Improving a Lagrangian decomposition for the unconstrained binary quadratic programming problem

This paper presents a new alternative of Lagrangian decomposition based on column generation technique to solve the unconstrained binary quadratic programming problem. We use a mixed binary linear version of the original quadratic problem with constraints represented by a graph. This graph is partit...

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Published in:	Computers & operations research Vol. 39; no. 7; pp. 1577 - 1581
Main Authors:	Mauri, Geraldo Regis, Lorena, Luiz Antonio Nogueira
Format:	Journal Article
Language:	English
Published:	New York Elsevier Ltd 01.07.2012 Elsevier Pergamon Press Inc
Subjects:	Clusters Column generation Decomposition Forming Graph theory Graphs Lagrange multiplier Lagrangian decomposition Mathematical analysis Mathematical models Operations research Quadratic programming Studies Quadratic programming Lagrangian decomposition Column generation
ISSN:	0305-0548, 1873-765X, 0305-0548
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Abstract	This paper presents a new alternative of Lagrangian decomposition based on column generation technique to solve the unconstrained binary quadratic programming problem. We use a mixed binary linear version of the original quadratic problem with constraints represented by a graph. This graph is partitioned into clusters of vertices forming subproblems whose solutions use the dual variables obtained by a coordinator problem. Computational experiments consider a set of difficult instances and the results are compared against other methods reported recently in the literature.
AbstractList	This paper presents a new alternative of Lagrangian decomposition based on column generation technique to solve the unconstrained binary quadratic programming problem. We use a mixed binary linear version of the original quadratic problem with constraints represented by a graph. This graph is partitioned into clusters of vertices forming subproblems whose solutions use the dual variables obtained by a coordinator problem. Computational experiments consider a set of difficult instances and the results are compared against other methods reported recently in the literature. [PUBLICATION ABSTRACT] This paper presents a new alternative of Lagrangian decomposition based on column generation technique to solve the unconstrained binary quadratic programming problem. We use a mixed binary linear version of the original quadratic problem with constraints represented by a graph. This graph is partitioned into clusters of vertices forming subproblems whose solutions use the dual variables obtained by a coordinator problem. Computational experiments consider a set of difficult instances and the results are compared against other methods reported recently in the literature.
Author	Lorena, Luiz Antonio Nogueira Mauri, Geraldo Regis
Author_xml	– sequence: 1 givenname: Geraldo Regis surname: Mauri fullname: Mauri, Geraldo Regis email: mauri@cca.ufes.br, grmauri@gmail.com organization: Federal University of Espírito Santo – UFES, Alto Universitário s/n, Guararema, Alegre-ES 29500-000, Brazil – sequence: 2 givenname: Luiz Antonio Nogueira surname: Lorena fullname: Lorena, Luiz Antonio Nogueira email: lorena@lac.inpe.br organization: National Institute for Space Research – INPE, Av. dos Astronautas 1758, Jd. da Granja, São José dos Campos-SP 12210-970, Brazil
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SubjectTerms	Clusters Column generation Decomposition Forming Graph theory Graphs Lagrange multiplier Lagrangian decomposition Mathematical analysis Mathematical models Operations research Quadratic programming Studies
Title	Improving a Lagrangian decomposition for the unconstrained binary quadratic programming problem
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