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An overview of MINLP algorithms and their implementation in Muriqui Optimizer

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 an overview of the main algorithms in the literature for convex mixed integer nonlinear programming and discuss aspects of their implementation in a new open source computational package called Muriqui Optimizer. We provide extensive computational results comparing the implementations of all approaches considered on a set of 343 benchmark test problems. Finally, we present to the technical and scientific community the new software Muriqui Optimizer.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:286:y:2020:i:1:d:10.1007_s10479-018-2872-5
    DOI: 10.1007/s10479-018-2872-5
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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. Arthur F. Veinott, 1967. "The Supporting Hyperplane Method for Unimodal Programming," Operations Research, INFORMS, vol. 15(1), pages 147-152, February.
    3. 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.
    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. 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.
    6. 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.
    7. 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.
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    Cited by:

    1. 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.
    2. Andreas Lundell & Jan Kronqvist & Tapio Westerlund, 2022. "The supporting hyperplane optimization toolkit for convex MINLP," Journal of Global Optimization, Springer, vol. 84(1), pages 1-41, September.

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