## 4 Model Training and Evaluation Methods
### Hyperparameter Optimization with GA  
In this section hyperparameter optimization using the GA will be performed for each ML model. In this study, the mutation rate, which is the probability of random changes in the genes of individuals, will be defined as 0.05, which means that 5% of individuals can change their parameters randomly. Also, the elitism rate is defined as 0.1, which means that 10% of the best individuals will be passed on to the next generation. The default parameters of all ML models that we will use in this section are given in Table 4. \begin{table}
\begin{tabular}{l l l} \hline \hline
**ML Models** & **Parameters and Their Ranges** & **ML Models** & **Parameters and Their Ranges** \\ \hline \multirow{7}{*}{DT} & criterion: squared\_error, friendman\_mse, & n\_estimators: 10 values in increments of 10 in the range [100, 1000] \\  & absolute\_error, poisson & & range [100, 1000] \\  & max\_depth: 10 values in increments of 1 in the range [1; 10] & & min\_samples\_leaf: 10 values in increments of \\  & max\_leaf\_nodes: 10 values in the range [2; 500] & & 10 in the range [2; 20] \\  & min\_samples\_leaf: 10 values in increments of 1 & & criterion: squared\_error, absolute\_error, \\  & in the range [1; 10] & & \multicolumn{1}{c}{} \\ \end{tabular}
\end{table} 
Table 4: Default parameters of the ML models. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**MetricsMLModels** & **DT** & **RF** & **K-NNs** & **AdaBoost** & **GBM** & **ETR** & **BR** & **SVR** & **HGBR** & **XGBoost** \\ \hline MBE & 0 & \(-\)0.0021 & \(-\)0.0154 & \(-\)0.0009 & \(-\)0.0011 & \(-\)0.0002 & \(-\)0.0022 & 0.0069 & \(-\)0.0017 & 0.0018 \\ \hline erMAX & 48.1298 & 45.2616 & 81.5312 & 58.4733 & 43.281 & 42.6166 & 40.3193 & 30.0223 & 41.4007 & 44.147 \\ \hline SD & 0.329 & 0.2428 & 0.2886 & 0.2613 & 0.2258 & 0.2466 & 0.2597 & 0.2031 & 0.2213 & 0.2398 \\ \hline t-stat & \(-\)0.0013 & \(-\)0.1935 & \(-\)1.1649 & \(-\)0.0759 & \(-\)0.1024 & \(-\)0.0189 & \(-\)0.1821 & 0.7483 & \(-\)0.1669 & 0.1657 \\ \hline U\({}_{95}\) & 0.0295 & 0.0217 & 0.0258 & 0.0234 & 0.0202 & 0.0221 & 0.0233 & 0.0182 & 0.0198 & 0.0215 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._When determining the hyperparameter ranges for the GA and grid search methods, a balanced approach was adopted to ensure adequate representation of the search space while keeping the computational cost reasonable. Instead of trying 800 combinations in K-NNs, hyperparameter optimization was performed with GA by taking the population number as 20 and the gene number as 10; 200 combinations were completed, and a 75% screening saving was achieved by this combination. In the AdaBoost model, instead of scanning 600 combinations, hyperparameter optimization was applied with GA by taking the population number as 20 and the gene number as 10; 150 combinations were tried, and a 75% screening saving was achieved by the combination. While a total of 4000 combinations were to be scanned in all other algorithms, hyperparameter optimization was applied with GA by taking the population number as 100 and the gene number as 10, and a 75% screening saving was achieved by scanning the 1000 combinations. The aim of this strategy is to increase the applicability of the methods by preserving the representativeness of the search space and to provide a consistent basis for comparative analysis. Some of these calculations are described in the following:  
GA-based hyperparameter optimization in the DT model started by restricting the search space to four different criteria values: squared_error, friedman_mse, absolute_error and poisson. The depth parameter was defined in ten equal steps in the range max_depth [1; 10], while the number of leaf nodes was divided into ten equal parts in the range max_leaf_nodes [2; 500]. Furthermore, the min_samples_leaf parameter, which determines the minimum number of samples that can be found in each leaf, is set to consist of ten possible values ranging from 1 to 10.