A multi-objective synergistic optimization framework for gas distribution quality and output performance in proton exchange membrane fuel cells

Proton exchange membrane fuel cells (PEMFCs) are promising electrochemical energy conversion devices for hydrogen-based power generation. However, their output performance and internal oxygen distribution are highly sensitive to operating conditions, making it challenging to simultaneously maintain electrochemical output, oxygen supply sufficiency, and gas distribution uniformity. To address this issue, this paper proposes a synergistic optimization framework that integrates interpretable machine learning, surrogate modeling, and multi-objective optimization. First, a Random-Forest-based local interpretable model is developed to quantify the effects of operating parameters on key performance indicators and to identify the decision variables for subsequent optimization. Then, the mean oxygen concentration in the catalyst layer, the oxygen concentration standard deviation, and the output current density are selected as optimization objectives to represent oxygen supply sufficiency, oxygen distribution uniformity, and electrochemical output capability, respectively. An iTransformer-inspired variable-token regression model is further constructed to characterize the nonlinear mapping between operating parameters and performance responses, thereby reducing the computational cost of repeated multiphysics simulations. Based on 2,000 samples, the proposed surrogate achieves the lowest mean normalized RMSE of 0.2920±0.0105% over 10 repeated data partitions among the six compared surrogate models. The three-dimensional multiphysics model is further validated against experimental polarization measurements under the baseline operating condition, achieving an R2 of 0.9939 and an RMSE of 0.0106 V. Quantitative comparisons based on hypervolume, inverted generational distance, and spacing support the use of NSGA-II for Pareto search. Entropy-weighted LINMAP is subsequently employed to identify one load-dependent preferred compromise operating condition at each prescribed voltage. Three-dimensional back-calculation shows that the maximum surrogate-to-model deviations for the three optimization objectives remain below 1.11%. The results demonstrate that the proposed framework provides an effective approach for coordinating oxygen supply, gas-distribution uniformity, and electrochemical output under different PEMFC operating conditions.