Use este identificador para citar ou linkar para este item: http://repositorio.ufla.br/jspui/handle/1/15628
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dc.creatorPereira, Dilson Lucas-
dc.creatorGendreau, Michel-
dc.creatorCunha, Alexandre Salles da-
dc.date.accessioned2017-11-06T19:46:33Z-
dc.date.available2017-11-06T19:46:33Z-
dc.date.issued2015-11-
dc.identifier.citationPEREIRA, D. L.; GENDEREAU, M.; CUNHA, A. S. da. Lower bounds and exact algorithms for the quadratic minimum spanning tree problem. Computers & Operations Research, New York, v. 63, p. 149-160, Nov. 2015.pt_BR
dc.identifier.urihttp://www.sciencedirect.com/science/article/pii/S0305054815001008pt_BR
dc.identifier.urihttp://repositorio.ufla.br/jspui/handle/1/15628-
dc.description.abstractWe address the quadratic minimum spanning tree problem (QMSTP), the problem of finding a spanning tree of a connected and undirected graph such that a quadratic cost function is minimized. We first propose an integer programming formulation based on the reformulation–linearization technique (RLT). We then use the idea of partitioning spanning trees into forests of a given fixed size and obtain a QMSTP reformulation that generalizes the RLT model. The reformulation is such that the larger the size of the forests, the stronger lower bounds provided. Thus, a hierarchy of formulations is obtained. At the lowest hierarchy level, one has precisely the RLT formulation, which is already stronger than previous formulations in the literature. The highest hierarchy level provides the convex hull of integer feasible solutions for the problem. The formulations introduced here are not compact, so the direct evaluation of their linear programming relaxation bounds is not practical. To overcome that, we introduce two lower bounding procedures based on Lagrangian relaxation. These procedures are embedded into two parallel branch-and-bound algorithms. As a result of our study, several instances in the literature were solved to optimality for the first time.pt_BR
dc.languageen_USpt_BR
dc.publisherElsevierpt_BR
dc.rightsrestrictAccesspt_BR
dc.sourceComputers & Operations Researchpt_BR
dc.subjectQuadratic 0-1 programmingpt_BR
dc.subjectLagrangian relaxationpt_BR
dc.subjectSpanning treespt_BR
dc.titleLower bounds and exact algorithms for the quadratic minimum spanning tree problempt_BR
dc.typeArtigopt_BR
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