Lagrangean decompositions for the unconstrained binary quadratic programming problem

The unconstrained binary quadratic programming problem (QP) is a classical non‐linear problem of optimizing a quadratic objective by a suitable choice of binary decision variables. This paper proposes new Lagrangean decompositions to find bounds for QP. The methods presented treat a mixed binary lin...

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Vydáno v:International transactions in operational research Ročník 18; číslo 2; s. 257 - 270
Hlavní autoři: Mauri, Geraldo Regis, Lorena, Luiz Antonio Nogueira
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford, UK Blackwell Publishing Ltd 01.03.2011
Pergamon
Témata:
bounds
Lagrangean decomposition
Nonlinear programming
Operations research
Optimization
Quadratic programming
Studies
ISSN:0969-6016, 1475-3995
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Shrnutí:The unconstrained binary quadratic programming problem (QP) is a classical non‐linear problem of optimizing a quadratic objective by a suitable choice of binary decision variables. This paper proposes new Lagrangean decompositions to find bounds for QP. The methods presented treat a mixed binary linear version (LQP) of QP with constraints represented by a graph. This graph is partitioned into clusters of vertices forming a dual problem that is solved by a subgradient algorithm. The subproblems formed by the generated subgraphs are solved by CPLEX. Computational experiments consider a data set formed by several difficult instances with different features. The results show the efficiency of the proposed methods over traditional Lagrangean relaxations and other methods found in the literature.
Bibliografie:ArticleID:ITOR743
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SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0969-6016
1475-3995
DOI:10.1111/j.1475-3995.2009.00743.x