Two-row and two-column mixed-integer presolve using hashing-based pairing methods

EURO Journal on Computational Optimization - Tập 8 - Trang 205-240 - 2020
Patrick Gemander1, Wei-Kun Chen2, Dieter Weninger1, Leona Gottwald3, Ambros Gleixner3, Alexander Martin1
1Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
2School of Mathematics and Statistics, Beijing Institute of Technology, 100081 Beijing, China
3Department of Mathematical Optimization, Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany.

Tài liệu tham khảo

Achterberg T (2007) Constraint integer programming. Ph.D. thesis, Technische Universität Berlin Achterberg, 2013, 449 Achterberg T, Bixby RE, Gu Z, Rothberg E, Weninger D (2014) Multi-row presolve reductions in mixed integer programming. In: T. Hosei University (ed) Proceedings of the twenty-sixth RAMP symposium, pp 181–196. http://www.orsj.or.jp/ramp/2014/paper/4-4.pdf Achterberg, 2019, Presolve reductions in mixed integer programming, INFORMS J Comput Andersen, 1995, Presolving in linear programming, Math Program, 71, 221, 10.1007/BF01586000 Atamtürk, 2005, Integer-programming software systems, Ann Oper Res, 140, 67, 10.1007/s10479-005-3968-2 Balas, 1980, An algorithm for large zero-one knapsack problems, Oper Res, 28, 1130, 10.1287/opre.28.5.1130 Belotti, 2013, Bound reduction using pairs of linear inequalities, J Glob Optim, 56, 787, 10.1007/s10898-012-9848-9 Belotti P, Cafieri S, Lee J, Liberti L (2010) Feasibility-based bounds tightening via fixed points. In: International conference on combinatorial optimization and applications, pp 65–76. Springer, Berlin Bixby, 1987, A note on detecting simple redundancies in linear systems, Oper Res Lett, 6, 15, 10.1016/0167-6377(87)90004-6 Bixby, 2007, Progress in computational mixed integer programming—a look back from the other side of the tipping point, Ann Oper Res, 149, 37, 10.1007/s10479-006-0091-y Bixby, 2004, Mixed-integer programming: a progress report, 309 Brearley, 1975, Analysis of mathematical programming problems prior to applying the simplex algorithm, Math Program, 8, 54, 10.1007/BF01580428 Chang, 1993, Implementation and computational results for the hierarchical algorithm for making sparse matrices sparser, ACM Trans Math Softw, 19, 419, 10.1145/155743.152620 Crowder, 1983, Solving large-scale zero-one linear programming problems, Oper Res, 31, 803, 10.1287/opre.31.5.803 Danna E (2008) Performance variability in mixed integer programming. In: Presentation at workshop on mixed integer programming Dantzig, 1957, Discrete-variable extremum problems, Oper Res, 5, 266, 10.1287/opre.5.2.266 Davis, 1987, Constraint propagation with interval labels, Artif intell, 32, 281, 10.1016/0004-3702(87)90091-9 Gamrath, 2015, Progress in presolving for mixed integer programming, Math Program Comput, 7, 367, 10.1007/s12532-015-0083-5 Gamrath G, Fischer T, Gally T, Gleixner A, Hendel G, Koch T, Maher SJ, Miltenberger M, üller BM, Pfetsch ME, Puchert C, Rehfeldt D, Schenker S, Schwarz R, Serrano F, Shinano Y, Vigerske S, Weninger D, Winkler M, Witt J.T, Witzig J (2016) The SCIP optimization suite 3.2. Technical report 15-60, ZIB, Berlin Gleixner A, Eifler L, Gally T, Gamrath G, Gemander P, Gottwald R.L, Hendel G, Hojny C, Koch T, Miltenberger M, Müller B, Pfetsch ME, Puchert C, Rehfeldt D, Schlösser F, Serrano F, Shinano Y, Viernickel JM, Vigerske S, Weninger D, Witt JT, Witzig J (2017) The SCIP optimization suite 5.0. Technical report, optimization online. http://www.optimization-online.org/DB_HTML/2017/12/6385.html Gleixner A, Hendel G, Gamrath G, Achterberg T, Bastubbe M, Berthold T, Christophel PM, Jarck K, Koch T, Linderoth J, Lübbecke M, Mittelmann HD, Ozyurt D, Ralphs TK, Salvagnin D, Shinano Y (2019) MIPLIB 2017: data-driven compilation of the 6th mixed-integer programming library. Technical report, optimization online. http://www.optimization-online.org/DB_HTML/2019/07/7285.html Gondzio, 1997, Presolve analysis of linear programs prior to applying an interior point method, INFORMS J Comput, 9, 73, 10.1287/ijoc.9.1.73 Guignard, 1981, Logical reduction methods in zero-one programming: minimal preferred variables, Oper Res, 29, 49, 10.1287/opre.29.1.49 Hoffman, 1991, Improving LP-representations of zero-one linear programs for branch-and-cut, ORSA J Comput, 3, 121, 10.1287/ijoc.3.2.121 Johnson, 1980, Experiments in integer programming, Discrete Appl Math, 2, 39, 10.1016/0166-218X(80)90053-0 Knuth, 1998 Küçükyavuz S (2019) Tsccp testset. http://faculty.washington.edu/simge/IntMixOS.zip Liu, 2019, On intersection of two mixing sets with applications to joint chance-constrained programs, Math Program, 175, 29, 10.1007/s10107-018-1231-2 Lodi, 2013, Performance variability in mixed-integer programming, Tutor Oper Res Maher SJ, Fischer T, Gally T, Gamrath G, Gleixner A, Gottwald RL, Hendel G, Koch T, Lübbecke ME, Miltenberger M, et al (2017) The SCIP optimization suite 4.0. Technical report, ZIB, Berlin Martin, 2001, General mixed integer programming: computational issues for branch-and-cut algorithms, 1 miplib2017 (2018) MIPLIB 2017, 2018. http://miplib.zib.de Quesada, 1995, Global optimization of bilinear process networks with multicomponent flows, Comput Chem Eng, 19, 1219, 10.1016/0098-1354(94)00123-5 Savelsbergh, 1994, Preprocessing and probing techniques for mixed integer programming problems, ORSA J Comput, 6, 445, 10.1287/ijoc.6.4.445 Schewe, 2020, A decomposition heuristic for mixed-integer supply chain problems, Oper Res Lett, 10.1016/j.orl.2020.02.006 Schrijver, 1986 Shectman, 1998, A finite algorithm for global minimization of separable concave programs, J Glob Optim, 12, 1, 10.1023/A:1008241411395 Sinha, 1979, The multiple-choice knapsack problem, Oper Res, 27, 503, 10.1287/opre.27.3.503 Suhl, 1994, Supernode processing of mixed-integer models, Comput Optim Appl, 3, 317, 10.1007/BF01299207