## 3 Materials and Methods
### Hyperparameter Optimization: GWO  
Every model consists of various parameters which define the accuracy and performance of the model. These parameters can be varied to obtain better results for any particular model. There are a lot of optimization techniques that optimize the hyperparameters of the classifier. In our work, we have used a swarm intelligence-based gray wolf optimization (GWO) model to tune the hyperparameters. This meta-heuristic algorithm is used in our work to optimize the hyperparameters of XGB. GWO represents the social hierarchy of wolves and their approach to attacking and encircling their prey while maintaining \begin{table}
\begin{tabular}{c c c} \hline \hline
**Hyperparameter** & **Value (TRSP)** & **Value Range** \\ \hline learning\_rate & 8.64 \(\times\) 10\({}^{-2}\) & (1.5 \(\times\) 10\({}^{-15}\)–0.9) \\ \hline gamma & 3.13 \(\times\) 10\({}^{-2}\) & (1 \(\times\) 10\({}^{-9}\)–1.0) \\ \hline colsample\_bytes & 1.06 \(\times\) 10\({}^{-1}\) & (0.001–1.00) \\ \hline max\_depth & 8.31 \(\times\) 10\({}^{1}\) & (1–200) \\ \hline min\_child\_weight & 1.12 \(\times\) 10\({}^{0}\) & (1–200) \\ \hline subsample & 5.95 \(\times\) 10\({}^{-1}\) & (1–200) \\ \hline alpha & 5.78\(\times\) 10\({}^{-6}\) & (1 \(\times\) 10\({}^{-6}\)–1.0) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The hyperparameters and their values for the TRSP dataset. nature-inspired categorization. Canis Lupus is known as gray wolves who are the topmost hunters in the food chain. Depending on the hunting approach and decision-making power, wolves are categorized as alpha (\(\alpha\)), beta (\(\beta\)), delta (\(\delta\)), and omega (\(\omega\)) [11]. The most dominant and leading wolves are the alpha ones and other wolves follow their instructions. Beta wolves are advisors who help the other wolves to support the commands as well as the feedback suggestions. Delta wolves are the predators or guards, and the omega wolves are from the lowest hierarchy [18]. In our TRSP dataset, this optimization technique is applied where the statistical structure of the model is based on the hunting behavior of the wolves. The hunting mechanism has three steps: tracking the prey, encircling it, and attacking. Alpha wolves are the best solutions, and beta as well as delta wolves are next. In our work, GWO is applied to find out the best hyperparameter values. In this study, we have used accuracy as the objective function for the optimization task. The mathematical derivation for the objective function is as follows:  
\[\text{Objective Function, }F_{obj}=1-[\text{Accuracy\_score}]\]  
Here, the accuracy score (A) of the XGB classifier can be represented as  
\[\text{Accuracy score}=1-\bigg{(}\frac{\text{{Misclassified samples}}}{ \text{{total number of samples}}}\bigg{)} \tag{8}\]  
* ROC Curve  
The receiver operating characteristic (ROC) curve visually depicts the performance of a binary classification system as the decision threshold changes. It is created by plotting the true positive rate (TPR) against the false positive Rate (FPR) for different threshold values. This curve illustrates the balance between the TPR and FPR for the classifier, allowing for an assessment of its performance. But here, we have used a multiclass ROC curve. A multiclass ROC curve is an extension of the traditional ROC curve that is used for binary classification problems to handle multiclass classification problems, where the target variable has more than two classes. In a multiclass classification problem, the ROC curve is computed for each class and the results are combined to obtain a single ROC curve. * Sensitivity and Specificity  
In ROC analysis, the sensitivity and specificity of a binary classifier are key metrics. Sensitivity, or the true positive rate (TPR), measures the proportion of correctly identified positive cases, while specificity, or the true negative rate, evaluates the proportion of correctly identified negative cases. The false positive rate (FPR) is calculated as one minus the specificity.