## 2 Method Description
### The Second Phase of the Proposed Method
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dataset** & **BFGS** & **ADAM** & **NEAT** &
\begin{tabular}{c} **RBF-** \\ **KMEANS** \\ \end{tabular} & **GENRBF** & **Proposed** \\ \hline Abalone & 5.69 & 4.30 & 9.88 & 7.37 & 9.98 & 5.10 \\ \hline Airfoil & 0.003 & 0.005 & 0.067 & 0.27 & 0.121 & 0.004 \\ \hline Auto & 60.97 & 70.84 & 56.06 & 17.87 & 16.78 & 9.68 \\ \hline Baseball & 119.63 & 77.90 & 100.39 & 93.02 & 98.91 & 86.19 \\ \hline BK & 0.28 & 0.03 & 0.15 & 0.02 & 0.023 & 0.153 \\ \hline BL & 2.55 & 0.28 & 0.05 & 0.013 & 0.005 & 0.0002 \\ \hline Concrete & 0.066 & 0.078 & 0.081 & 0.011 & 0.015 & 0.006 \\ \hline Dee & 2.36 & 0.630 & 1.512 & 0.17 & 0.25 & 0.16 \\ \hline Housing & 97.38 & 80.20 & 56.49 & 57.68 & 95.69 & 18.70 \\ \hline Friedman & 1.26 & 22.90 & 19.35 & 7.23 & 16.24 & 1.45 \\ \hline FA & 0.426 & 0.11 & 0.19 & 0.015 & 0.15 & 0.019 \\ \hline FY & 0.22 & 0.038 & 0.08 & 0.041 & 0.041 & 0.077 \\ \hline HO & 0.62 & 0.035 & 0.169 & 0.03 & 0.076 & 0.01 \\ \hline Laser & 0.015 & 0.03 & 0.084 & 0.03 & 0.075 & 0.003 \\ \hline MB & 0.129 & 0.06 & 0.061 & 2.16 & 0.41 & 5.49 \\ \hline Mortgage & 8.23 & 9.24 & 14.11 & 1.45 & 1.92 & 0.14 \\ \hline NT & 0.129 & 0.12 & 0.33 & 8.14 & 0.02 & 0.007 \\ \hline PL & 0.29 & 0.117 & 0.098 & 2.12 & 0.155 & 0.023 \\ \hline Plastic & 20.32 & 11.71 & 20.77 & 8.62 & 25.91 & 2.29 \\ \hline PY & 0.578 & 0.09 & 0.075 & 0.012 & 0.029 & 0.019 \\ \hline Quake & 0.42 & 0.06 & 0.298 & 0.07 & 0.79 & 0.036 \\ \hline SN & 0.40 & 0.026 & 0.174 & 0.027 & 0.027 & 0.024 \\ \hline Stock & 302.43 & 180.89 & 12.23 & 12.23 & 25.18 & 1.53 \\ \hline Treasury & 9.91 & 11.16 & 15.52 & 2.02 & 1.89 & 0.51 \\ \hline
**Average** & **26.43** & **19.62** & **12.84** & **9.19** & **12.28** & **5.48** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental results for regression datasets. Numbers in cells represent average regression error as calculated on the corresponding test set. Table 3 displays the absolute error values resulting from the application of the various machine learning models (BFGS, ADAM, NEAT, RBF-KMEANS, GENRBF, proposed) on the regression datasets. Each row corresponds to a dataset, while each column shows the error of a specific model. The last row records the average error for each model. Lower error values indicate better model performance. The analysis shows that the proposed model has the lowest average error (5.48), making it the most efficient choice among the available models. The second-best model is RBF-KMEANS, with an average error of 9.19, while other models, such as BFGS (26.43) and ADAM (19.62), exhibit significantly higher error values. The performance of the proposed model is particularly impressive on datasets such as BL, where its error is nearly negligible (0.0002), and Mortgage, where it has a very low error (0.14) compared to other models. On datasets like Stock and Plastic, where errors are high across all models, the proposed model still outperforms the other models, with error values of 1.53 and 2.29, respectively. However, there are instances where the performance difference of the proposed model relative to others is small or even unfavorable. For example, on the Laser dataset, the ADAM model has an error of 0.03, slightly higher than the proposed model's 0.003, while on the HO dataset, the proposed model performs better (0.01), but the RBF-KMEANS model is comparably close (0.03). In summary, the proposed model achieves the lowest average error and the most consistent performance across most datasets, making it an ideal choice for regression problems. Nonetheless, certain models, such as RBF-KMEANS, may demonstrate competitive performance in specific cases, suggesting that model selection depends on the unique characteristics of each dataset. An analysis of significance levels for the classification datasets, as illustrated in Figure 6, reveals that the proposed model statistically significantly outperforms all other models in every comparison pair.