Estimating the Size of Branch-and-Bound Trees
Published Online:29 Oct 2021https://doi.org/10.1287/ijoc.2021.1103
References
- (2013) Mixed integer programming: Analyzing 12 years of progress. Jünger M, Reinelt G, eds. Facets of Combinatorial Optimization (Springer, Berlin), 449–481.Crossref, Google Scholar
- (2006) MIPLIB 2003. Oper. Res. Lett. 34(4):1–12.Crossref, Google Scholar
- (2010) An empirical study of optimization for maximizing diffusion in networks. Cohen D, ed. Principles and Practice of Constraint Programming (Springer, Berlin), 514–521.Google Scholar
- (2016) Online learning for strong branching approximation in branch-and-bound. Technical report, Université de Liège, Liège, Belgium.Google Scholar
- (2017) A machine learning-based approximation of strong branching. INFORMS J. Comput. 29(1):185–195.Link, Google Scholar
- (2019) Clairvoyant restarts in branch-and-bound search using online tree-size estimation. Proc. 33rd AAAI Conf. Artificial Intelligence (AAAI Press, Palo Alto, CA), 1427–1434.Google Scholar
- (2018) Learning to branch. Dy J, Krause A, eds. Proc. 35th Internat. Conf. Machine Learning, Stockholm, 353–362.Google Scholar
- (2017) Estimating the size of search trees by sampling with domain knowledge. Proc. 26th Internat. Joint Conf. Artificial Intelligence, Melbourne, Australia, 473–479.Google Scholar
- (1998) An updated mixed integer programming library: MIPLIB 3.0. Optima 58:12–15.Google Scholar
- (2001) Random forests. Machine Learning 45(1):5–32.Crossref, Google Scholar
- (1983) Classification and Regression Trees (Chapman & Hall/CRC, Boca Raton, FL).Google Scholar
- (1992) Heuristic sampling: A method for predicting the performance of tree searching programs. SIAM J. Comput. 21(2):295–315.Crossref, Google Scholar
- Coral (2016) Coral MIP benchmark library. Accessed August 24, 2021, http://coral.ise.lehigh.edu/data-sets/mixed-integer-instances.Google Scholar
- (2006) Early estimates of the size of branch-and-bound trees. INFORMS J. Comput. 18(1):86–96.Link, Google Scholar
- (1965) A tree-search algorithm for mixed integer programming problems. Comput. J. 8(3):250–255.Crossref, Google Scholar
- (2019) Learning MILP resolution outcomes before reaching time-limit. Rousseau LM, Stergiou K, eds. Integration of Constraint Programming, Artificial Intelligence, and Operations Research (Springer, Cham, Switzerland), 275–291.Crossref, Google Scholar
- (2001) Greedy function approximation: A gradient boosting machine. Ann. Statist. 29(5):1189–1232.Crossref, Google Scholar
- (2020) The SCIP optimization suite 7.0. ZIB-Report 20-10, Zuse Institute Berlin, http://nbn-resolving.de/urn:nbn:de:0297-zib-78023.Google Scholar
- (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness (W. H. Freeman, New York).Google Scholar
- (2019) MIPLIB 2017: Data-driven compilation of the 6th mixed-integer programming library. Preprint, submitted July 12, http://www.optimization-online.org/DB_HTML/2019/07/7285.html.Google Scholar
- (1999) Clique is hard to approximate within n1−ε. Acta Math. 182(1):105–142.Crossref, Google Scholar
- (2018) Adaptive large neighborhood search for mixed integer programming. ZIB-Report 18-60, Zuse Institute Berlin, https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/7116.Google Scholar
- (2004) Forecasting seasonals and trends by exponentially weighted moving averages. Internat. J. Forecasting 20(1):5–10.Crossref, Google Scholar
- (2008) Forecasting with Exponential Smoothing: The State Space Approach (Springer, Berlin).Crossref, Google Scholar
- (2014) Linear-time FPT algorithms via network flow. Chekuri C, ed. Proc. 2014 Annual ACM-SIAM Sympos. Discrete Algorithms (SIAM, Philadelphia), 1749–1761.Google Scholar
- (2017) Learning to run heuristics in tree search. Proc. 26th Internat. Joint Conf. Artificial Intelligence, Melbourne, Australia, 659–666.Google Scholar
- (2016) Learning to branch in mixed integer programming. Proc. 30th AAAI Conf. Artificial Intelligence (AAAI Press, Palo Alto, CA), 724–731.Google Scholar
- (2006) Estimating search tree size. Proc. 21st National Conf. Artificial Intelligence, vol. 2 (AAAI Press, Palo Alto, CA), 1014–1019.Google Scholar
- (1975) Estimating the efficiency of backtrack programs. Math. Comp. 29(129):121–136.Crossref, Google Scholar
- (2011) MIPLIB 2010. Math. Programming Comput. 3(2):103–163.Crossref, Google Scholar
- (1960) An automatic method of solving discrete programming problems. Econometrica 28(3):497–520.Crossref, Google Scholar
- (2015) How important are branching decisions: Fooling MIP solvers. Oper. Res. Lett. 43(3):273–278.Crossref, Google Scholar
- (2013) Predicting the size of depth-first branch and bound search trees. Proc. 23rd Internat. Joint Conf. Artificial Intelligence, Beijing, (AAAI Press, Palo Alto, CA), 594–600.Google Scholar
- (2010) Mixed integer programming computation. Jünger M, Liebling TM, Naddef D, Nemhauser GL, Pulleyblank WR, Reinelt G, Rinaldi G, Wolsey LA, eds. 50 Years of Integer Programming 1958–2008—From the Early Years to the State-of-the-Art (Springer, Berlin), 619–645.Crossref, Google Scholar
- (1974) Properties of vertex packing and independence system polyhedra. Math. Programming 6(1):48–61.Crossref, Google Scholar
- (1975) Vertex packings: Structural properties and algorithms. Math. Programming 8(1):232–248.Crossref, Google Scholar
- (2003) A branch-and-cut algorithm for the single-commodity, uncapacitated, fixed-charge network flow problem. Networks 41(3):143–158.Crossref, Google Scholar
- (2011) Predicting the solution time of branch-and-bound algorithms for mixed-integer programs. INFORMS J. Comput. 23(3):392–403.Link, Google Scholar
- (2008) Branch-and-cut for the maximum feasible subsystem problem. SIAM J. Optim. 19(1):21–38.Crossref, Google Scholar
- (1977) On the integer-valued packing problem variables in the linear vertex packing problem. Math. Programming 12:97–101.Crossref, Google Scholar
- (1978) Tree size by partial backtracking. SIAM J. Comput. 7(4):481–491.Crossref, Google Scholar
- (2012) ParaSCIP—A parallel extension of SCIP. Bischof C, Hegering HG, Nagel WE, Wittum G, eds. Competence High Performance Comput. 2010 (Springer, Berlin), 135–148.Google Scholar

