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Integrality gap minimization heuristics for binary mixed integer nonlinear programming

Author

Listed:
  • Wendel Melo

    (Federal University of Uberlandia)

  • Marcia Fampa

    (Federal University of Rio de Janeiro)

  • Fernanda Raupp

    (National Laboratory for Scientific Computing (LNCC) of the Ministry of Science, Technology and Innovation)

Abstract

We present two feasibility heuristics for binary mixed integer nonlinear programming. Called integrality gap minimization algorithm (IGMA)—versions 1 and 2, our heuristics are based on the solution of integrality gap minimization problems with a space partitioning scheme defined over the integer variables of the problem addressed. Computational results on a set of benchmark instances show that the proposed approaches present satisfactory results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:3:d:10.1007_s10898-018-0623-4
    DOI: 10.1007/s10898-018-0623-4
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    References listed on IDEAS

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    1. M. Raghavachari, 1969. "On Connections Between Zero-One Integer Programming and Concave Programming Under Linear Constraints," Operations Research, INFORMS, vol. 17(4), pages 680-684, August.
    2. 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.
    3. 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.
    4. M. W. P. Savelsbergh, 1994. "Preprocessing and Probing Techniques for Mixed Integer Programming Problems," INFORMS Journal on Computing, INFORMS, vol. 6(4), pages 445-454, November.
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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. Ana Maria A. C. Rocha & M. Fernanda P. Costa & Edite M. G. P. Fernandes, 2018. "Preface to the Special Issue “GOW’16”," Journal of Global Optimization, Springer, vol. 71(3), pages 441-442, July.
    3. Zhe Liu & Shurong Li, 2022. "A numerical method for interval multi-objective mixed-integer optimal control problems based on quantum heuristic algorithm," Annals of Operations Research, Springer, vol. 311(2), pages 853-898, April.
    4. 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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