Bi-dynamic constraint aggregation and subproblem reduction

Authors:
Issmail Elhallaoui;Guy Desaulniers;Abdelmoutalib Metrane;François Soumis
Affiliations:
ícole Polytechnique and GERAD, Département de Mathématiques et de Génie Industriel, C.P. 6079, Succ. Centre-Ville, Montréal, Que., Canada H3C3A7;ícole Polytechnique and GERAD, Département de Mathématiques et de Génie Industriel, C.P. 6079, Succ. Centre-Ville, Montréal, Que., Canada H3C3A7;ícole Polytechnique and GERAD, Département de Mathématiques et de Génie Industriel, C.P. 6079, Succ. Centre-Ville, Montréal, Que., Canada H3C3A7;ícole Polytechnique and GERAD, Département de Mathématiques et de Génie Industriel, C.P. 6079, Succ. Centre-Ville, Montréal, Que., Canada H3C3A7
Venue:
Computers and Operations Research
Year:
2008

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Abstract

Dynamic constraint aggregation was recently introduced by Elhallaoui et al. [Dynamic aggregation of set partitioning constraints in column generation. Operations Research 2005; 53: 632-45] for efficiently solving the linear relaxation of a class of set partitioning type problems in a column generation context. It reduces the master problem size by aggregating some of its constraints and updates this aggregation when needed. In this paper, we present an advanced version of the dynamic constraint aggregation that reduces both the master problem and the subproblem sizes. This version is called the bi-dynamic constraint aggregation method because aggregation is dynamically applied to both the master problem and the subproblem. We also discuss solution integrality. Computational results for the mass transit simultaneous vehicle and crew scheduling problem are reported.