## 5 Results
### Model Fitting Results Obtained by the Optimization Methods  
We analyzed the performance of the optimization methods in fitting the model by comparing results obtained by GBA, GA, and HOM. The model exhibited a strong fit to experimental data for all the optimization methods, with HOM showing the overall best fit at both 0.5 and 2.0 m/s\({}^{2}\) rms (Figures 8 and 9). Furthermore, we established goodness of fit criteria, \(\varepsilon\) as suggested by [PERSON] [32], to quantitatively evaluate the model-fitting results:  
\[\varepsilon=1-\left(\sqrt{\sum\frac{\left(T_{Exp.}-T_{Model}\right)^{2}}{N-2}} /\sum\frac{T_{Exp.}}{N}\right), \tag{26}\]  
where \(N\) is the number of experimental data points used in the goodness of fit comparison. A value of \(\varepsilon\) close to 1 indicates a good fit, with values over 80% considered an acceptable tolerance of error for analysis. As shown in Tables 3 and 4, an average of 94% and 95% was obtained at forcing amplitude of 0.5 and 2.0 m/s\({}^{2}\) rms for all the optimization methods. The HOM achieved the highest \(\varepsilon\) value, signifying the best fit among the three optimization methods.  
Figure 8: Model fitting results obtained by GBA, GA, and HOM at 0.5 m/s\({}^{2}\) rms forcing amplitude.  
The performance of the optimization methods was also evaluated based on the objective function value at the final solutions, _FVAL_. Figure 10 demonstrates that when comparing the individual use of GBA or GA to the proposed method, HOM consistently achieved the lowest objective function value for all body segments. Moreover, by incorporating the GBA-optimized values in the MGA step, the computation process was expedited. The initial objective function value of approximately 0.400 rapidly decreased to a minimum of 0.0145 within the first 10 generations, as shown in Figure 11. Typically, the objective function values improve rapidly in initial generations and then level off as the optimal value is approached [28]. Detailed _FVAL_ results for GBA, GA, and HOM for each body segment are presented in Tables 5 and 6.  
Furthermore, the computation time of HOM is significantly reduced compared to using GBA and GA separately. Specifically, the computation time of GBA and GA steps in the HOM process is over five times reduced for GBA and about 30% for GA, as shown in Tables 7 and 8. However, the combined time of HOM is still nearly the same as that of GA and a bit more than GBA.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Head (\%)** & **Trunk (\%)** & **Thigh (\%)** & **Leg (\%)** & **Average (\%)** \\ \hline GBA & 90.5 & 91.4 & 90.7 & 92.9 & 91.4 \\ GA & 99.9 & 99.5 & 93.4 & 94.2 & 96.7 \\ HOM & 99.5 & 98.9 & 98.7 & 95.9 & 98.2 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Goodness of fit at 2.0 m/s\({}^{2}\) rms.  
Figure 9: Model fitting results obtained by GBA, GA, and HOM at 2.0 m/s\({}^{2}\) rms forcing amplitude.  
Figure 11: Target and mean value of _FVAL_ by mGA with respect to the generations of evolution in the HOM process.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**HOM Steps** & \multicolumn{3}{c}{**Objective Function Value, _FVAL_**} \\ \hline  & Head & Trunk & Thigh & Leg \\ \hline GA step & 0.0328 & 0.0333 & 0.0394 & 0.0348 \\ \hline GBA step & 0.0227 & 0.0293 & 0.0263 & 0.0301 \\ \hline MGA step & 0.0145 & 0.0175 & 0.0145 & 0.0181 \\ \hline \hline \end{tabular}
\end{table}
Table 6: _FVAL_ obtained for the combined HOM steps.  
Figure 10: Comparison of the objective function values by optimization methods.  
Overall, the optimization methods performed well in fitting the model, with HOM being the most effective. The use of HOM also produced lower objective function values and faster computation time, which significantly improved the optimization process.