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Strong-branching inequalities for convex mixed integer nonlinear programs

Author

Listed:
  • Mustafa Kılınç
  • Jeff Linderoth
  • James Luedtke
  • Andrew Miller

Abstract

Strong branching is an effective branching technique that can significantly reduce the size of the branch-and-bound tree for solving mixed integer nonlinear programming (MINLP) problems. The focus of this paper is to demonstrate how to effectively use “discarded” information from strong branching to strengthen relaxations of MINLP problems. Valid inequalities such as branching-based linearizations, various forms of disjunctive inequalities, and mixing-type inequalities are all discussed. The inequalities span a spectrum from those that require almost no extra effort to compute to those that require the solution of an additional linear program. In the end, we perform an extensive computational study to measure the impact of each of our proposed techniques. Computational results reveal that existing algorithms can be significantly improved by leveraging the information generated as a byproduct of strong branching in the form of valid inequalities. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Mustafa Kılınç & Jeff Linderoth & James Luedtke & Andrew Miller, 2014. "Strong-branching inequalities for convex mixed integer nonlinear programs," Computational Optimization and Applications, Springer, vol. 59(3), pages 639-665, December.
    • Handle: RePEc:spr:coopap:v:59:y:2014:i:3:p:639-665
    DOI: 10.1007/s10589-014-9690-8
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    References listed on IDEAS

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    1. Balas, Egon & Jeroslow, Robert G., 1980. "Strengthening cuts for mixed integer programs," European Journal of Operational Research, Elsevier, vol. 4(4), pages 224-234, April.
    2. Samir Elhedhli, 2006. "Service System Design with Immobile Servers, Stochastic Demand, and Congestion," Manufacturing & Service Operations Management, INFORMS, vol. 8(1), pages 92-97, December.
    3. Yves Pochet & Laurence A. Wolsey, 1993. "Lot-Sizing with Constant Batches: Formulation and Valid Inequalities," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 767-785, November.
    4. Atamturk, Alper & Nemhauser, George L. & Savelsbergh, Martin W. P., 2000. "Conflict graphs in solving integer programming problems," European Journal of Operational Research, Elsevier, vol. 121(1), pages 40-55, February.
    5. GÜNLÜK, Oktay & POCHET, Yves, 2001. "Mixing mixed-integer inequalities," LIDAM Reprints CORE 1504, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. POCHET, Yves & WOLSEY, Laurence A., 1993. "Lot-sizing with constant batches: formulation and valid inequalities," LIDAM Reprints CORE 1066, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Egon Balas & Sebastián Ceria & Gérard Cornuéjols, 1996. "Mixed 0-1 Programming by Lift-and-Project in a Branch-and-Cut Framework," Management Science, INFORMS, vol. 42(9), pages 1229-1246, September.
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