(347a) Combined Bayesian Optimization and Global Sensitivity Analysis for the Optimization of Simulation-Based Flowsheets

Flowsheet optimization is used to enhance process performance in terms of cost, efficiency, and environmental impact by finding optimal operating conditions that minimize/maximize the desired key performance indicators (KPIs). Flowsheet optimization usually involves the use of optimization algorithms to find the optimal operating conditions and equipment configurations based on a mathematical model of the process at hand. It can be employed at a unit operation level, where the emphasis is on individual process units such as reactors or distillation columns, or at the flowsheet level, where the emphasis is on the upstream, downstream or overall process [1,2]. Simulation-based techno-economic analysis is a well-established methodology for the quantification of process performance. Most of commercially available simulators are based on steady-state process and economic models, heuristic rules, and expert knowledge to find feasible process configurations. Normally, the underlying algebraic equations used by commercial process simulators are unavailable to the user and this can challenge further optimization studies as the derivatives and convexity properties are unknown. An effective approach to simulation-based flowsheet optimization is data-driven and surrogate-based optimization [3], where the flowsheet model is treated as an inexpensive black-box function. An estimate of the objective function can be then obtained by simulating scenarios through quasi-random or adaptive sampling.

In this work, we propose an integrated computational framework for process design and black-box optimization which can use as input results from tools from which only inputs and outputs are available. The framework combines (1) Techno-economic Assessment (TEA), (2) Global Sensitivity Analysis (GSA), and (3) Bayesian optimization (BO) for the design and optimization of simulation-based flowsheets. GSA based on the Random Sampling-High Dimensional Model Representation (RS-HDMR) is utilized for uncertainty quantification and critical parameter identification, through the apportionment of KPI variability to individual parameters and their second-order interactions [4]. The use of GSA enables the ranking of uncertain parameters and hence dimensionality reduction of the design space by only considering the most influential inputs. Single-objective and multi-objective constrained BO is then performed in the reduced design space based on Gaussian Process (GP) surrogates, in order to find the optimal operating conditions. The framework is tested for different acquisition functions– Probability of Improvement (PI), Expected Improvement (EI), Expected Hypervolume Improvement (EHI), Augmented Expected Improvement (AEI), Upper (or Lower) Confidence Bound (UCB or LCB), and max-value entropy search (MES) [5].

The capabilities of the proposed framework are presented through a case study on the production of pharmaceutical plasmid DNA (pDNA) using SuperPro Designer [6]. pDNA represents a critical raw material for the production of advanced therapeutics such as cell and gene therapies and mRNA or viral-vector-based vaccines. The framework was applied through a SobolGSA (Kucherenko, 2013)-Matlab-Component Object Model (COM)-SuperPro Designer- Python interface. Results for single-objective Bayesian optimization suggest that optimal manufacturing recipes are projected to achieve an up to 170% increase in the batch size and a 34.7% decrease in the operating cost per batch.

Keywords: flowsheet optimization, Bayesian optimization, global sensitivity analysis

References

[1] F. Boukouvala, M. Ierapetritou, 2013, Surrogate-Based Optimization of Expensive Flowsheet Modeling for Continuous Pharmaceutical Manufacturing, Journal of Pharmaceutical Innovation, 8, 131–145.

[2] Z. Wang, M. Sebastian Escotet-Espinoza, M. Ierapetritou, 2017, Process analysis and optimization of continuous pharmaceutical manufacturing using flowsheet models, Computers and Chemical Engineering, 107, 77–91.

[3] D. van de Berg, T. Savage, P. Petsagkourakis, D. Zhang, N. Shah, E. A. del Rio-Chanona, 2022, Data-driven optimization for process systems engineering applications, Chemical Engineering Science, 248, 117135.

[4] S. Kucherenko, 2013, SobolHDMR: A general-purpose modeling software. Methods in Molecular Biology, 1073, 191–224.

[5] M. Balandat, B. Karrer, D. R. Jiang, S. Daulton, B. Letham, A. Gordon Wilson, E. Bakshy, 2020, BoTorch: A Framework for Efficient Monte-Carlo Bayesian Optimization, Advances in Neural Information Processing Systems, 33.

[6] R. Ferreira, D. Petrides, 2021, Plasmid DNA (pDNA) Large Scale Manufacturing – Process Modeling and Techno-Economic Assessment (TEA) using SuperPro Designer, doi: 10.13140/RG.2.2.12780.28800.