There has been an increasing interest in the use of automated self-optimising continuous flow platforms for the development and manufacture in synthesis in recent years. Such processes include multiple reactive and work-up steps, which need to be efficiently optimised. Here, we report the combination of multi-objective optimisation based on machine learning methods (TSEMO algorithm) with self-optimising platforms for the optimisation of multi-step continuous reaction processes. This is demonstrated for a pharmaceutically relevant Sonogashira reaction. We demonstrate how optimum reaction conditions are re-evaluated with the changing downstream work-up specifications in the active learning process. Furthermore, a Claisen-Schmidt condensation reaction with subsequent liquid-liquid separation was optimised with respect to three-objectives. This approach provides the ability to simultaneously optimise multi-step processes with respect to multiple objectives, and thus has the potential to make substantial savings in time and resources.

Nonlinear model predictive control requires the solution of nonlinear programs with potentially multiple local solutions. Here, deterministic global optimization can guarantee to find a global optimum. However, its application is currently severely limited by computational cost and requires further developments in problem formulation, optimization solvers, and computing architectures. In this work, we propose a reduced-space formulation for the global optimization of problems with recurrent neural networks (RNN) embedded, based on our recent work on feed-forward artificial neural networks embedded. The method reduces the dimensionality of the optimization problem significantly, lowering the computational cost. We implement the NMPC problem in our open-source solver MAiNGO and solve it using parallel computing on 40 cores. We demonstrate real-time capability for the illustrative van de Vusse CSTR case study. We further propose two alternatives to reduce computational time: i) reformulate the RNN model by exposing a selected state variable to the optimizer; ii) replace the RNN with a neural multi-model. In our numerical case studies each proposal results in a reduction of computational time by an order of magnitude.

Extensive literature has considered reduced, but still highly accurate, nonlinear dynamic process models, particularly for distillation columns. Nevertheless, there is a need for continuing research in this field. Herein, opportunities from the integration of machine learning into existing reduction approaches are discussed. First, key concepts for dynamic model reduction and their limitations are briefly reviewed. Afterwards, promising model structures for reduced hybrid mechanistic/data-driven models are outlined. Finally, crucial future challenges as well as promising research perspectives are presented.

Prediction of combustion-related properties of (oxygenated) hydrocarbons is an important and challenging task for which quantitative structure-property relationship (QSPR) models are frequently employed. Recently, a machine learning method, graph neural networks (GNNs), has shown promising results for the prediction of structure-property relationships. GNNs utilize a graph representation of molecules, where atoms correspond to nodes and bonds to edges containing information about the molecular structure. More specifically, GNNs learn physicochemical properties as a function of the molecular graph in a supervised learning setup using a backpropagation algorithm. This end-to-end learning approach eliminates the need for selection of molecular descriptors or structural groups, as it learns optimal fingerprints through graph convolutions and maps the fingerprints to the physicochemical properties by deep learning. We develop GNN models for predicting three fuel ignition quality indicators, i.e., the derived cetane number (DCN), the research octane number (RON), and the motor octane number (MON), of oxygenated and nonoxygenated hydrocarbons. In light of limited experimental data in the order of hundreds, we propose a combination of multitask learning, transfer learning, and ensemble learning. The results show competitive performance of the proposed GNN approach compared to state-of-the-art QSPR models, making it a promising field for future research. The prediction tool is available via a web front-end at www.avt.rwth-aachen.de/gnn.

Optimal reaction pathways for the conversion of renewable feedstocks are often examined by reaction network flux analysis. An alternative modelling approach for reaction networks is a Petri net. These explicitly take the reaction sequence into account. In the optimisation of a network, this can allow the implementation of constraints on circular reaction structures, which are common substructures in chemical reaction networks. In this study, we compare the performance of the models in an illustrative minimal working example of a circular reaction substructure. The reaction network flux analysis is shown to be a relaxation of the Petri net formulation. Most notable, this work contributes to well-reasoned model choices for reaction networks.

Synthetic membranes for desalination and ion separation processes are a prerequisite for the supply of safe and sufficient drinking water as well as smart process water tailored to its application. This requires a versatile membrane fabrication methodology. Starting from an extensive set of new ion separation membranes synthesized with a layer-by-layer methodology, we demonstrate for the first time that an artificial neural network (ANN) can predict ion retention and water flux values based on membrane fabrication conditions. The predictive ANN is used in a local single-objective optimization approach to identify manufacturing conditions that improve permeability of existing membranes. A deterministic global multi-objective optimization is performed in order to identify the upper bound (Pareto front) of the delicate trade-off between ion retention characteristics and permeability. Ultimately, a coupling of the ANN into a hybrid model enables physical insight into the influence of fabrication conditions on apparent membrane properties.

