Pressure swing adsorption (PSA) is an energy-efficient technology for gas separation, while the multiobjective optimization of PSA is a challenging task. To tackle this, we propose a hybrid optimization framework (TSEMO + DyOS), which integrates two steps. In the first step, a Bayesian stochastic multiobjective optimization algorithm (i.e., TSEMO) searches the entire decision space and identifies an approximated Pareto front within a small number of simulations. Within TSEMO, Gaussian process (GP) surrogate models are trained to approximate the original full process models. In the second step, a gradient-based deterministic algorithm (i.e., DyOS) is initialized at the approximated Pareto front to further refine the solutions until local optimality. Therein, the full process model is used in the optimization. The proposed hybrid framework is efficient, because it benefits from the coarse-to-fine function evaluations and stochastic-to-deterministic searching strategy. When the result is far away from the optima, TSEMO can efficiently approximate a trade-off curve as good as a commonly used evolutional algorithm, i.e., Nondominated Sorting Genetic Algorithm II (NSGA-II), while TSEMO only uses around 1/16th of CPU time of NSGA-II. This is because the GP-based surrogate model is utilized for function evaluations in the initial coarse search. When the result is near the optima, the searching efficiency of TSEMO dramatically decreases, while DyOS can accelerate the searching efficiency by over 10 times. This is because, in the proximity of optima, the exploitation capacity of DyOS is significantly higher than that of TSEMO.

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.