Stabilized Benders Methods for Large-Scale Combinatorial Optimization, with Application to Data Privacy

References

• Ben Amor H, Desrosiers J, Frangioni A (2009) On the choice of explicit stabilizing terms in column generation. Discrete Appl. Math. 157:1167–1184.Crossref, Google Scholar
• Ben-Ameur W, Neto J (2007) Acceleration of cutting-plane and column generation algorithms: Applications to network design. Networks 49:3–17.Crossref, Google Scholar
• Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4(1):238–252. [Benders JF (2005) Partitioning procedures for solving mixed-variables programming problems. Comput. Management Sci. 2:3–19.]Google Scholar
• Birge JR, Louveaux F (1997) Introduction to Stochastic Programming (Springer, New York).Google Scholar
• Boland N, Fischetti M, Monaci M, Savelsbergh M (2016) Proximity Benders: A decomposition heuristic for stochastic programs. J. Heuristics 22:181–198.Crossref, Google Scholar
• Briant O, Lemaréchal C, Meurdesoif Ph, Michel S, Perrot N, Vanderbeck F (2008) Comparison of bundle and classical column generation. Math. Programming 113(2):299–344.Crossref, Google Scholar
• Castro J (2007) A shortest paths heuristic for statistical disclosure control in positive tables. INFORMS J. Comput. 19:520–533.Link, Google Scholar
• Castro J (2012) Recent advances in optimization techniques for statistical tabular data protection. Eur. J. Oper. Res. 21:257–269.Crossref, Google Scholar
• Castro J, Via A (2016) Revisiting interval protection, a.k.a. partial cell suppression, for tabular data. Domingo-Ferrer J, Péjic-Bach M, eds. Privacy in Statistical Databases, Lecture Notes in Computer Science, vol. 9867 (Springer, Cham, Switzerland), 3–14.Crossref, Google Scholar
• Castro J, Nasini S, Saldanha-da-Gama F (2017) A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method. Math. Programming 163:411–444.Crossref, Google Scholar
• Costa AM (2005) A survey on Benders decomposition applied to fixed-charge network design problems. Comput. Oper. Res. 32:1429–1450.Crossref, Google Scholar
• d’Ambrosio C, Frangioni A, Liberti L, Lodi A (2010) On interval-subgradient cuts and no-good cuts. Oper. Res. Lett. 38:341–345.Crossref, Google Scholar
• de Wolf P-P, Hundepool A, Giessing S, Salazar JJ, Castro J (2014) τ-Argus User’s Manual (Statistics Netherlands, The Hague, Netherlands). Accessed April 24, 2019, http://neon.vb.cbs.nl/casc/Software/TauManualV4.1.pdf.Google Scholar
• Dolan ED, Moré JJ (2002) Benchmarking optimization software with performance profiles. Math. Programming 91:201–213.Crossref, Google Scholar
• Fischetti M, Lodi A (2003) Local branching. Math. Programming 98:23–47.Crossref, Google Scholar
• Fischetti M, Salazar JJ (1999) Models and algorithms for the 2-dimensional cell suppression problem in statistical disclosure control. Math. Programming 84:283–312.Crossref, Google Scholar
• Fischetti M, Salazar JJ (2001) Solving the cell suppression problem on tabular data with linear constraints. Management Sci. 47:1008–1026.Link, Google Scholar
• Fischetti M, Salvagnin D (2010) An In Out Approach to Disjunctive Optimization, Lecture Notes in Computer Science, vol. 6140 (Springer, Cham, Switzerland), 136–140.Google Scholar
• Fischetti M, Ljubić I, Sinnl M (2017) Redesigning Benders decomposition for large-scale facility location. Management Sci. 63:2146–2162.Link, Google Scholar
• Fischetti M, Salvagnin D, Zanette A (2010) A note on the selection of Benders cuts. Math. Programming 124:175–182.Crossref, Google Scholar
• Frangioni A, Gendron B (2013) A stabilized structured Dantzig-Wolfe decomposition method. Math. Programming 140:45–76.Crossref, Google Scholar
• Geoffrion AM (1972) Generalized Benders decomposition. J. Optim. Theory Appl. 10:238–260.Crossref, Google Scholar
• Gleeson J, Ryan J (1990) Identifying minimally infeasible subsystems of inequalities. ORSA J. Comput. 2:61–63.Link, Google Scholar
• Hiriart-Urruty JB, Lemaréchal C (1996) Convex Analysis and Minimization Algorithms, vol II (Springer, Berlin).Google Scholar
• Hundepool A, Domingo-Ferrer J, Franconi L, Giessing S, Schulte Nordholt E, Spicer K, de Wolf P-P (2012) Statistical Disclosure Control (Wiley, Chichester, UK).Crossref, Google Scholar
• Kelly JP, Golden BL, Assad AA (1992) Cell suppression: Disclosure protection for sensitive tabular data. Networks 22:28–55.Crossref, Google Scholar
• Magnanti TL, Wong R (1981) Accelerating Benders decomposition: Algorithmic enhancement and model selection criteria. Oper. Res. 29:464–484.Link, Google Scholar
• Nasri A, Kazempour SJ, Conejo AJ, Ghandhari M (2016) Network-constrained AC unit commitment under uncertainty: A Benders’ decomposition approach. IEEE Trans. Power Systems 31:412–422.Crossref, Google Scholar
• Rahmaniani R, Crainic TG, Gendreau M, Rei W (2017) The Benders decomposition algorithm: A literature review. Eur. J. Oper. Res. 259:801–817.Crossref, Google Scholar
• Rei W, Cordeau JF, Gendreau M, Soriano P (2009) Accelerating Benders decomposition by local branching. INFORMS J. Comput. 21:333–345.Link, Google Scholar
• Santoso T, Ahmed S, Goetschalckx M, Shapiro A (2005) A stochastic programming approach for supply chain network design under uncertainty. Eur. J. Oper. Res. 167:96–115.Crossref, Google Scholar
• Tahanan M, van Ackooij W, Frangioni A, Lacalandra F (2015) Large-scale unit commitment under uncertainty. 4OR 13(2):115–171.Google Scholar
• van Ackooij W, Frangioni A, de Oliveira W (2016) Inexact stabilized Benders’ decomposition approaches with application to chance-constrained problems with finite support. Comput. Optim. Appl. 65(3):637–669.Crossref, Google Scholar
• Willenborg L, de Waal T (2000) Elements of Statistical Disclosure Control, Lecture Notes in Statistics, vol 155 (Springer, New York).Google Scholar
• Zakeri G, Philpott AB, Ryan DM (2000) Inexact cuts in Benders decomposition. SIAM J. Optim. 10:643–657.Crossref, Google Scholar