Please use this identifier to cite or link to this item: http://repositorio.ufla.br/jspui/handle/1/33320
metadata.artigo.dc.title: Polyhedral results, branch‐and‐cut and Lagrangian relaxation algorithms for the adjacent only quadratic minimum spanning tree problem
metadata.artigo.dc.creator: Pereira, Dilson Lucas
Cunha, Alexandre Salles da
metadata.artigo.dc.subject: Branch‐and‐cut algorithms
Adjacent only quadratic minimum spanning tree problem
Lagrangian relaxation
Algoritmos branch-and-cut
Problema de árvore estendida mínima quadrática adjacente
Relaxamento Lagrangiano
metadata.artigo.dc.publisher: Wiley
metadata.artigo.dc.date.issued: Jan-2018
metadata.artigo.dc.identifier.citation: PEREIRA, D. L.; CUNHA, A. S. da. Polyhedral results, branch‐and‐cut and Lagrangian relaxation algorithms for the adjacent only quadratic minimum spanning tree problem. Networks, New York, v. 71, n. 1, p. 31-50, Jan. 2018.
metadata.artigo.dc.description.abstract: Given a complete and undirected graph G, the adjacent only quadratic minimum spanning tree problem (AQMSTP) consists of finding a spanning tree that minimizes a quadratic function of its adjacent edges. The strongest AQMSTP linear integer programming formulation in the literature works on an extended variable space, using exponentially many decision variables assigned to the stars of G. In this article, we characterize three families of facet defining inequalities by investigating the projection of that formulation onto the space of the canonical linearization variables. On the algorithmic side, we introduce four new branch‐and‐bound algorithms. Three of them are branch‐and‐cut algorithms based on the inequalities characterized by projection. The fourth is based on a Lagrangian relaxation scheme, also devised for the star reformulation. Two of the branch‐and‐cut algorithms provide very good results, almost always dominating the previously best algorithm for the problem. The Lagrangian relaxation based branch‐and‐bound algorithm provides even better results. It manages to solve all previously solved AQMSTP instances in the literature in about one tenth of the time needed by its competitors. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 71(1), 31–50 2018
metadata.artigo.dc.identifier.uri: https://onlinelibrary.wiley.com/doi/full/10.1002/net.21787
http://repositorio.ufla.br/jspui/handle/1/33320
metadata.artigo.dc.language: en_US
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