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dc.contributor.authorBaena, Daniel
dc.contributor.authorCastro Pérez, Jordi
dc.contributor.authorFrangioni, Antonio
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Estadística i Investigació Operativa
dc.identifier.citationBaena, D, Castro, J., Frangioni, A. "Stabilized Benders methods for large-scale combinatorial optimization, with appllication to data privacy". 2017.
dc.description.abstractThe Cell Suppression Problem (CSP) is a challenging Mixed-Integer Linear Problem arising in statistical tabular data protection. Medium sized instances of CSP involve thousands of binary variables and million of continuous variables and constraints. However, CSP has the typical structure that allows application of the renowned Benders’ decomposition method: once the “complicating” binary variables are fixed, the problem decomposes into a large set of linear subproblems on the “easy” continuous ones. This allows to project away the easy variables, reducing to a master problem in the complicating ones where the value functions of the subproblems are approximated with the standard cutting-plane approach. Hence, Benders’ decomposition suffers from the same drawbacks of the cutting-plane method, i.e., oscillation and slow convergence, compounded with the fact that the master problem is combinatorial. To overcome this drawback we present a stabilized Benders decomposition whose master is restricted to a neighborhood of successful candidates by local branching constraints, which are dynamically adjusted, and even dropped, during the iterations. Our experiments with randomly generated and real-world CSP instances with up to 3600 binary variables, 90M continuous variables and 15M inequality constraints show that our approach is competitive with both the current state-of-the-art (cutting-plane-based) code for cell suppression, and the Benders implementation in CPLEX 12.7. In some instances, stabilized Benders is able to quickly provide a very good solution in less than one minute, while the other approaches were not able to find any feasible solution in one hour.
dc.format.extent32 p.
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa
dc.subject.otherBenders’ decomposition
dc.subject.otherMixed-Integer Linear Problems
dc.subject.otherlocal branching
dc.subject.otherlarge-scale optimization
dc.subject.otherstatistical tabular data protection
dc.subject.othercell suppression problem
dc.titleStabilized Benders methods for large-scale combinatorial optimization, with appllication to data privacy
dc.typeExternal research report
dc.contributor.groupUniversitat Politècnica de Catalunya. GNOM - Grup d'Optimització Numèrica i Modelització
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::90 Operations research, mathematical programming
dc.rights.accessOpen Access
upcommons.citation.authorBaena, D; Castro, J.; Frangioni, A.

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