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Branch-and-Model: a derivative-free global optimization algorithm

Author

Listed:
  • Kaiwen Ma

    (Carnegie Mellon University)

  • Luis Miguel Rios

    (End-to-End Analytics)

  • Atharv Bhosekar

    (GAMS Development Corporation)

  • Nikolaos V. Sahinidis

    (Georgia Institute of Technology)

  • Sreekanth Rajagopalan

    (The Dow Chemical Company)

Abstract

This paper presents a novel derivative-free global optimization algorithm Branch-and-Model (BAM). The BAM algorithm partitions the search domain dynamically, builds surrogate models around carefully selected evaluated points, and uses these models to exploit local function trends and speed up convergence. For model construction, BAM employs Automated Learning of Algebraic Models (ALAMO). The ALAMO algorithm generates algebraic models of the black-box function using various base functions and selection criteria. BAM’s potentially optimal identification scheme saves computational effort and prevents delays in searching for optimal solutions. The BAM algorithm is guaranteed to converge to the globally optimal function value under mild assumptions. Extensive computational experiments over 500 publicly open-source test problems and one industrially-relevant application show that BAM outperforms state-of-the-art DFO algorithms regardless of problem convexity and smoothness, especially for higher-dimensional problems.

Suggested Citation

  • Kaiwen Ma & Luis Miguel Rios & Atharv Bhosekar & Nikolaos V. Sahinidis & Sreekanth Rajagopalan, 2023. "Branch-and-Model: a derivative-free global optimization algorithm," Computational Optimization and Applications, Springer, vol. 85(2), pages 337-367, June.
    • Handle: RePEc:spr:coopap:v:85:y:2023:i:2:d:10.1007_s10589-023-00466-3
    DOI: 10.1007/s10589-023-00466-3
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    References listed on IDEAS

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    1. Donald R. Jones & Joaquim R. R. A. Martins, 2021. "The DIRECT algorithm: 25 years Later," Journal of Global Optimization, Springer, vol. 79(3), pages 521-566, March.
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    Cited by:

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    2. Mittal, Prateek & Christopoulos, Giorgos & Subramanian, Sriram, 2024. "Energy enhancement through noise minimization using acoustic metamaterials in a wind farm," Renewable Energy, Elsevier, vol. 224(C).

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