Abstract
Branch-and-bound methods for mixed-integer programming (MIP) are traditionally based on solving a linear programming (LP) relaxation and branching on a variable which takes a fractional value in the (single) computed relaxation optimum. In this paper we study branching strategies for mixed-integer programs that exploit the knowledge of multiple alternative optimal solutions (a cloud) of the current LP relaxation. These strategies naturally extend state-of-the-art methods like strong branching, pseudocost branching, and their hybrids.
We show that by exploiting dual degeneracy, and thus multiple alternative optimal solutions, it is possible to enhance traditional methods. We present preliminary computational results, applying the newly proposed strategy to full strong branching, which is known to be the MIP branching rule leading to the fewest number of search nodes. It turns out that cloud branching can reduce the mean running time by up to 30% on standard test sets.
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References
Benichou, M., Gauthier, J., Girodet, P., Hentges, G., Ribiere, G., Vincent, O.: Experiments in mixed-integer programming. Mathematical Programming 1, 76–94 (1971)
Linderoth, J.T., Savelsbergh, M.W.P.: A computational study of strategies for mixed integer programming. INFORMS Journal on Computing 11, 173–187 (1999)
Achterberg, T., Koch, T., Martin, A.: Branching rules revisited. Operations Research Letters 33, 42–54 (2005)
Achterberg, T.: Constraint Integer Programming. PhD thesis, Technische Universität Berlin (2007), http://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/1018
Bixby, R., Fenelon, M., Gu, Z., Rothberg, E., Wunderling, R.: MIP: Theory and practice – closing the gap. In: Powell, M., Scholtes, S. (eds.) Systems Modelling and Optimization: Methods, Theory, and Applications, pp. 19–49. Kluwer Academic Publisher (2000)
Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J.: Finding cuts in the TSP (A preliminary report). Technical Report 95-05, DIMACS (1995)
Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton University Press, USA (2007)
Fischetti, M., Monaci, M.: Branching on nonchimerical fractionalities. OR Letters 40(3), 159–164 (2012)
Achterberg, T., Berthold, T.: Hybrid branching. In: van Hoeve, W.-J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 309–311. Springer, Heidelberg (2009)
Patel, J., Chinneck, J.W.: Active-constraint variable ordering for faster feasibility of mixed integer linear programs. Mathematical Programming 110, 445–474 (2007)
Karamanov, M., Cornuéjols, G.: Branching on general disjunctions. Mathematical Programming 128(1-2), 403–436 (2011)
Li, C.M., Anbulagan: Look-ahead versus look-back for satisfiability problems. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 341–355. Springer, Heidelberg (1997)
Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: Proceedings of the 38th Annual Design Automation Conference (DAC 2001), pp. 530–535 (2001), doi:10.1145/378239.379017
Kılınç Karzan, F., Nemhauser, G.L., Savelsbergh, M.W.P.: Information-based branching schemes for binary linear mixed-integer programs. Mathematical Programming Computation 1(4), 249–293 (2009)
Fischetti, M., Monaci, M.: Backdoor branching. In: Günlük, O., Woeginger, G.J. (eds.) IPCO 2011. LNCS, vol. 6655, pp. 183–191. Springer, Heidelberg (2011)
Koch, T., Achterberg, T., Andersen, E., Bastert, O., Berthold, T., Bixby, R.E., Danna, E., Gamrath, G., Gleixner, A.M., Heinz, S., Lodi, A., Mittelmann, H., Ralphs, T., Salvagnin, D., Steffy, D.E., Wolter, K.: MIPLIB 2010 - Mixed Integer Programming Library version 5. Mathematical Programming Computation 3, 103–163 (2011), http://miplib.zib.de
Achterberg, T., Koch, T., Martin, A.: MIPLIB 2003. Operations Research Letters 34(4), 1–12 (2006), http://miplib.zib.de/miplib2003/
Zamora, J.M., Grossmann, I.E.: A branch and contract algorithm for problems with concave univariate, bilinear and linear fractional terms. Journal of Global Optimization 14, 217–249 (1999), doi:10.1023/A:1008312714792
Caprara, A., Locatelli, M.: Global optimization problems and domain reduction strategies. Mathematical Programming 125, 123–137 (2010), doi:10.1007/s10107-008-0263-4
Fischetti, M., Glover, F., Lodi, A.: The feasibility pump. Mathematical Programming 104(1), 91–104 (2005), doi:10.1007/s10107-004-0570-3
Achterberg, T.: LP basis selection and cutting planes. Presentation Slides from MIP 2010 Conference in Atlanta (2010), http://www2.isye.gatech.edu/mip2010/program/program.pdf
Achterberg, T.: SCIP: Solving Constraint Integer Programs. Mathematical Programming Computation 1(1), 1–41 (2009), doi:10.1007/s12532-008-0001-1
Wunderling, R.: Paralleler und objektorientierter Simplex-Algorithmus. PhD thesis, Technische Universität Berlin (1996)
COR@L: MIP Instances (2010), http://coral.ie.lehigh.edu/data-sets/mixed-integer-instances/
Czyzyk, J., Mesnier, M., Moré, J.: The NEOS server. IEEE Computational Science & Engineering 5(3), 68–75 (1998), http://www.neos-server.org/neos/
Bixby, R.E., Ceria, S., McZeal, C.M., Savelsbergh, M.W.: An updated mixed integer programming library: MIPLIB 3.0. Optima (58), 12–15 (1998), http://miplib.zib.de/miplib3/miplib.html
Cohen, P.R.: Empirical Methods for Artificial Intelligence. MIT Press (1995)
Gamrath, G.: Improving strong branching by propagation. In: Gomes, C., Sellmann, M. (eds.) CPAIOR 2013. LNCS, vol. 7874, pp. 347–354. Springer, Heidelberg (2013)
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Berthold, T., Salvagnin, D. (2013). Cloud Branching. In: Gomes, C., Sellmann, M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2013. Lecture Notes in Computer Science, vol 7874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38171-3_3
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DOI: https://doi.org/10.1007/978-3-642-38171-3_3
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