The min-Knapsack problem with compactness constraints and applications in statistics

In the min-Knapsack problem, one is given a set of items, each having a certain cost and weight. The objective is to select a subset with minimum cost, such that the sum of the weights is not smaller than a given constant. In this paper, we introduce an extension of the min-Knapsack problem with add...

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Detalles Bibliográficos
Autores: Santini, Alberto, Malaguti, Enrico
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10230/59230
Acceso en línea:http://hdl.handle.net/10230/59230
http://dx.doi.org/10.1016/j.ejor.2023.07.020
Access Level:acceso abierto
Palabra clave:Cutting
Knapsack problems
Applications in statistics
Dynamic programming
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spelling The min-Knapsack problem with compactness constraints and applications in statisticsSantini, AlbertoMalaguti, EnricoCuttingKnapsack problemsApplications in statisticsDynamic programmingIn the min-Knapsack problem, one is given a set of items, each having a certain cost and weight. The objective is to select a subset with minimum cost, such that the sum of the weights is not smaller than a given constant. In this paper, we introduce an extension of the min-Knapsack problem with additional “compactness constraints” (mKPC), stating that selected items cannot lie too far apart. This extension has applications in statistics, including in algorithms for change-point detection in time series. We propose three solution methods for the mKPC. The first two methods use the same Mixed-Integer Programming (MIP) formulation but with two different approaches: passing the complete model with a quadratic number of constraints to a black-box MIP solver or dynamically separating the constraints using a branch-and-cut algorithm. Numerical experiments highlight the advantages of this dynamic separation. The third approach is a dynamic programming labelling algorithm. Finally, we focus on the particular case of the unit-cost mKPC (1c-mKPC), which has a specific interpretation in the context of the statistical applications mentioned above. We prove that the 1c-mKPC is solvable in polynomial time with a different ad-hoc dynamic programming algorithm. Experimental results show that this algorithm vastly outperforms both generic approaches for the mKPC and a simple greedy heuristic from the literature.Elsevier202420242023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/59230http://dx.doi.org/10.1016/j.ejor.2023.07.020reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésEuropean Journal of Operational Research. 2023;312:385-97.© 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:10230/592302026-05-29T05:05:01Z
dc.title.none.fl_str_mv The min-Knapsack problem with compactness constraints and applications in statistics
title The min-Knapsack problem with compactness constraints and applications in statistics
spellingShingle The min-Knapsack problem with compactness constraints and applications in statistics
Santini, Alberto
Cutting
Knapsack problems
Applications in statistics
Dynamic programming
title_short The min-Knapsack problem with compactness constraints and applications in statistics
title_full The min-Knapsack problem with compactness constraints and applications in statistics
title_fullStr The min-Knapsack problem with compactness constraints and applications in statistics
title_full_unstemmed The min-Knapsack problem with compactness constraints and applications in statistics
title_sort The min-Knapsack problem with compactness constraints and applications in statistics
dc.creator.none.fl_str_mv Santini, Alberto
Malaguti, Enrico
author Santini, Alberto
author_facet Santini, Alberto
Malaguti, Enrico
author_role author
author2 Malaguti, Enrico
author2_role author
dc.subject.none.fl_str_mv Cutting
Knapsack problems
Applications in statistics
Dynamic programming
topic Cutting
Knapsack problems
Applications in statistics
Dynamic programming
description In the min-Knapsack problem, one is given a set of items, each having a certain cost and weight. The objective is to select a subset with minimum cost, such that the sum of the weights is not smaller than a given constant. In this paper, we introduce an extension of the min-Knapsack problem with additional “compactness constraints” (mKPC), stating that selected items cannot lie too far apart. This extension has applications in statistics, including in algorithms for change-point detection in time series. We propose three solution methods for the mKPC. The first two methods use the same Mixed-Integer Programming (MIP) formulation but with two different approaches: passing the complete model with a quadratic number of constraints to a black-box MIP solver or dynamically separating the constraints using a branch-and-cut algorithm. Numerical experiments highlight the advantages of this dynamic separation. The third approach is a dynamic programming labelling algorithm. Finally, we focus on the particular case of the unit-cost mKPC (1c-mKPC), which has a specific interpretation in the context of the statistical applications mentioned above. We prove that the 1c-mKPC is solvable in polynomial time with a different ad-hoc dynamic programming algorithm. Experimental results show that this algorithm vastly outperforms both generic approaches for the mKPC and a simple greedy heuristic from the literature.
publishDate 2023
dc.date.none.fl_str_mv 2023
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10230/59230
http://dx.doi.org/10.1016/j.ejor.2023.07.020
url http://hdl.handle.net/10230/59230
http://dx.doi.org/10.1016/j.ejor.2023.07.020
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv European Journal of Operational Research. 2023;312:385-97.
dc.rights.none.fl_str_mv https://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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