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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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    3. Joseph Scott & Matthew Stuber & Paul Barton, 2011. "Generalized McCormick relaxations," Journal of Global Optimization, Springer, vol. 51(4), pages 569-606, December.
    4. Kamil A. Khan & Harry A. J. Watson & Paul I. Barton, 2017. "Differentiable McCormick relaxations," Journal of Global Optimization, Springer, vol. 67(4), pages 687-729, April.
    5. Kamil A. Khan & Matthew Wilhelm & Matthew D. Stuber & Huiyi Cao & Harry A. J. Watson & Paul I. Barton, 2018. "Corrections to: Differentiable McCormick relaxations," Journal of Global Optimization, Springer, vol. 70(3), pages 705-706, March.
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    2. 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.
    3. 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).
    4. 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.
    5. Ding, Yuxing & Liu, Yurong & Wang, Meihong & Du, Wenli & Qian, Feng, 2024. "Heat integration, simultaneous structure and parameter optimisation, and techno-economic evaluation of waste heat recovery systems for petrochemical industry," Energy, Elsevier, vol. 296(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. Gandhi, Akhilesh & Zantye, Manali S. & Faruque Hasan, M.M., 2022. "Cryogenic energy storage: Standalone design, rigorous optimization and techno-economic analysis," Applied Energy, Elsevier, vol. 322(C).
    8. 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.
    9. Jianyuan Zhai & Fani Boukouvala, 2022. "Data-driven spatial branch-and-bound algorithms for box-constrained simulation-based optimization," Journal of Global Optimization, Springer, vol. 82(1), pages 21-50, January.
    10. Andrea Bacigalupo & Giorgio Gnecco & Marco Lepidi & Luigi Gambarotta, 2020. "Machine-Learning Techniques for the Optimal Design of Acoustic Metamaterials," Journal of Optimization Theory and Applications, Springer, vol. 187(3), pages 630-653, December.
    11. Huster, Wolfgang R. & Schweidtmann, Artur M. & Mitsos, Alexander, 2020. "Globally optimal working fluid mixture composition for geothermal power cycles," Energy, Elsevier, vol. 212(C).

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