The MeLOn toolbox: Machine Learning Models for Optimization

Machine Learning models for Optimization (MeLOn) is a toolbox that integrates machine learning models into optimization problems.

MeLOn provides scripts for the training of various machine learning models and their C++ implementation, which can be used in the open-source global solver MAiNGO. The repository currently contains artificial neural networks for regression and Gaussian processes for regression (also known as Kriging). MeLOn is a submodule of MAiNGO, so it is included automatically when you download MAiNGO, and the trained machine learning models can then be used within MAiNGO.

MeLOn was developed during Artur M. Schweidtmann's PhD research at the Process Systems Engineering group (AVT.SVT) of RWTH Aachen University.

Open-source code

The open-source code of MeLOn is available in the MeLOn repository. MAiNGO is available in the MAiNGO repository.

Applications

A reduced-space formulation is very efficient for the deterministic global optimization of problems with artificial neural networks and Gaussian processes embedded. It allows for the efficient optimization of hybrid mechanistic/data-driven models in which artificial neural networks, for example, replace complex thermodynamics or describe experimental data.

The method has been used in various applications.

Deterministic global optimization with artificial neural networks embedded

• Hybrid modeling of chemical processes and process optimization [Schweidtmann and Mitsos, 2019]
• Rational design of ion separation membranes [Rall et al., 2019, Rall et al., 2020a, Rall et al., 2020b]
• Optimization of energy processes where accurate thermodynamics are learned by neural networks, with applications to organic Rankine cycle optimization [Schweidtmann et al., 2019, Huster et al., 2019] and working fluid selection [Huster et al., 2020]
• Neural networks as surrogates with guaranteed accuracy, with application to flash models [Schweidtmann et al., 2019]
• Scheduling of a compressed air energy storage system where the efficiency maps of compressors and turbines are learned by neural networks [Schäfer et al., 2020]

Deterministic global optimization with Gaussian processes embedded

• Chance-constrained programming with Gaussian processes, and Bayesian optimization with global optimization of the acquisition function [Schweidtmann et al., 2021]

Key publications

• Schweidtmann, A. M., & Mitsos, A. (2019). Deterministic global optimization with artificial neural networks embedded. Journal of Optimization Theory and Applications, 180(3), 925–948. doi:10.1007/s10957-018-1396-0
• Schweidtmann, A. M., Bongartz, D., Grothe, D., Kerkenhoff, T., Lin, X., Najman, J., & Mitsos, A. (2021). Deterministic global optimization with Gaussian processes embedded. Mathematical Programming Computation, 13(3), 553–581. doi:10.1007/s12532-021-00204-y
• Schweidtmann, A. M., Weber, J. M., Wende, C., Netze, L., & Mitsos, A. (2022). Obey validity limits of data-driven models through topological data analysis and one-class classification. Optimization and Engineering, 23(2), 855–876. doi:10.1007/s11081-021-09608-0
• Schweidtmann, A. M., Huster, W. R., Lüthje, J. T., & Mitsos, A. (2019). Deterministic global process optimization: Accurate (single-species) properties via artificial neural networks. Computers & Chemical Engineering, 121, 67–74. doi:10.1016/j.compchemeng.2018.10.007
• Schweidtmann, A. M., Bongartz, D., Huster, W. R., & Mitsos, A. (2019). Deterministic global process optimization: Flash calculations via artificial neural networks. Computer Aided Chemical Engineering, 46, 937–942. doi:10.1016/B978-0-12-818634-3.50157-0
• Rall, D., Menne, D., Schweidtmann, A. M., Kamp, J., von Kolzenberg, L., Mitsos, A., & Wessling, M. (2019). Rational design of ion separation membranes. Journal of Membrane Science, 569, 209–219. doi:10.1016/j.memsci.2018.10.013
• Rall, D., Schweidtmann, A. M., Aumeier, B. M., Kamp, J., Karwe, J., Ostendorf, K., Mitsos, A., & Wessling, M. (2020). Simultaneous rational design of ion separation membranes and processes. Journal of Membrane Science, 600, 117860. doi:10.1016/j.memsci.2020.117860
• Rall, D., Schweidtmann, A. M., Kruse, M., Evdochenko, E., Mitsos, A., & Wessling, M. (2020). Multi-scale membrane process optimization with high-fidelity ion transport models through machine learning. Journal of Membrane Science, 608, 118208. doi:10.1016/j.memsci.2020.118208
• Huster, W. R., Schweidtmann, A. M., & Mitsos, A. (2019). Impact of accurate working fluid properties on the globally optimal design of an organic Rankine cycle. Computer Aided Chemical Engineering, 47, 427–432. doi:10.1016/B978-0-12-818597-1.50068-0
• Huster, W. R., Schweidtmann, A. M., & Mitsos, A. (2020). Working fluid selection for organic Rankine cycles via deterministic global optimization of design and operation. Optimization and Engineering, 21, 517–536. doi:10.1007/s11081-019-09454-1
• Huster, W. R., Schweidtmann, A. M., & Mitsos, A. (2020). Globally optimal working fluid mixture composition for geothermal power cycles. Energy, 212, 118731. doi:10.1016/j.energy.2020.118731
• Huster, W. R., Schweidtmann, A. M., Lüthje, J. T., & Mitsos, A. (2020). Deterministic global superstructure-based optimization of an organic Rankine cycle. Computers & Chemical Engineering, 141, 106996. doi:10.1016/j.compchemeng.2020.106996
• Schäfer, P., Schweidtmann, A. M., Lenz, P. H., Markgraf, H. M., & Mitsos, A. (2020). Wavelet-based grid-adaptation for nonlinear scheduling subject to time-variable electricity prices. Computers & Chemical Engineering, 132, 106598. doi:10.1016/j.compchemeng.2019.106598