A Bayesian optimization approach for stochastic data-driven Petlyuk distillation columns design

In recent years, the drive to enhance process efficiency and reduce energy consumption has spurred interest in alternative systems, such as Petlyuk distillation columns. These systems have been demonstrated to achieve significant energy and cost savings compared to conventional distillation columns. Consequently, from an economic standpoint, the feasibility of a process is not solely defined by achieving high-purity products. Instead, achieving a balance between product purity and cost requires a multi-objective optimization approach. While traditional optimization methods are effective, emerging strategies such as Bayesian optimization offer distinct advantages for handling complex systems without requiring explicit mathematical models. Bayesian optimization can effectively handle the optimization process even when starting from a single initial point. However, as a black-box method, it demands careful examination of the impact of hyperparameters on the optimization process. This study explores two Petlyuk distillation columns as case studies, introducing a bi-level strategy for hyperparameter selection, including the acquisition function, kernel type, and the number of initial points. Furthermore, the influence of uncertainty in the Bayesian optimization process is explored, as this factor is critical in addressing real-world challenges. To simulate such conditions, the study incorporates scenarios designed to mimic the effects of uncertainty, providing valuable insights into its role in optimization outcomes.