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Pesquisa Operacional

versão impressa ISSN 0101-7438versão On-line ISSN 1678-5142

Resumo

MAURI, Geraldo Regis  e  LORENA, Luiz Antonio Nogueira. Decomposições Lagrangeanas para o problema de programação quadrática binária irrestrita. Pesqui. Oper. [online]. 2009, vol.29, n.1, pp.111-127. ISSN 0101-7438.  https://doi.org/10.1590/S0101-74382009000100006.

The Unconstrained Binary Quadratic Programming Problem - PQ is a classical non-linear problem of optimizing a quadratic objective by suitable choice of binary decisions variables. This paper proposes new alternatives of Lagrangean decomposition to find bounds for PQ. The presented methods treat a mixed binary linear version (PQL) of PQ with constraints represented by a graph. This graph is partitioned in clusters of vertices forming a dual problem that is solved by a subgradient algorithm. The subproblems formed by the generated subgraphs are solved by the CPLEX. Computational experiments consider with a data set formed by several difficult instances with different characteristics. The results show the efficiency of the proposed methods over traditional Lagrangean relaxations and other methods found in literature.

Palavras-chave : quadratic programming; Lagrangean decomposition; bounds.

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