitner, Markus ; Ljubic, Ivana ; Salazar-Gonzalez, Juan Jose ; Sinnl, Markus. / An algorithmic framework for the exact solution of tree-star problems. In: European Journal of Operational Research. 2017 ; Vol. 261, No. 1. pp. 54-66.

Bibtex

@article{ff715371c756459bbf32bbc896733002,
title = "An algorithmic framework for the exact solution of tree-star problems",
abstract = "Many problems arising in the area of telecommunication ask for solutions with a tree-star topology. This paper proposes a general procedure for finding optimal solutions to a family of these problems. The family includes problems in the literature named as connected facility location, rent-or-buy and generalized Steiner tree-star. We propose a solution framework based on a branch-and-cut algorithm which also relies on sophisticated reduction and heuristic techniques. An important ingredient of this framework is a dual ascent procedure for asymmetric connected facility location. This paper shows how this procedure can be exploited in combination with various mixed integer programming formulations. Using the new framework, many benchmark instances in the literature for which only heuristic results were available so far, can be solved to provable optimality within seconds. To better assess the computational performance of the new approach, we additionally consider larger instances and provide optimal solutions for most of them too.",
keywords = "Combinatorial optimization, Connected facility location, Branch-and-cut, Dual ascent, Benders decomposition",
author = "Markus Leitner and Ivana Ljubic and Salazar-Gonzalez, {Juan Jose} and Markus Sinnl",
note = "This is the author{\textquoteright}s version of a work that was accepted for publication in European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Operational Research",
year = "2017",
month = aug,
day = "16",
doi = "10.1016/j.ejor.2017.02.011",
language = "English",
volume = "261",
pages = "54--66",
journal = "European Journal of Operational Research",
issn = "0377-2217",
publisher = "Elsevier Science B.V.",
number = "1",

}

RIS

TY - JOUR

T1 - An algorithmic framework for the exact solution of tree-star problems

AU - Leitner, Markus

AU - Ljubic, Ivana

AU - Salazar-Gonzalez, Juan Jose

AU - Sinnl, Markus

N1 - This is the author’s version of a work that was accepted for publication in European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Operational Research

PY - 2017/8/16

Y1 - 2017/8/16

N2 - Many problems arising in the area of telecommunication ask for solutions with a tree-star topology. This paper proposes a general procedure for finding optimal solutions to a family of these problems. The family includes problems in the literature named as connected facility location, rent-or-buy and generalized Steiner tree-star. We propose a solution framework based on a branch-and-cut algorithm which also relies on sophisticated reduction and heuristic techniques. An important ingredient of this framework is a dual ascent procedure for asymmetric connected facility location. This paper shows how this procedure can be exploited in combination with various mixed integer programming formulations. Using the new framework, many benchmark instances in the literature for which only heuristic results were available so far, can be solved to provable optimality within seconds. To better assess the computational performance of the new approach, we additionally consider larger instances and provide optimal solutions for most of them too.

AB - Many problems arising in the area of telecommunication ask for solutions with a tree-star topology. This paper proposes a general procedure for finding optimal solutions to a family of these problems. The family includes problems in the literature named as connected facility location, rent-or-buy and generalized Steiner tree-star. We propose a solution framework based on a branch-and-cut algorithm which also relies on sophisticated reduction and heuristic techniques. An important ingredient of this framework is a dual ascent procedure for asymmetric connected facility location. This paper shows how this procedure can be exploited in combination with various mixed integer programming formulations. Using the new framework, many benchmark instances in the literature for which only heuristic results were available so far, can be solved to provable optimality within seconds. To better assess the computational performance of the new approach, we additionally consider larger instances and provide optimal solutions for most of them too.

KW - Combinatorial optimization

KW - Connected facility location

KW - Branch-and-cut

KW - Dual ascent

KW - Benders decomposition

U2 - 10.1016/j.ejor.2017.02.011

DO - 10.1016/j.ejor.2017.02.011

M3 - Journal article

VL - 261

SP - 54

EP - 66

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 1

ER -