## 1 Introduction
The results showed good performance in the constraint optimization of H\({}_{2}\) separation [23]. ANNs have the advantage of not requiring previously specified appropriate fitting functions and the capability for universal approximation, enabling them to closely approximate a wide range of nonlinear functions, such as quadratic functions. Nonetheless, ANNs have certain limitations, as they are unable to ensure globally optimal solutions. To overcome this limitation, researchers have explored integrating ANNs with other techniques to enhance performance. [PERSON] and [PERSON] [24] implemented a hybrid method for heat pipes, using Bayesian techniques and GAs to refine the structure of ANN models and identify the optimal operating point. The findings indicated that the introduced model was capable of decreasing operational and maintenance expenses. Numerous studies have shown that optimizing ANN models through the application of heuristic approaches (like genetic algorithms) and statistical methods (like Bayesian techniques) can elevate the accuracy and precision of their predictions. However, the computational process of ANNs operates as a \"black box\", rendering the observation of intermediate results unfeasible. Given the constraints associated with RSM and ANN methods, this work introduces a novel approach. In this work, a frequently utilized ANN model, known as the back propagation neural network (BPNN), was selected. Subsequently, a BPNN structure, optimized through the use of a GA (referred to as BPNN-GA), was designed for the PSA process. Furthermore, a novel optimization model was developed, which integrates the BBD with BPNN-GA (termed BBD-BPNN-GA), to further enhance the hydrogen purification performance of the PSA process. In this work, a dynamic adsorption model was established using Aspen Adsorption software (version V9). The adsorption column was packed with a blend of activated carbon and zeolite 5A as adsorbent. A mixture gas as used: H\({}_{2}\): 56.4 mol%, CH\({}_{4}\): 26.6 mol%, CO: 8.4 mol%, N\({}_{2}\): 5.5 mol%, CO\({}_{2}\): 0.1 mol%. The breakthrough curves were validated against experimental data sourced from reference [25]. To ascertain the ideal operating conditions for purification performance, a six-step PSA cycle model was implemented. Quadratic regression equations between purification performance indicators--namely, hydrogen purity and productivity--and operating parameters were established using the BBD method. However, due to the complex, nonlinear nature of the system, the desired prediction accuracy could not always be achieved solely with the BBD quadratic polynomial in limiting cases. The primary objective of this work was to identify the optimal neural network architecture based on the BPNN-GA model. The secondary objective was to compare different approaches for optimizing operating conditions. Experimental data generated from the BBD were integrated with the BPNN-GA to form the BBD-BPNN-GA model, which was used for predicting and optimizing the PSA process. In this work, the optimization of purification conditions was conducted using both the BPNN-GA model and the integrated BBD-BPNN-GA model.