@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

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    dct:description """
              Extended formulations are now widely used to solve hard combinatorial optimization problems. Such formulations have prohibitively-many variables and are generally solved via Column Generation (CG). CG algorithms are known to have frequent convergence issues, and, up to a sometimes large number of iterations, classical Lagrangian dual bounds may be weak. This paper is devoted to set-covering problems in which all elements to cover require a given \\emph{resource consumption} and all feasible configurations have to verify a \\emph{resource constraint}. We propose an iterative aggregation method for determining convergent dual bounds using the extended formulation of such problems. The set of dual variables is partitioned into $k$ groups and all variables in each group are artificially linked using the following groupwise restriction: the dual values in a group have to follow a linear function of their corresponding resource consumptions. This leads to a restricted model of smaller dimension, with only $2k$ dual variables. The method starts with one group ($k=1$) and iteratively splits the groups. Our algorithm has three advantages: (i) it produces good dual bounds even for low $k$ values, (ii) it reduces the number of dual variables, and (iii) it may reduce the time needed to solve sub-problems, in particular when dynamic programming is used. We experimentally tested our approach on two variants of the cutting-stock problem: in many cases, the method produces near optimal dual bounds after a small number of iterations. Moreover the average computational effort to reach the optimum is reduced compared to a classical column generation algorithm.
            """ ;
    dct:identifier "hal-00747375" ;
    dct:issued "2026-05-07T19:51:11.885253"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-07T19:51:11.885258"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Convergent Dual Bounds Using an Aggregation of Set-Covering Constraints for Capacitated Problems" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00747375v2/resource/9e44bffe-dddd-4643-8dec-474be3cab7a6> ;
    dcat:keyword "aggregation",
        "column-generation",
        "duality",
        "infoeu-reposemanticspreprint",
        "infoinfo-rocomputer-science-csoperations-research-mathoc",
        "preprints-working-papers-" ;
    dcat:landingPage <https://hal.science/hal-00747375> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00747375v2/resource/9e44bffe-dddd-4643-8dec-474be3cab7a6> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-07T19:51:11.886483"^^xsd:dateTime ;
    dct:modified "2026-05-07T19:51:11.875931"^^xsd:dateTime ;
    dct:title "Convergent Dual Bounds Using an Aggregation of Set-Covering Constraints for Capacitated Problems" ;
    dcat:accessURL <https://hal.science/hal-00747375> .

<https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> a foaf:Agent ;
    foaf:name "test_moissonnage_selune" .

<https://hal.science/hal-00747375> a foaf:Document .