## 2 Method Description
### The Second Phase of the Proposed Method
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & \(N_{g}=25\) & \(N_{g}=50\) & \(N_{g}=100\) & \(N_{g}=200\) \\ \hline Abalone & 6.08 & 5.74 & 5.65 & 5.10 \\ \hline Airfoil & 0.004 & 0.004 & 0.004 & 0.004 \\ \hline Auto & 10.37 & 9.71 & 9.60 & 9.68 \\ \hline Baseball & 89.23 & 90.91 & 81.42 & 86.19 \\ \hline BK & 0.028 & 0.032 & 0.10 & 0.153 \\ \hline BL & 0.001 & 0.0003 & 0.0006 & 0.0002 \\ \hline Concrete & 0.007 & 0.007 & 0.006 & 0.006 \\ \hline Dee & 0.16 & 0.16 & 0.17 & 0.16 \\ \hline Housing & 17.72 & 18.00 & 18.23 & 18.70 \\ \hline Friedman & 3.22 & 2.41 & 1.81 & 1.45 \\ \hline FA & 0.025 & 0.051 & 0.05 & 0.019 \\ \hline FY & 0.078 & 0.29 & 0.17 & 0.077 \\ \hline HO & 0.009 & 0.009 & 0.009 & 0.01 \\ \hline Laser & 0.004 & 0.003 & 0.003 & 0.003 \\ \hline MB & 0.15 & 0.37 & 0.27 & 5.49 \\ \hline Mortgage & 0.29 & 0.23 & 0.48 & 0.14 \\ \hline NT & 0.006 & 0.006 & 0.007 & 0.007 \\ \hline PL & 0.02 & 0.018 & 0.016 & 0.023 \\ \hline Plastic & 2.33 & 2.32 & 2.22 & 2.29 \\ \hline PY & 0.02 & 0.018 & 0.016 & 0.019 \\ \hline Quake & 0.036 & 0.036 & 0.036 & 0.036 \\ \hline SN & 0.026 & 0.025 & 0.025 & 0.024 \\ \hline Stock & 2.29 & 1.96 & 1.98 & 1.53 \\ \hline Treasury & 0.82 & 0.75 & 0.75 & 0.51 \\ \hline
**Average** & **5.54** & **5.55** & **5.13** & **5.48** \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Experimental results using the proposed method and a series of numbers of generations for the regression datasets. Similar reductions are observed on \"Stock\" (2.29 to 1.53) and \"Treasury\" (0.82 to 0.51). However, there are datasets such as \"Auto\", where the reduction is negligible, and the error slightly increases from 9.60 at \(N_{g}=100\) to 9.68 at \(N_{g}=200\). Furthermore, on the \"Housing\" dataset, a gradual increase in error is observed, from 17.72 to 18.70, suggesting that the increased number of generations did not improve performance. On the \"MB\" dataset, the error rises significantly, from 0.15 at \(N_{g}=25\) to 5.49 at \(N_{g}=200\), indicating potential instability of the method on this specific dataset. The average across all datasets shows a nonlinear pattern, with values fluctuating. The average error decreases from 5.54 at \(N_{g}=25\) to 5.13 at \(N_{g}=100\), but then increases to 5.48 at \(N-=200\). This indicates that increasing the number of generations does not always lead to consistent improvement in performance across regression datasets. In conclusion, the statistical analysis reveals that increasing the number of generations \(N_{g}\) can improve the performance of the genetic algorithm on certain datasets; however, its impact is not always consistent. The outcome depends on the specific characteristics of each dataset as well as the inherent properties of the method. Figure 13 pertains to the regression datasets and shows that the performance differences between consecutive \(N_{g}\) values are not statistically significant. Specifically, for \(N_{g}=25\) versus \(N_{g}=50\), p is 0.46, for \(N_{g}=50\) versus \(N_{g}=100\), p is 0.27, and for \(N_{g}=100\) versus \(N_{g}=200\), p is 0.9. These results suggest that increasing the number of generations in regression datasets does not lead to significant performance changes, indicating that the characteristics of these datasets may limit the effectiveness of the approach. Figure 12: Statistical comparison of the experimental results by the application of the proposed method with different values for the number of generations \(N_{g}\). The method was applied on the classification datasets. ## 4 Conclusions

The article focuses on optimizing the parameter tuning process in radial basis function networks through a multidimensional and innovative approach that combines techniques such as Simulated Annealing and genetic algorithms. The proposed method surpasses traditional two-stage approaches, where parameters are typically determined using fixed processes like K-means clustering followed by a split between training and validation phases. Instead, the article introduces a three-phase process.