Rational solvent selection remains a significant challenge in process development. Here we describe a hybrid mechanistic-machine learning approach, geared towards automated process development workflow. A library of 459 solvents was used, for which 12 conventional molecular descriptors, two reaction-specific descriptors, and additional descriptors based on screening charge density, were calculated. Gaussian process surrogate models were trained on experimental data from a Rh(CO)₂(acac)/Josiphos catalysed asymmetric hydrogenation of a chiral α-β unsaturated γ-lactam. With two simultaneous objectives-high conversion and high diastereomeric excess-the multi-objective algorithm, trained on the initial dataset of 25 solvents, has identified solvents leading to better reaction outcomes. In addition to being a powerful design of experiments (DoE) methodology, the resulting Gaussian process surrogate model for conversion is, in statistical terms, predictive, with a cross-validation correlation coefficient of 0.84. After identifying promising solvents, the composition of solvent mixtures and optimal reaction temperature were found using a black-box Bayesian optimisation. We then demonstrated the application of a new genetic programming approach to select an appropriate machine learning model for a specific physical system, which should allow the transition of the overall process development workflow into the future robotic laboratories.

Global deterministic process optimization problems have recently been solved efficiently in a reduced-space by automatic propagation of McCormick relaxations (Bongartz and Mitsos, J. Global Optim, 2017). However, the previous optimizations have been limited to simplified thermodynamic property models. Herein, we propose a method that learns accurate thermodynamic properties via artificial neural networks (ANNs) and integrates those in deterministic global process optimization. The resulting hybrid process model is solved using the recently developed method for deterministic global optimization problems with ANNs embedded (Schweidtmann and Mitsos, J. Optim. Theory Appl., 2018). The optimal operation of a validated steady state model of an organic Rankine cycle is solved as a case study. It is especially challenging as the thermodynamic properties are given by the implicit Helmholtz equation of state. The results show that modeling of thermodynamic properties via ANNs performs favorable in deterministic optimization. This method can rapidly be extended to include properties from existing thermodynamic libraries, based on models or data.

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.

Deterministic global optimization of process flowsheets has so far mostly been limited to simplified thermodynamic models. Herein, we demonstrate a way to integrate accurate thermodynamic models for the optimal process design of an organic Rankine cycle (ORC) via the use of artificial neural networks (ANNs). We generate training data using the thermodynamic library Coolprop and learn thermodynamic properties. The ANNs are subsequently embedded in the process design optimization problem in a reduced-space, which is solved to global optimality using our in-house optimization software MAiNGO. The importance of accurate thermodynamics is illustrated for the design of an ORC for geothermal power generation. We show that the use of an accurate thermodynamic model leads to different design decisions in comparison to a simplified model. Furthermore, we investigate the influence of the network architecture and complexity on accuracy, optimization results and computational performance.

beta version is available open-source works well for problems formulated in reduced space runs on parallel computing can be extended to the user's needs can be used as general-purpose solver.

We recently demonstrated the potential of deterministic global optimization in a reduced-space formulation for flowsheet optimization. However, the consideration of implicit unit operations such as flash calculations is still challenging and the solution of complex flowsheets incorporating such operations can be intractable. We show that the solution of flash equations can be integrated in global optimization via artificial neural networks (ANNs). Thus, flash calculations are no longer performed within the flowsheet optimization. Instead, flash equations are solved offline and then learned using ANNs. ANNs have been used successfully in the literature to learn flash equilibria but have not yet been included in deterministic global optimization for this task. We embed the ANNs in a hybrid model and use deterministic global optimization to solve it. In addition, we utilize deterministic global optimization to calculate a guaranteed worst-case accuracy of ANNs compared to a rigorous model. We demonstrate the proposed approach on an illustrative five-component vapor-liquid equilibrium flash using our in-house solver MAiNGO.

Many engineering problems require the optimization of expensive, black-box functions involving multiple conflicting criteria, such that commonly used methods like multiobjective genetic algorithms are inadequate. To tackle this problem several algorithms have been developed using surrogates. However, these often have disadvantages such as the requirement of a priori knowledge of the output functions or exponentially scaling computational cost with respect to the number of objectives. In this paper a new algorithm is proposed, TSEMO, which uses Gaussian processes as surrogates. The Gaussian processes are sampled using spectral sampling techniques to make use of Thompson sampling in conjunction with the hypervolume quality indicator and NSGA-II to choose a new evaluation point at each iteration. The reference point required for the hypervolume calculation is estimated within TSEMO. Further, a simple extension was proposed to carry out batch-sequential design. TSEMO was compared to ParEGO, an expected hypervolume implementation, and NSGA-II on nine test problems with a budget of 150 function evaluations. Overall, TSEMO shows promising performance, while giving a simple algorithm without the requirement of a priori knowledge, reduced hypervolume calculations to approach linear scaling with respect to the number of objectives, the capacity to handle noise and lastly the ability for batch-sequential usage.

