Column generation algorithms for bi-objective combinatorial optimization problems with a min–max objective

Many practical combinatorial optimization problems can be described by integer linear programs having an exponential number of variables, and they are efficiently solved by column generation algorithms. For these problems, column generation is used to compute good dual bounds that can be incorporate...

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Autores principales:	Christian Artigues, Nicolas Jozefowiez, BoaduM. Sarpong
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2018
Materias:	90-08 90C10 90C29 90C27 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/274b8c7f786a41458abd92fca2fb2cfe
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spelling	oai:doaj.org-article:274b8c7f786a41458abd92fca2fb2cfe2021-12-02T05:01:06ZColumn generation algorithms for bi-objective combinatorial optimization problems with a min–max objective2192-440610.1007/s13675-017-0090-6https://doaj.org/article/274b8c7f786a41458abd92fca2fb2cfe2018-06-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2192440621000976https://doaj.org/toc/2192-4406Many practical combinatorial optimization problems can be described by integer linear programs having an exponential number of variables, and they are efficiently solved by column generation algorithms. For these problems, column generation is used to compute good dual bounds that can be incorporated in branch-and-price algorithms. Recent research has concentrated on describing lower and upper bounds of bi-objective and general multi-objective problems with sets of points (bound sets). An important issue to address when computing a bound set by column generation is how to efficiently search for columns corresponding to each point of the bound set. In this work, we propose a generalized column generation scheme to compute bound sets for bi-objective combinatorial optimization problems. We present specific implementations of the generalized scheme for the case where one objective is a min–max function by using a variant of the ε-constraint method to efficiently model these problems. The proposed strategies are applied to a bi-objective extension of the multi-vehicle covering tour problem, and their relative performances based on different criteria are compared. The results show that good bound sets can be obtained in reasonable times if columns are efficiently managed. The variant of the ε-constraint presented is also better than a standard ε-constraint method in terms of the quality of the bound sets.Christian ArtiguesNicolas JozefowiezBoaduM. SarpongElsevierarticle90-0890C1090C2990C27Applied mathematics. Quantitative methodsT57-57.97Electronic computers. Computer scienceQA75.5-76.95ENEURO Journal on Computational Optimization, Vol 6, Iss 2, Pp 117-142 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	90-08 90C10 90C29 90C27 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
spellingShingle	90-08 90C10 90C29 90C27 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95 Christian Artigues Nicolas Jozefowiez BoaduM. Sarpong Column generation algorithms for bi-objective combinatorial optimization problems with a min–max objective
description	Many practical combinatorial optimization problems can be described by integer linear programs having an exponential number of variables, and they are efficiently solved by column generation algorithms. For these problems, column generation is used to compute good dual bounds that can be incorporated in branch-and-price algorithms. Recent research has concentrated on describing lower and upper bounds of bi-objective and general multi-objective problems with sets of points (bound sets). An important issue to address when computing a bound set by column generation is how to efficiently search for columns corresponding to each point of the bound set. In this work, we propose a generalized column generation scheme to compute bound sets for bi-objective combinatorial optimization problems. We present specific implementations of the generalized scheme for the case where one objective is a min–max function by using a variant of the ε-constraint method to efficiently model these problems. The proposed strategies are applied to a bi-objective extension of the multi-vehicle covering tour problem, and their relative performances based on different criteria are compared. The results show that good bound sets can be obtained in reasonable times if columns are efficiently managed. The variant of the ε-constraint presented is also better than a standard ε-constraint method in terms of the quality of the bound sets.
format	article
author	Christian Artigues Nicolas Jozefowiez BoaduM. Sarpong
author_facet	Christian Artigues Nicolas Jozefowiez BoaduM. Sarpong
author_sort	Christian Artigues
title	Column generation algorithms for bi-objective combinatorial optimization problems with a min–max objective
title_short	Column generation algorithms for bi-objective combinatorial optimization problems with a min–max objective
title_full	Column generation algorithms for bi-objective combinatorial optimization problems with a min–max objective
title_fullStr	Column generation algorithms for bi-objective combinatorial optimization problems with a min–max objective
title_full_unstemmed	Column generation algorithms for bi-objective combinatorial optimization problems with a min–max objective
title_sort	column generation algorithms for bi-objective combinatorial optimization problems with a min–max objective
publisher	Elsevier
publishDate	2018
url	https://doaj.org/article/274b8c7f786a41458abd92fca2fb2cfe
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_version_	1718400818676236288

Column generation algorithms for bi-objective combinatorial optimization problems with a min–max objective

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