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Undercover Branching

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Experimental Algorithms (SEA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7933))

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Abstract

In this paper, we present a new branching strategy for nonconvex MINLP that aims at driving the created subproblems towards linearity. It exploits the structure of a minimum cover of an MINLP, a smallest set of variables that, when fixed, render the remaining system linear: whenever possible, branching candidates in the cover are preferred.

Unlike most branching strategies for MINLP, Undercover branching is not an extension of an existing MIP branching rule. It explicitly regards the nonlinearity of the problem while branching on integer variables with a fractional relaxation solution. Undercover branching can be naturally combined with any variable-based branching rule.

We present computational results on a test set of general MINLPs from MINLPLib, using the new strategy in combination with reliability branching and pseudocost branching. The computational cost of Undercover branching itself proves negligible. While it turns out that it can influence the variable selection only on a smaller set of instances, for those that are affected, significant improvements in performance are achieved.

The authors gratefully acknowledge the support of the DFG Research Center Matheon Mathematics for key technologies in Berlin and the Berlin Mathematical School.

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References

  1. Land, A.H., Doig, A.G.: An automatic method of solving discrete programming problems. Econometrica 28(3), 497–520 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  2. 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)

    Google Scholar 

  3. Achterberg, T.: Constraint Integer Programming. PhD thesis, TU Berlin (2007)

    Google Scholar 

  4. Vigerske, S.: Decomposition in Multistage Stochastic Programming and a Constraint Integer Programming Approach to MINLP. PhD thesis, HU Berlin (2012)

    Google Scholar 

  5. Belotti, P., Lee, J., Liberti, L., Margot, F., Wächter, A.: Branching and bounds tightening techniques for non-convex MINLP. Optimization Methods & Software 24, 597–634 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Karamanov, M., Cornuéjols, G.: Branching on general disjunctions. Math. Prog. 128(1-2), 403–436 (2011)

    Article  MATH  Google Scholar 

  7. Benichou, M., Gauthier, J., Girodet, P., Hentges, G., Ribiere, G., Vincent, O.: Experiments in mixed-integer programming. Math. Prog. 1, 76–94 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  8. Linderoth, J.T., Savelsbergh, M.W.P.: A computational study of search strategies for mixed integer programming. INFORMS J. Comput. 11, 173–187 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. 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)

    Google Scholar 

  10. Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton University Press, USA (2007)

    Google Scholar 

  11. Achterberg, T., Koch, T., Martin, A.: Branching rules revisited. Operations Research Letters 33, 42–54 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. 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)

    Chapter  Google Scholar 

  13. Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: Proc. of the DAC (July 2001)

    Google Scholar 

  14. Li, C.M., Anbulagan: Look-ahead versus look-back for satisfiability problems. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 342–356. Springer, Heidelberg (1997)

    Google Scholar 

  15. Kılınç Karzan, F., Nemhauser, G.L., Savelsbergh, M.W.P.: Information-based branching schemes for binary linear mixed-integer programs. Math. Prog. Computation 1(4), 249–293 (2009)

    Article  MATH  Google Scholar 

  16. Fischetti, M., Monaci, M.: Backdoor branching. In: Günlük, O., Woeginger, G.J. (eds.) IPCO 2011. LNCS, vol. 6655, pp. 183–191. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  17. Fischetti, M., Monaci, M.: Branching on nonchimerical fractionalities. OR Letters 40(3), 159–164 (2012)

    MathSciNet  MATH  Google Scholar 

  18. Tawarmalani, M., Sahinidis, N.V.: Global optimization of mixed-integer nonlinear programs: A theoretical and computational study. Math. Prog. 99, 563–591 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. Berthold, T., Gleixner, A.M.: Undercover – a primal heuristic for MINLP based on sub-MIPs generated by set covering. In: Bonami, P., Liberti, L., Miller, A.J., Sartenaer, A. (eds.) Proc. of the EWMINLP, pp. 103–112 (April 2010)

    Google Scholar 

  20. Berthold, T., Gleixner, A.M.: Undercover: a primal MINLP heuristic exploring a largest sub-MIP. Math. Prog. (2013) doi:10.1007/s10107-013-0635-2

    Google Scholar 

  21. Bussieck, M.R., Drud, A.S., Meeraus, A.: MINLPLib – a collection of test models for mixed-integer nonlinear programming. INFORMS J. Comput. 15(1), 114–119 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  22. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)

    MATH  Google Scholar 

  23. SCIP: Solving Constraint Integer Programs, http://scip.zib.de

  24. CppAD: A Package for Differentiation of C++ Algorithms, http://www.coin-or.org/CppAD

  25. Berthold, T., Heinz, S., Vigerske, S.: Extending a CIP framework to solve MIQCPs. In: Lee, J., Leyffer, S. (eds.) Mixed Integer Nonlinear Programming. The IMA Volumes in Mathematics and its Applications, vol. 154, pp. 427–444. Springer (2012)

    Google Scholar 

  26. Achterberg, T.: Conflict analysis in mixed integer programming. Discrete Optimization 4(1), 4–20 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  27. IBM: CPLEX Optimizer, http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/

  28. Wächter, A., Biegler, L.T.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Prog. 106(1), 25–57 (2006)

    Article  MATH  Google Scholar 

  29. GAMS: MINLP Library, http://www.gamsworld.org/minlp/minlplib.html

  30. Harjunkoski, I., Westerlund, T., Pörn, R., Skrifvars, H.: Different transformations for solving non-convex trim-loss problems by MINLP. Eur. J. Oper. Res. 105(3), 594–603 (1998)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany

    Timo Berthold & Ambros M. Gleixner

Authors
  1. Timo Berthold
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  2. Ambros M. Gleixner
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Editor information

Editors and Affiliations

  1. Institute for Systems Analysis and Computer Science (IASI), National Research Council (CNR), Viale Manzoni 30, 00185, Rome, Italy

    Vincenzo Bonifaci

  2. Department of Computer and Systems Science, Sapienza University of Rome, Via Ariosto 25, 00185, Rome, Italy

    Camil Demetrescu  & Alberto Marchetti-Spaccamela  & 

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Berthold, T., Gleixner, A.M. (2013). Undercover Branching. In: Bonifaci, V., Demetrescu, C., Marchetti-Spaccamela, A. (eds) Experimental Algorithms. SEA 2013. Lecture Notes in Computer Science, vol 7933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38527-8_20

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  • DOI: https://doi.org/10.1007/978-3-642-38527-8_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38526-1

  • Online ISBN: 978-3-642-38527-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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