Automated development of chemical processes requires access to sophisticated algorithms for multi-objective optimization, since single-objective optimization fails to identify the trade-offs between conflicting performance criteria. Herein we report the implementation of a new multi-objective machine learning optimization algorithm for self-optimization, and demonstrate it in two exemplar chemical reactions performed in continuous flow. The algorithm successfully identified a set of optimal conditions corresponding to the trade-off curve (Pareto front) between environmental and economic objectives in both cases. Thus, it reveals the complete underlying trade-off and is not limited to one compromise as is the case in many other studies. The machine learning algorithm proved to be extremely data efficient, identifying the optimal conditions for the objectives in a lower number of experiments compared to single-objective optimizations. The complete underlying trade-off between multiple objectives is identified without arbitrary weighting factors, but via true multi-objective optimization.

Dynamic modeling is an important tool to gain better understanding of complex bioprocesses and to determine optimal operating conditions for process control. Currently, two modeling methodologies have been applied to biosystems: kinetic modeling, which necessitates deep mechanistic knowledge, and artificial neural networks (ANN), which in most cases cannot incorporate process uncertainty. The goal of this study is to introduce an alternative modeling strategy, namely Gaussian processes (GP), which incorporates uncertainty but does not require complicated kinetic information. To test the performance of this strategy, GPs were applied to model microalgae growth and lutein production based on existing experimental datasets and compared against the results of previous ANNs. Furthermore, a dynamic optimization under uncertainty is performed, avoiding over-optimistic optimization outside of the model's validity. The results show that GPs possess comparable prediction capabilities to ANNs for long-term dynamic bioprocess modeling, while accounting for model uncertainty. This strongly suggests their potential applications in bioprocess systems engineering.

This paper explores the feasibility of controlling the selectivity of a partial oxidation reaction by simultaneous modulation of local oxygen concentration and coolant temperature along the length of a reactor. The microstructured membrane reactor (MMR) concept consists of an oxygen-permeable membrane for distributing the oxygen feed with the coolant channel divided into zones of different temperatures. The reactor concept was explored in simulation of the selective oxidation of o-xylene to phthalic anhydride (PA). A mathematical model of the reactor was developed and optimization performed with the objective of maximising PA selectivity at the reactor outlet. Dosing of oxygen at uniform wall temperature results in PA selectivity increase by 6.3%, albeit with a reduction in o-xylene conversion of about 8% compared to a conventional fixed bed reactor. However, simultaneous modulation of both reactor wall temperatures and local oxygen concentration results in an improved conversion of o-xylene without a detrimental effect on selectivity, thus giving maximum yield of PA.

A decision support tool has been developed that uses global multiobjective optimization based on 1) the environmental impacts, evaluated within the framework of full life cycle assessment; and 2) process costs, evaluated by using rigorous process models. This approach is particularly useful in developing biorenewable-based energy solutions and chemicals manufacturing, for which multiple criteria must be evaluated and optimization-based decision-making processes are particularly attractive. The framework is demonstrated by using a case study of the conversion of terpenes derived from biowaste feedstocks into reactive intermediates. A two-step chemical conversion/separation sequence was implemented as a rigorous process model and combined with a life cycle model. A life cycle inventory for crude sulfate turpentine was developed, as well as a conceptual process of its separation into pure terpene feedstocks. The performed single- and multiobjective optimizations demonstrate the functionality of the optimization-based process development and illustrate the approach. The most significant advance is the ability to perform multiobjective global optimization, resulting in identification of a region of Pareto-optimal solutions.

A techno-economic optimization of a commercial-scale, amine-based, post-combustion CO₂ capture process is carried out. The most economically favorable process configuration, sizing and operating conditions are identified using a superstructure formulation. The superstructure has 12 288 possible process configurations and unit operations in the superstructure are described using rigorous, rate-based models. In order to simplify the optimization problem, the problem is decomposed and process simulations are explicitly handled in the process simulator. Optimization is performed externally using a genetic algorithm. The best found process configuration includes the absorber intercooling, the rich vapor recompression, and the cold solvent split. The result of this study is compared in terms of the cost of capture basis and shows 38% reduction on the annual operation cost, compared to the conventional amine-based CO₂ capture process. Moreover, the savings on the total annualized cost is ∼13%, which is an increase of 30% on the annualized investment cost resulting from additional unit operations. (Figure Presented).