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The decomposition-based outer approximation algorithm for convex mixed-integer nonlinear programming

Author

Listed:
  • Pavlo Muts

    (Hamburg University of Applied Sciences)

  • Ivo Nowak

    (Hamburg University of Applied Sciences)

  • Eligius M. T. Hendrix

    (University of Málaga)

Abstract

This paper presents a new two-phase method for solving convex mixed-integer nonlinear programming (MINLP) problems, called Decomposition-based Outer Approximation Algorithm (DECOA). In the first phase, a sequence of linear integer relaxed sub-problems (LP phase) is solved in order to rapidly generate a good linear relaxation of the original MINLP problem. In the second phase, the algorithm solves a sequence of mixed integer linear programming sub-problems (MIP phase). In both phases the outer approximation is improved iteratively by adding new supporting hyperplanes by solving many easier sub-problems in parallel. DECOA is implemented as a part of Decogo (Decomposition-based Global Optimizer), a parallel decomposition-based MINLP solver implemented in Python and Pyomo. Preliminary numerical results based on 70 convex MINLP instances up to 2700 variables show that due to the generated cuts in the LP phase, on average only 2–3 MIP problems have to be solved in the MIP phase.

Suggested Citation

  • Pavlo Muts & Ivo Nowak & Eligius M. T. Hendrix, 2020. "The decomposition-based outer approximation algorithm for convex mixed-integer nonlinear programming," Journal of Global Optimization, Springer, vol. 77(1), pages 75-96, May.
    • Handle: RePEc:spr:jglopt:v:77:y:2020:i:1:d:10.1007_s10898-020-00888-x
    DOI: 10.1007/s10898-020-00888-x
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    References listed on IDEAS

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    1. Ivo Nowak & Norman Breitfeld & Eligius M. T. Hendrix & Grégoire Njacheun-Njanzoua, 2018. "Decomposition-based Inner- and Outer-Refinement Algorithms for Global Optimization," Journal of Global Optimization, Springer, vol. 72(2), pages 305-321, October.
    2. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    3. Ruth Misener & Christodoulos Floudas, 2014. "ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations," Journal of Global Optimization, Springer, vol. 59(2), pages 503-526, July.
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    Cited by:

    1. Alireza Olama & Eduardo Camponogara & Paulo R. C. Mendes, 2023. "Distributed primal outer approximation algorithm for sparse convex programming with separable structures," Journal of Global Optimization, Springer, vol. 86(3), pages 637-670, July.
    2. Andreas Lundell & Jan Kronqvist, 2022. "Polyhedral approximation strategies for nonconvex mixed-integer nonlinear programming in SHOT," Journal of Global Optimization, Springer, vol. 82(4), pages 863-896, April.
    3. Alexander Murray & Timm Faulwasser & Veit Hagenmeyer & Mario E. Villanueva & Boris Houska, 2021. "Partially distributed outer approximation," Journal of Global Optimization, Springer, vol. 80(3), pages 523-550, July.
    4. 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.
    5. Chen, Zebin & D’Ariano, Andrea & Li, Shukai & Tessitore, Marta Leonina & Yang, Lixing, 2024. "Robust dynamic train regulation integrated with stop-skipping strategy in urban rail networks: An outer approximation based solution method," Omega, Elsevier, vol. 128(C).

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