## 2 Method Description
### The Second Phase of the Proposed Method
In the first phase, initial parameter estimation is performed using K-means, ensuring a stable starting point. In the second phase, the application of Simulated Annealing provides an advanced mechanism for exploring the parameter space, avoiding local minima and examining a broader range of potential values. Finally, the third phase integrates genetic algorithms, enabling the optimization of parameters based on the model's actual performance. This process ensures a comprehensive and adaptive approach, reducing the likelihood of overfitting and numerical instability. The novelty of the method lies not only in the three-phase process but also in the model's ability to adapt to datasets with diverse characteristics, such as those involving complex nonlinear relationships or multidimensional dependencies. The experimental results demonstrate the method's superiority compared to traditional techniques, such as BFGS, ADAM, NEAT, and RBF-KMEANS, achieving improvements in terms of average error rates across both classification and regression datasets. The article's conclusions clearly highlight the superiority of the proposed method. In classification datasets, the method achieves lower average error rates, particularly when the parameters \(a\) and \(F\) are optimally configured. For instance, in classification datasets, the parameter \(F\) significantly influences performance, with \(F=5.0\) proving to be the most effective value in many cases. On datasets such as \"Ionosphere\" and \"Wine\", dramatic reductions in error rates are observed as the value of \(F\) increases, emphasizing the importance of selecting this parameter correctly. Similarly, on the regression datasets, the proposed model demonstrates exceptional performance, with notable examples including datasets like \"Abalone\" and \"Friedman\", where the error decreases significantly compared to tra

Figure 13: Statistical comparison of the experimental results by the application of the proposed method for different values of the number of generations \(N_{S}\). The method was applied on the regression datasets. The ns symbol denotes \(p>0.05\) (Not significant) and the symbol * stands for \(p<0.05\) (significant). ditional techniques. The \"MB\" dataset is particularly interesting, as the use of Simulated Annealing contributes to a substantial performance improvement, avoiding errors commonly encountered in traditional approaches. Despite the generally positive results, there are cases where the method's performance is suboptimal, such as on the \"Segment\" dataset, indicating that the method is not universally generalizable without adjustment to the characteristics of each dataset. The need for further research on the parameters \(a\) and \(F\) is evident, as these parameters critically impact performance across numerous datasets. For the future, the article proposes numerous directions for further exploration and development. Initially, applying the method to more diverse data categories, such as time series, image data, or even genetic data, could broaden its application scope. Additionally, the dynamic adjustment of the parameters \(a\) and \(F\) during training, using reinforcement learning techniques, could further enhance performance by eliminating the need for manual tuning. Furthermore, integrating the method into deep learning systems, such as convolutional or recurrent neural networks, could lead to hybrid approaches that combine the flexibility of RBFs with the computational power of deep neural networks. Moreover, investigating the robustness of the method in environments with dynamic or imbalanced data could provide additional insights into its generalizability. Finally, analyzing the method's performance on big data and integrating it with technologies like distributed processing or cloud computing could open new avenues, enabling its scalability to larger-scale problems. The methodology proposed in the article not only sets new standards for the performance of RBFs but also paves the way for further innovation in the field of machine learning.