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Deterministic Global Optimization with Artificial Neural Networks Embedded
- Source :
- Journal of Optimization Theory and Applications. 180:925-948
- Publication Year :
- 2018
- Publisher :
- Springer Science and Business Media LLC, 2018.
-
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.
- Subjects :
- Mathematical optimization
021103 operations research
Control and Optimization
Optimization problem
Artificial neural network
Applied Mathematics
Activation function
0211 other engineering and technologies
010103 numerical & computational mathematics
02 engineering and technology
Function (mathematics)
Management Science and Operations Research
Solver
01 natural sciences
Nonlinear system
Multilayer perceptron
Theory of computation
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 15732878 and 00223239
- Volume :
- 180
- Database :
- OpenAIRE
- Journal :
- Journal of Optimization Theory and Applications
- Accession number :
- edsair.doi...........6a21f955c20a64fca990b3ad7a00a82b