# A Sea Horse Optimization-Based Approach for PEM Fuel Cell Model Parameter Estimation
## 5 Discussion  
In this study, the SHO algorithm is applied for the first time to determine the PEMFC model parameters. Unlike techniques such as genetic algorithms, particle swarm optimization (PSO), and genetic algorithms (GAs), which are frequently used in the literature, the multi-stage exploration-exploitation strategy of SHO, based on seahorse behaviors, provides more flexible and balanced navigation in the solution space. While the spiral and Brownian motion-based search mechanisms allow for extensive exploration in the early iterations, hunting and reproductive behaviors prevent the model from getting stuck in local minima. Parametric analyses demonstrate in detail how the parametric changes of the SHO algorithm affect these situations. The parametric analyses revealed that control parameters such as \(\lambda\), \(l\), \(\beta_{t}\), \(r_{1}\), and \(r_{2}\) used in the SHO algorithm are not only technical settings but also play a decisive role in the algorithm's exploration-exploitation balance, convergence time, and solution quality. Figure 4: Simulation graphic results. (**a**) Comparison of model and experimental data. (**b**) Convergence curve. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Limit Range** & **RMSE** & **Best SSE** \\ \hline Literature values in Table 7 & 0.001322 & 0.00001 \\
10\% Narrowed & 0.002709 & 0.000044 \\
10\% Expanded & 0.002629 & 0.000041 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Boundary limits for unknown parameters in PEMFC model. It was observed that \(\lambda=1.5\), \(l=0.05\), and \(\beta_{l}=0.8\) values enable SHO to perform extensive searches and find solutions with high accuracy. Furthermore, the choice of \(r_{1}\) and \(r_{2}\) distribution fundamentally affects the algorithm's behavior, as it determines whether individuals exhibit spiral or Brownian movements, or it affects the exploration-exploitation balance. These findings demonstrate that conducting a preliminary analysis of the SHO algorithm at the parameter level before applying it to different problem types is critical to its performance. This study contributes to the literature by clearly demonstrating how the structural flexibility of SHO can be optimized with correct parameter selections. The modeling process yielded a Mean Absolute Error (MAE) of 0.001079 and a coefficient of determination \(R^{2}\) of 0.999791, which indicates a satisfactory level of accuracy. Furthermore, the developed model, using the optimal parameter set, demonstrated a 99.92% agreement with experimental data, underscoring the high-resolution optimization capability of the SHO algorithm. With an average convergence time of only 1.74 s, SHO exhibits low computational demand, suggesting its suitability for real-time applications. This renders it particularly promising for embedded systems or time-sensitive applications, such as in automotive systems or portable fuel cell devices. As seen in Table 9, the use of Brownian motion and Levy flights in SHO leads to a unique balance between exhaustive local search and long-distance exploratory leaps. This structure allows the algorithm to escape local optima more effectively than traditional metaheuristics that lack such movement diversity. SHO's hybrid structure, which includes Brownian motion and Levy flights, appears to provide a natural balance between exploration and convergence without the need for parameter tuning. This structure provides strong resistance to avoiding local minima while also supporting the algorithm's convergence stability. While algorithms such as GWO or PSO are typically based on fixed leadership or social components, direction updates in SHO occur stochastically and adaptively. This structure is one of the main reasons for SHO's high performance in complex solution spaces. The resulting improvement in convergence stability and solution quality is supported both theoretically and experimentally in the presented results.