Decomposition Branching for Mixed Integer Programming

References

• Achterberg T (2009) SCIP: Solving constraint integer programs. Math. Programming Comput. 1(1):1–41.Crossref, Google Scholar
• Achterberg T, Koch T, Martin A (2005) Branching rules revisited. Oper. Res. Lett. 33(1):42–54.Crossref, Google Scholar
• Achterberg T, Koch T, Martin A (2006) MIPLIB 2003. Oper. Res. Lett. 34(4):361–372. Crossref, Google Scholar
• Applegate D, Bixby R, Chvatal V, Cook W (1995) Finding cuts in the TSP. Technical report, Center for Research in Parallel Computing, Rice University, Houston. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.53.6763&rep=rep1&type=pdf.Google Scholar
• Barnhart C, Johnson EL, Nemhauser GL, Savelsbergh MW, Vance PH (1998) Branch-and-price: Column generation for solving huge integer programs. Oper. Res. 46(3):316–329.Link, Google Scholar
• Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numerical Math. 4:238–252.Crossref, Google Scholar
• Bénichou M, Gauthier J-M, Girodet P, Hentges G, Ribière G, Vincent O (1971) Experiments in mixed-integer linear programming. Math. Programming 1(1):76–94.Crossref, Google Scholar
• Bergner M, Caprara A, Ceselli A, Furini F, Lübbecke ME, Malaguti E, Traversi E (2015) Automatic Dantzig–Wolfe reformulation of mixed integer programs. Math. Programming 149(1–2):391–424.Crossref, Google Scholar
• Bixby R (2012) A brief history of linear and mixed-integer programming computation. Documenta Math. Extra Volume: Optimization Stories, 107–121.Google Scholar
• Bodur M, Ahmed S, Boland N, Nemhauser GL (2016) Decomposition of loosely coupled integer programs: A multiobjective perspective(Optimization Online).Google Scholar
• Conforti M, Cornuejols G, Zambelli G (2014) Integer Programming (Springer, Berlin).Crossref, Google Scholar
• Dantzig GB, Wolfe P (1960) Decomposition principle for linear programs. Oper. Res. 8:101–111.Link, Google Scholar
• Daskin MS, Tucker EL (2018) The trade-off between the median and range of assigned demand in facility location models. Internat. J. Production Res. 56(1–2):97–119.Crossref, Google Scholar
• Dey SS, Molinaro M, Wang Q (2017) Analysis of sparse cutting planes for sparse milps with applications to stochastic milps. Math. Oper. Res. 43(1):304–332.Link, Google Scholar
• Dilkina B, Khalil EB, Nemhauser GL (2017) Comments on: On learning and branching: A survey. TOP 25(2):242–246.Crossref, Google Scholar
• Gamrath G (2010) Generic branch-cut-and-price. PhD thesis. Optimization Online.Google Scholar
• Gamrath G, Koch T, Martin A, Miltenberger M, Weninger D (2015) Progress in presolving for mixed integer programming. Math. Programming Comput. 7(4):367–398.Crossref, Google Scholar
• Gamrath G, Anderson D, Bestuzheva K, Chen W-K, Eifler L, Gasse M, Gemander P, et al. (2020) The SCIP Optimization Suite 7.0. Accessed August 1, 2018, http://www.optimization-online.org/DB_HTML/2020/03/7705.html. Google Scholar
• Garey MR, Johnson DS (2002) Computers and Intractability, vol. 29 (WH Freeman, New York).Google Scholar
• Geoffrion AM (1974) Lagrangian relaxation for integer programming. Math. Programming Stud. 2:82–114.Crossref, Google Scholar
• Jünger M, Liebling T, Naddef D, Nemhauser G, Pulleyblank W, Reinelt G, Rinaldi G, et al. (2010) 50 Years of Integer Programming 1958-2008 (Springer, Berlin).Crossref, Google Scholar
• Karp RM (1972) Reducibility among combinatorial problems. Complexity of Computer Computations (Springer, Berlin), 85–103.Crossref, Google Scholar
• Khalil E, Le Bodic P, Song L, Nemhauser G, Dilkina B (2016) Learning to branch in mixed integer programming. Proc. AAAI Conf. Artificial Intelligence 30(1):724–731.Google Scholar
• Koch T, Achterberg T, Andersen E, Bastert O, Berthold T, Bixby RE, Danna E, Gamrath G, Gleixner AM, Heinz S, Lodi A (2011) MIPLIB 2010. Math. Programming Computation 3(2):103–163.Google Scholar
• Kruber M, Lübbecke ME, Parmentier A (2017) Learning when to use a decomposition. Proc. Internat. Conf. on AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (Springer, Berlin), 202–210.Crossref, Google Scholar
• Land AH, Doig AG (1960) An automatic method of solving discrete programming problems. Econometrica 28:497–520.Crossref, Google Scholar
• Le Bodic P, Nemhauser GL (2015) How important are branching decisions: Fooling MIP solvers. Oper. Res. Lett. 43(3):273–278.Crossref, Google Scholar
• Linderoth JT, Savelsbergh MW (1999) A computational study of search strategies for mixed integer programming. INFORMS J. Comput. 11(2):173–187.Link, Google Scholar
• Lodi A, Zarpellon G (2017) On learning and branching: A survey. TOP 25(2):207–236.Crossref, Google Scholar
• Morrison DR, Jacobson SH, Sauppe JJ, Sewell EC (2016) Branch-and-bound algorithms: A survey of recent advances in searching, branching, and pruning. Discrete Optim. 19:79–102.Crossref, Google Scholar
• Nemhauser G, Wolsey L (1988) Integer and Combinatorial Optimization (John Wiley & Sons, Hoboken, NJ).Crossref, Google Scholar
• Schrijver A (1998) Theory of Linear and Integer Programming (John Wiley & Sons, Hoboken, NJ).Google Scholar
• U.S. Census Bureau (2018) Census regions and divisions of the United States. Accessed July 16, 2018, https://www2.census.gov/geo/pdfs/maps-data/maps/reference/us_regdiv.pdf. Google Scholar
• Vanderbeck F (2011) Branching in branch-and-price: a generic scheme. Math. Programmng 130(2):249–294.Crossref, Google Scholar
• Vanderbeck F, Savelsbergh MW (2006) A generic view of Dantzig–Wolfe decomposition in mixed integer programming. Oper. Res. Lett. 34(3):296–306.Crossref, Google Scholar
• Vanderbeck F, Wolsey LA (2010) Reformulation and decomposition of integer programs. 50 Years of Integer Programming 1958–2008 (Springer, Berlin), 431–502.Crossref, Google Scholar
• Wolsey L (1998) Integer Programming (John Wiley & Sons, Hoboken, NJ).Google Scholar