Stabilized Benders methods for large-scale combinatorial optimization, with application to data privacy

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Document typeArticle
Defense date2020-07
Rights accessOpen Access
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ProjectOPTIMIZACION DE MUY GRAN ESCALA: METODOS Y APLICACIONES (MINECO-MTM2015-65362-R)
MODELIZACION Y OPTIMIZACION DE PROBLEMAS ESTRUCTURADOS DE GRAN ESCALA Y APLICACIONES (AEI-RTI2018-097580-B-I00)
MODELIZACION Y OPTIMIZACION DE PROBLEMAS ESTRUCTURADOS DE GRAN ESCALA Y APLICACIONES (AEI-RTI2018-097580-B-I00)
Abstract
The Cell Suppression Problem (CSP) is a very large Mixed-IntegerLinear Problem arising in statistical disclosure control. However, CSPhas the typical structure that allows application of the Benders de-composition, which is known to suffer from oscillation and slow con-vergence, compounded with the fact that the master problem is com-binatorial. To overcome this drawback we present a stabilized Bendersdecomposition whose master is restricted to a neighborhood of success-ful candidates by local branching constraints, which are dynamicallyadjusted, and even dropped, during the iterations. Our experimentswith synthetic and real-world instances with up to 24000 binary vari-ables, 181M continuous variables and 367M constraints show that ourapproach is competitive with both the current state-of-the-art code forCSP, and the Benders implementation in CPLEX 12.7. In some in-stances, stabilized Benders provided a very good solution in less thanone minute, while the other approaches found no feasible solution inone hour.
CitationBaena, D.; Castro, J.; Frangioni, A. Stabilized Benders methods for large-scale combinatorial optimization, with application to data privacy. "Management science", Juliol 2020, vol. 66, núm. 7, p. 3051-3068.
ISSN0025-1909
Publisher versionhttps://pubsonline.informs.org/doi/10.1287/mnsc.2019.3341
Other identifiershttp://www-eio.upc.edu/~jcastro/publications/reports/dr2017-03.pdf
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