Branch-and-price-and-cut for large-scale multicommodity capacitated fixed-charge network design

We present a branch-and-price-and-cut algorithm for solving large-scale instances of the multicommodity capacitated fixed-charge network design problem. We assume good feasible solutions are already known and we focus on an efficient algorithm for proving the optimality of the solutions. The restric...

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Autores principales:	Bernard Gendron, Mathieu Larose
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2014
Materias:	90C11 Mixed integer programming 90C35 Programming involving graphs or networks 90B10 Network models deterministic Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/9fd39dea92a84415a7c7eafe5f8d9019
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spelling	oai:doaj.org-article:9fd39dea92a84415a7c7eafe5f8d90192021-12-02T05:00:38ZBranch-and-price-and-cut for large-scale multicommodity capacitated fixed-charge network design2192-440610.1007/s13675-014-0020-9https://doaj.org/article/9fd39dea92a84415a7c7eafe5f8d90192014-06-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2192440621000253https://doaj.org/toc/2192-4406We present a branch-and-price-and-cut algorithm for solving large-scale instances of the multicommodity capacitated fixed-charge network design problem. We assume good feasible solutions are already known and we focus on an efficient algorithm for proving the optimality of the solutions. The restricted master problem solved at each column generation iteration is obtained directly from the compact arc-based model by considering only a subset of the commodity flow variables. The pricing subproblem corresponds to a Lagrangian relaxation of the flow conservation and capacity constraints, leaving in the Lagrangian subproblem only the strong inequalities. The column generation procedure is completed by a cut generation step based on strong inequalities. The resulting column-and-row generation procedure is embedded within an enumerative scheme. Computational experiments on a large set of randomly generated instances are presented and analyzed.Bernard GendronMathieu LaroseElsevierarticle90C11 Mixed integer programming90C35 Programming involving graphs or networks90B10 Network modelsdeterministicApplied mathematics. Quantitative methodsT57-57.97Electronic computers. Computer scienceQA75.5-76.95ENEURO Journal on Computational Optimization, Vol 2, Iss 1, Pp 55-75 (2014)
institution	DOAJ
collection	DOAJ
language	EN
topic	90C11 Mixed integer programming 90C35 Programming involving graphs or networks 90B10 Network models deterministic Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
spellingShingle	90C11 Mixed integer programming 90C35 Programming involving graphs or networks 90B10 Network models deterministic Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95 Bernard Gendron Mathieu Larose Branch-and-price-and-cut for large-scale multicommodity capacitated fixed-charge network design
description	We present a branch-and-price-and-cut algorithm for solving large-scale instances of the multicommodity capacitated fixed-charge network design problem. We assume good feasible solutions are already known and we focus on an efficient algorithm for proving the optimality of the solutions. The restricted master problem solved at each column generation iteration is obtained directly from the compact arc-based model by considering only a subset of the commodity flow variables. The pricing subproblem corresponds to a Lagrangian relaxation of the flow conservation and capacity constraints, leaving in the Lagrangian subproblem only the strong inequalities. The column generation procedure is completed by a cut generation step based on strong inequalities. The resulting column-and-row generation procedure is embedded within an enumerative scheme. Computational experiments on a large set of randomly generated instances are presented and analyzed.
format	article
author	Bernard Gendron Mathieu Larose
author_facet	Bernard Gendron Mathieu Larose
author_sort	Bernard Gendron
title	Branch-and-price-and-cut for large-scale multicommodity capacitated fixed-charge network design
title_short	Branch-and-price-and-cut for large-scale multicommodity capacitated fixed-charge network design
title_full	Branch-and-price-and-cut for large-scale multicommodity capacitated fixed-charge network design
title_fullStr	Branch-and-price-and-cut for large-scale multicommodity capacitated fixed-charge network design
title_full_unstemmed	Branch-and-price-and-cut for large-scale multicommodity capacitated fixed-charge network design
title_sort	branch-and-price-and-cut for large-scale multicommodity capacitated fixed-charge network design
publisher	Elsevier
publishDate	2014
url	https://doaj.org/article/9fd39dea92a84415a7c7eafe5f8d9019
work_keys_str_mv	AT bernardgendron branchandpriceandcutforlargescalemulticommoditycapacitatedfixedchargenetworkdesign AT mathieularose branchandpriceandcutforlargescalemulticommoditycapacitatedfixedchargenetworkdesign
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Branch-and-price-and-cut for large-scale multicommodity capacitated fixed-charge network design

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