Hybrid metaheuristic optimization for accurate PEM fuel cell parameter estimation: combining Grey Wolf Optimizer and Harris Hawks Optimization

Abstract Accurate parameter identification is essential for predictive proton-exchange membrane fuel-cell (PEMFC) modelling, yet it remains challenging because commonly used semi-empirical formulations are strongly nonlinear and exhibit pronounced parameter coupling. This paper focuses on the optimisation engine rather than proposing a new PEMFC model. We introduce a sequential hybrid metaheuristic that combines the leader-guided exploration of the Grey Wolf Optimizer (GWO) with the adaptive exploitation mechanisms of Harris Hawks Optimization (HHO). The resulting method, denoted GWO–HHO, estimates the key parameters of a standard single-cell/stack model by minimising the sum of squared errors (SSE) between measured and simulated stack voltages. A unified identification protocol is applied to three public PEMFC benchmarks (Horizon 500 W, BCS 500 W, and Nedstack PS6), as well as to a suite of standard unimodal and multimodal test functions used to stress the optimiser itself. On the fuel-cell datasets, the proposed hybrid achieves SSE values of 0.0110, 0.0116, and 2.0655, respectively, and exhibits smooth convergence with low variance across repeated runs. Compared with several recent optimisers under the same computational budget, GWO–HHO delivers competitive accuracy and robust behaviour across datasets. The method therefore provides a practical optimisation tool for reliable PEMFC parameter estimation using established physics-based models.