  This study presents a methodology for surrogate optimization of cyclic
adsorption processes, focusing on enhancing Pressure Swing Adsorption units for
carbon dioxide ($CO_{2}$) capture. We developed and implemented a
multiple-input, single-output (MISO) framework comprising two deep neural
network (DNN) models, predicting key process performance indicators. These
models were then integrated into an optimization framework, leveraging particle
swarm optimization (PSO) and statistical analysis to generate a comprehensive
Pareto front representation. This approach delineated feasible operational
regions (FORs) and highlighted the spectrum of optimal decision-making
scenarios. A key aspect of our methodology was the evaluation of optimization
effectiveness. This was accomplished by testing decision variables derived from
the Pareto front against a phenomenological model, affirming the surrogate
models reliability. Subsequently, the study delved into analyzing the feasible
operational domains of these decision variables. A detailed correlation map was
constructed to elucidate the interplay between these variables, thereby
uncovering the most impactful factors influencing process behavior. The study
offers a practical, insightful operational map that aids operators in
pinpointing the optimal process location and prioritizing specific operational
goals.
