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Integrating nonlinear branch-and-bound and outer approximation for convex Mixed Integer Nonlinear Programming

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  • Wendel Melo
  • Marcia Fampa
  • Fernanda Raupp

Abstract

In this paper, we present a new hybrid algorithm for convex Mixed Integer Nonlinear Programming (MINLP). The proposed hybrid algorithm is an improved version of the classical nonlinear branch-and-bound (BB) procedure, where the enhancements are obtained with the application of the outer approximation algorithm on some nodes of the enumeration tree. The two methods are combined in such a way that each one collaborates to the convergence of the other. Computational experiments with benchmark instances of the MINLP problem show the good performance of the proposed algorithm, which is compared to the outer approximation algorithm, the nonlinear BB algorithm and the hybrid algorithm implemented in the solver Bonmin. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Wendel Melo & Marcia Fampa & Fernanda Raupp, 2014. "Integrating nonlinear branch-and-bound and outer approximation for convex Mixed Integer Nonlinear Programming," Journal of Global Optimization, Springer, vol. 60(2), pages 373-389, October.
    • Handle: RePEc:spr:jglopt:v:60:y:2014:i:2:p:373-389
    DOI: 10.1007/s10898-014-0217-8
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    References listed on IDEAS

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    1. Omprakash K. Gupta & A. Ravindran, 1985. "Branch and Bound Experiments in Convex Nonlinear Integer Programming," Management Science, INFORMS, vol. 31(12), pages 1533-1546, December.
    2. Still, Claus & Westerlund, Tapio, 2006. "A sequential cutting plane algorithm for solving convex NLP problems," European Journal of Operational Research, Elsevier, vol. 173(2), pages 444-464, September.
    3. Walter Murray & Kien-Ming Ng, 2010. "An algorithm for nonlinear optimization problems with binary variables," Computational Optimization and Applications, Springer, vol. 47(2), pages 257-288, October.
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    Cited by:

    1. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2022. "Two linear approximation algorithms for convex mixed integer nonlinear programming," Annals of Operations Research, Springer, vol. 316(2), pages 1471-1491, September.
    2. Marcia Fampa & Jon Lee & Wendel Melo, 2016. "A specialized branch-and-bound algorithm for the Euclidean Steiner tree problem in n-space," Computational Optimization and Applications, Springer, vol. 65(1), pages 47-71, September.
    3. Arash Kaviani & Russell G. Thompson & Abbas Rajabifard & Majid Sarvi, 2020. "A model for multi-class road network recovery scheduling of regional road networks," Transportation, Springer, vol. 47(1), pages 109-143, February.
    4. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2018. "Integrality gap minimization heuristics for binary mixed integer nonlinear programming," Journal of Global Optimization, Springer, vol. 71(3), pages 593-612, July.
    5. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2020. "An overview of MINLP algorithms and their implementation in Muriqui Optimizer," Annals of Operations Research, Springer, vol. 286(1), pages 217-241, March.

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