Innovative Diversity Metrics in Hierarchical Population-Based Differential Evolution for PEM Fuel Cell Parameter Optimization

The optimization of parameters in proton exchange membrane fuel cell (PEMFC) models is essential for enhancing the design and control of fuel cells and is currently a vibrant area of research. This involves a complex, nonlinear, and multivariable numerical optimization challenge. Recently, various metaheuristic approaches have been applied to efficiently identify optimal configurations for PEMFC models, capable of exploring a broad search space to locate ideal solutions promptly. In this study, the recently developed hierarchical population-based differential evolution (HPDE) was employed for parameter optimization of PEMFCs due to its robustness and demonstrated superiority over other optimization algorithms. This research tested the proposed optimization algorithm by identifying parameters for 12 distinct PEMFCs, including BCS 500 W PEMFC, Nedstack 600 W PS6 PEMFC, SR-12500 W PEMFC, H-12 PEMFC, STD 250 W PEMFC, and HORIZON 500 W PEMFC, four variants of 250 W PEMFC, and two variants of H-12 12 W PEMFC. The performance of HPDE was also benchmarked against other advanced evolutionary algorithms (EAs), such as E-QUATRE, iLSHADE, CRADE, L-SHADE, jSO, HARD-DE, LSHADE-cnEpSin, DE, and PCM-DE. Despite its simplicity, the results reveal that HPDE can precisely and swiftly extract the parameters of PEMFC models. Furthermore, the voltage-current (V-I), power-current (P-I), and error characteristics derived from the HPDE algorithm consistently align with both simulated and experimental data across all seven models of PEMFCs. Additionally, HPDE has shown to outperform various versions of DE algorithms, providing superior results.