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Deterministic Global Optimization with Artificial Neural Networks Embedded

Artur M Schweidtmann (artur.schweidtmann***at***avt.rwth-aachen.de)
Alexander Mitsos (amitsos***at***alum.mit.edu)

Abstract: Artificial neural networks (ANNs) 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 ANN embedded optimization problems. The proposed method is based on relaxations of algorithms using McCormick relaxations in a reduced-space [\textit{SIOPT}, 20 (2009), pp. 573-601] including the convex and concave envelopes of the nonlinear activation function of ANNs. The optimization problem is solved using our in-house global deterministic solver MAiNGO. 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 optimization. The results show that computational solution time is favorable compared to the global general-purpose optimization solver BARON.

Keywords: Surrogate-based optimization, Multilayer perceptron, McCormick relaxations, Machine learning, Deep learning, Fermentation process, Compressor plant, Cumene process

Category 1: Applications -- Science and Engineering (Chemical Engineering )

Category 2: Global Optimization

Category 3: Nonlinear Optimization

Citation: Schweidtmann, A.M. & Mitsos, A. J Optim Theory Appl (2018). https://doi.org/10.1007/s10957-018-1396-0

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Entry Submitted: 12/22/2017
Entry Accepted: 12/22/2017
Entry Last Modified: 10/15/2018

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