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Deterministic Global Optimization with Artificial Neural Networks Embedded

Author

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  • Artur M. Schweidtmann

    (RWTH Aachen University)

  • Alexander Mitsos

    (RWTH Aachen University)

Abstract

Artificial neural networks are used in various applications for data-driven black-box modeling and subsequent optimization. Herein, we present an efficient method for deterministic global optimization of optimization problems with artificial neural networks embedded. The proposed method is based on relaxations of algorithms using McCormick relaxations in a reduced space (Mitsos et al. in SIAM J Optim 20(2):573–601, 2009) employing the convex and concave envelopes of the nonlinear activation function. The optimization problem is solved using our in-house deterministic global solver. The performance of the proposed method is shown in four optimization examples: an illustrative function, a fermentation process, a compressor plant and a chemical process. The results show that computational solution time is favorable compared to a state-of-the-art global general-purpose optimization solver.

Suggested Citation

  • Artur M. Schweidtmann & Alexander Mitsos, 2019. "Deterministic Global Optimization with Artificial Neural Networks Embedded," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 925-948, March.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:3:d:10.1007_s10957-018-1396-0
    DOI: 10.1007/s10957-018-1396-0
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    References listed on IDEAS

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    1. Arne Stolbjerg Drud, 1994. "CONOPT—A Large-Scale GRG Code," INFORMS Journal on Computing, INFORMS, vol. 6(2), pages 207-216, May.
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    3. Jaromił Najman & Dominik Bongartz & Angelos Tsoukalas & Alexander Mitsos, 2017. "Erratum to: Multivariate McCormick relaxations," Journal of Global Optimization, Springer, vol. 68(1), pages 219-225, May.
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    3. Jason Ye & Joseph K. Scott, 2023. "Extended McCormick relaxation rules for handling empty arguments representing infeasibility," Journal of Global Optimization, Springer, vol. 87(1), pages 57-95, September.
    4. Fajemisin, Adejuyigbe O. & Maragno, Donato & den Hertog, Dick, 2024. "Optimization with constraint learning: A framework and survey," European Journal of Operational Research, Elsevier, vol. 314(1), pages 1-14.
    5. Majidi Nezhad, Meysam & Neshat, Mehdi & Sylaios, Georgios & Astiaso Garcia, Davide, 2024. "Marine energy digitalization digital twin's approaches," Renewable and Sustainable Energy Reviews, Elsevier, vol. 191(C).
    6. Tsay, Calvin, 2024. "A Quantile Neural Network Framework for Twostage Stochastic Optimization," DES - Working Papers. Statistics and Econometrics. WS 43773, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Zhihao Zhang & Zhe Wu & David Rincon & Panagiotis D. Christofides, 2019. "Real-Time Optimization and Control of Nonlinear Processes Using Machine Learning," Mathematics, MDPI, vol. 7(10), pages 1-25, September.
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