A comparative evaluation of metaphor-free optimization algorithms for PEMFC parameter identification

Accurate parameter identification of Proton Exchange Membrane Fuel Cell (PEMFC) models is essential for reliable simulation, performance prediction, and model-based applications. This study evaluates eight metaphor-free optimizers — JAYA, EJAYA, Rao-1, Rao-2, Rao-3, FISA, FNO, and BCR — for calibrating a seven-parameter semi-empirical model across five commercial PEMFC stacks. Each algorithm was run 30 times under a common computational protocol using the sum of squared errors (SSE) as the objective function. Performance was assessed using descriptive statistics, Friedman ranks, Wilcoxon signed-rank tests, convergence behavior, and complementary fitting metrics. EJAYA achieved the lowest mean Friedman rank, followed by BCR and FISA, and significantly outperformed the other seven algorithms across all five stacks. Ablation analysis showed that the complete EJAYA formulation yielded the lowest mean SSE in every case. A broader benchmark with 20 additional metaheuristics supported the competitiveness of EJAYA, BCR, and FISA. Expanding the literature-based parameter ranges reduced the best SSE by up to 42.25% for some stacks but produced marginal changes for others. Distinct parameter vectors also produced identical or nearly identical fitting errors, indicating parameter compensation and possible non-uniqueness. These findings emphasize the importance of considering fitting accuracy, run-to-run consistency, parameter bounds, and identifiability in PEMFC model calibration.