# Global Deterministic Optimization with Artificial Neural Networks Embedded

arXiv: https://arxiv.org/abs/1801.07114 · HTML: https://mlsanity.com/paper/1801.07114/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jan 2018.

## Built on by (most cited first, 30 of 33)

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## Abstract (arXiv)

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 [textitSIOPT, 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.