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

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.