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An efficient strategy for the activation of MIP relaxations in a multicore global MINLP solver

Author

Listed:
  • Kai Zhou

    (Zhejiang University)

  • Mustafa R. Kılınç

    (Carnegie Mellon University)

  • Xi Chen

    (Zhejiang University)

  • Nikolaos V. Sahinidis

    (Carnegie Mellon University)

Abstract

Solving mixed-integer nonlinear programming (MINLP) problems to optimality is a NP-hard problem, for which many deterministic global optimization algorithms and solvers have been recently developed. MINLPs can be relaxed in various ways, including via mixed-integer linear programming (MIP), nonlinear programming, and linear programming. There is a tradeoff between the quality of the bounds and CPU time requirements of these relaxations. Unfortunately, these tradeoffs are problem-dependent and cannot be predicted beforehand. This paper proposes a new dynamic strategy for activating and deactivating MIP relaxations in various stages of a branch-and-bound algorithm. The primary contribution of the proposed strategy is that it does not use meta-parameters, thus avoiding parameter tuning. Additionally, this paper proposes a strategy that capitalizes on the availability of parallel MIP solver technology to exploit multicore computing hardware while solving MINLPs. Computational tests for various benchmark libraries reveal that our MIP activation strategy works efficiently in single-core and multicore environments.

Suggested Citation

  • Kai Zhou & Mustafa R. Kılınç & Xi Chen & Nikolaos V. Sahinidis, 2018. "An efficient strategy for the activation of MIP relaxations in a multicore global MINLP solver," Journal of Global Optimization, Springer, vol. 70(3), pages 497-516, March.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:3:d:10.1007_s10898-017-0559-0
    DOI: 10.1007/s10898-017-0559-0
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    References listed on IDEAS

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    1. Michael R. Bussieck & Arne Stolbjerg Drud & Alexander Meeraus, 2003. "MINLPLib—A Collection of Test Models for Mixed-Integer Nonlinear Programming," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 114-119, February.
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    Cited by:

    1. 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.
    2. Jianxin Ma & Shuo Shi & Xuemai Gu & Fanggang Wang, 2020. "Heuristic mobile data gathering for wireless sensor networks via trajectory control," International Journal of Distributed Sensor Networks, , vol. 16(5), pages 15501477209, May.
    3. Akulker, Handan & Aydin, Erdal, 2023. "Optimal design and operation of a multi-energy microgrid using mixed-integer nonlinear programming: Impact of carbon cap and trade system and taxing on equipment selections," Applied Energy, Elsevier, vol. 330(PA).

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