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Deterministic global optimization with artificial neural networks embedded. (English) Zbl 1407.90263
Summary: 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 [the second author et al., SIAM J. Optim. 20, No. 2, 573–601 (2009; Zbl 1192.65083)] 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.

MSC:
90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming
90C90 Applications of mathematical programming
68T01 General topics in artificial intelligence
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