Improving a Lagrangian decomposition for the unconstrained binary quadratic programming problem

Authors:
Geraldo Regis Mauri;Luiz Antonio Nogueira Lorena
Affiliations:
Federal University of Espírito Santo - UFES, Alto Universitário s/n, Guararema, Alegre-ES 29500-000, Brazil;National Institute for Space Research - INPE, Av. dos Astronautas 1758, Jd. da Granja, São José dos Campos-SP 12210-970, Brazil
Venue:
Computers and Operations Research
Year:
2012

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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.