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...

Full description

Saved in:
Bibliographic Details
Published in:International transactions in operational research Vol. 18; no. 2; pp. 257 - 270
Main Authors: Mauri, Geraldo Regis, Lorena, Luiz Antonio Nogueira
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.03.2011
Pergamon
Subjects:
bounds
Lagrangean decomposition
Nonlinear programming
Operations research
Optimization
Quadratic programming
Studies
ISSN:0969-6016, 1475-3995
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ArticleID:ITOR743
istex:D329A380578ED0A1F83DC662236C29A47180F98D
ark:/67375/WNG-XMCH9NVV-D
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0969-6016
1475-3995
DOI:10.1111/j.1475-3995.2009.00743.x