(419a) A Surrogate-Based Method for Constrained Optimization with Black-Box Noisy Simulations
Zilong Wang, Marianthi Ierapetritou
Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, NJ, USA
Over the past decade, simulation and modeling techniques have been extensively investigated and implemented by the pharmaceutical manufacturing industry in order to enhance the process knowledge and improve the process efficiency . Together with experimental work, the development of process models is considered as a key component to facilitate the modernization of pharmaceutical manufacturing , which leads to reduction of the total cost, improvement of product quality, and increase of the overall process agility, flexibility, and robustness .
However, the increased complexity in process models also increases the difficulty of utilizing such models for optimization of pharmaceutical processes. A first issue that needs to be considered is the increasing computational complexity. This arises from the growing amount of calculations that are needed to account for the effects of different material properties and process conditions on the final product qualities. Additionally, in some cases the relationship between input factors and output variables is not explicitly expressed, and we may not have access to the closed-form expressions for the objective function and constraints . Furthermore, since the variability is playing an important role in the pharmaceutical product quality, it can be modeled in the simulation by incorporating a noise term, which is introduced at the beginning of an integrated process (e.g. feeders) and propagates along the whole process. The variability in pharmaceutical processes is commonly heteroscedastic in nature , and the relationship between variability and input factors is usually unknown after it is propagated in the simulation. To address those issues, an efficient approach is needed to solve the constrained optimization problem based on black-box noisy simulations for pharmaceutical manufacturing processes.
In this work, we propose a surrogate-based strategy to solve black-box constrained optimization problems. Two surrogate models are constructed separately for the objective function and the constraints. Stochastic Kriging  is used as the surrogate to account for the heteroscedastic noise that is inherent to the black-box simulations we encounter. We utilize an efficient adaptive sampling method to sequentially improve the two surrogate models and direct the search to a feasible optimum. This adaptive sampling is performed in two stages. In the first stage, it attempts to locate the feasible region boundaries that are defined by the black-box constraints. Then, in the second stage, the focus is on searching for the feasible optimum subject to the feasibility characterized in the first stage. The algorithm is suitable for black-box noisy simulations, and its performance is demonstrated with a case study on continuous pharmaceutical manufacturing process.
 Ierapetritou M, Muzzio F, Reklaitis G. Perspectives on the continuous manufacturing of powder-based pharmaceutical processes[J]. AIChE Journal, 2016, 62(6): 1846-1862.
 Lee S L, OâConnor T F, Yang X, et al. Modernizing pharmaceutical manufacturing: from batch to continuous production[J]. Journal of Pharmaceutical Innovation, 2015, 10(3): 191-199.
 OâConnor T F, Lawrence X Y, Lee S L. Emerging technology: A key enabler for modernizing pharmaceutical manufacturing and advancing product quality[J]. International journal of pharmaceutics, 2016, 509(1): 492-498.
 Wang Z, Escotet-Espinoza M S, Ierapetritou M. Process analysis and optimization of continuous pharmaceutical manufacturing using flowsheet models[J]. Computers & Chemical Engineering, 2017. (in press)
 Engisch W E, Muzzio F J. Method for characterization of loss-in-weight feeder equipment[J]. Powder technology, 2012, 228: 395-403.
 Ankenman B, Nelson B L, Staum J. Stochastic kriging for simulation metamodeling[J]. Operations research, 2010, 58(2): 371-382.