# A Sea Horse Optimization-Based Approach for PEM Fuel Cell Model Parameter Estimation
## 4 Simulation Study and Results  
### Parametric Analysis of SHO  
The Sea Horse Optimization (SHO) algorithm is an metaheuristic optimization method inspired by the natural swimming behavior of seahorses and models the exploration-exploitation balance based on biological movements. In this algorithm, the solution search process is guided by two fundamental behavior mechanisms: Levy flight and Brownian motion. Both behavior types are controlled by different parameters, and the selection of these parameters directly impacts the overall performance of the algorithm. In this study, to more clearly demonstrate the effects of the SHO algorithm on convergence behavior and solution accuracy, the lambda (\(\lambda\)) for Levy flight, the Brownian motion step coefficient (\(l\)), the random step size (\(\beta_{1}\)), and the deciding parameter \(r_{1}\) and \(r_{2}\) are analyzed in detail. Sensitivity analyses conducted for each parameter separately provide comprehensive insights into the search performance of SHO. In the Sea Horse Optimization (SHO) algorithm, when mathematically modeling the natural motion behavior of seahorses, Levy flight stands out  
Figure 3: Flowchart of the SHO algorithm. as a particularly important exploration mechanism. This movement pattern allows the algorithm to scan the solution space more broadly and directionally, increasing its ability to avoid local minima. The characteristics of Levy flight are determined by a parameter called \(\lambda\). In this study, a parametric analysis for \(\lambda\) is conducted to examine the effect on the solution accuracy and convergence time of the SHO algorithm. The \(\lambda\) parameter is generally defined between 0 and 2. The \(\lambda\) value used in analysis is determined between 0.5 and 1.9, and the SSE (sum of squared error), convergence time, and \(R^{2}\) (coefficient of determination) corresponding to each value are summarized in Table 2:  
The results show that a value of \(\lambda=1.5\) provides the most balanced results in terms of both solution accuracy and convergence time. A value of \(\lambda=0.5\) limited both exploration and exploitation capabilities due to excessively short jumps. \(\lambda=1.1\) and 1.3 also produced successful results, but the solution quality was slightly lower than 1.5. On the other hand, \(\lambda=1.7\) and 1.9 caused the algorithm to perform more exploration, which increased the convergence time and decreased the solution quality. Experimental analysis of the 1 parameter, which controls the step length of Brownian motion in the SHO algorithm, reveals that the algorithm's convergence behavior is highly sensitive to this parameter. A value of 1 = 0.05 provided optimal performance with both the lowest error value and the highest agreement coefficient; larger values of 1 were observed to increase exploration capability but delay convergence. These findings are given in Table 3.  
The effect of the \(\beta_{t}\) coefficient--which is included in the Brownian motion of the Sea Horse Optimization (SHO) algorithm and governs the jump behavior in the solution space--on the algorithm's performance is analyzed. The \(\beta_{t}\) parameter directly determines the exploration capacity by affecting the direction and amplitude of the solution and plays a significant role in the convergence process. In the experimental evaluation, the algorithm was run under the same initial conditions using different \(\beta_{t}\) values (0.2, 0.5, 0.8, 1.0, 1.2), and the results were evaluated based on three key metrics (SSE, time, \(R^{2}\)). The lowest SSE = 0.000012 and the highest \(R^{2}\) = 0.999733 were obtained with a value of \(\beta_{t}=0.8\)