## 3 Methodology
### Marine Predators Algorithm (MPA)  
To achieve the efficient and precise optimization of the XGBoost algorithm's parameters, this study utilized the Marine Predators Algorithm (MPA) [32]. Proposed by [PERSON] et al. in 2020 [33], MPA draws inspiration from the foraging behavior of marine predators. Specifically, the algorithm incorporates the Levy flight and Brownian motion patterns observed in marine predators. Levy flight is characterized by occasional long-distance jumps and frequent short-distance movements, enabling predators to search for prey efficiently in vast ocean environments. Brownian motion reflects the random displace \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Parameter Description** & **Data Range** \\ \hline \multirow{4}{*}{num\_trees} & This parameter plays a crucial role in assessing the model’s predictive performance. & \multirow{4}{*}{[1, 1000]} \\  & Generally, a higher value enhances learning and data processing capabilities, resulting in & \\  & more accurate predictions. However, an excessively high value may lead to the inefficient & \\  & utilization of computational resources, thereby diminishing overall efficiency. & \\  & This parameter, which specifies the maximum depth of the decision tree, plays a critical & \\  & role in controlling overfitting. Although larger values allow the model to capture more & \\  & complex patterns and improve training performance, they also increase the risk of & \\  & overfitting, thereby compromising the model’s ability to generalize to new data. & \\  & This parameter determines the step size for each iteration and plays a pivotal role in & \\  & influencing algorithm performance. Setting the value too high may degrade the & \\ eta & algorithm’s precision, while an excessively low value will significantly prolong execution & \\  & time. Both scenarios can adversely affect the algorithm’s overall effectiveness, thereby & \\  & highlighting the importance of carefully adjusting this parameter to achieve an & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: XGBoost calculation parameters. ment of particles in fluids, simulating the unpredictable movement of prey. Furthermore, MPA simulates the optimal encounter rate strategy between predators and prey, where predators adjust their behaviors to maximize encounter probability while minimizing energy expenditure [34]. This study demonstrates the application of MPA, offering novel insights into optimizing XGBoost parameters. The optimization process of the MPA comprises three key stages, as shown in Figure 4. In each specified stage, a corresponding number of iteration cycles is assigned. These steps are determined according to the rules governing predator-prey movements and mimic the behavioral patterns of predators and prey in natural ecosystems. (1) In the beginning, akin to most meta-heuristic algorithms, the MPA randomly determines the initial positions of the prey within the search space to start the optimization procedure. The mathematical representation is as follows:  
\[X_{0}\ =\ X_{min}\ +\ rand(X_{max}\ -\ X_{min}\ ) \tag{3}\]  
where \(X_{\max}\) and \(X_{\min}\) denote the upper and lower bounds of the search space, respectively, while rand () represents a random number generated within the interval [0, 1]. (2) During the initial stages of the iteration, the speed of the predator exceeds that of the prey. Consequently, the MPA employs an exploration strategy, which is mathematically formulated as follows:  
\[\left\{ \begin{array}{l}stepsize_{i}\ =\ R_{B}\otimes(Elite_{i}\ -\ R_{B}\otimes Prey_{i}\ )\\ Prey_{i}\ =\ Prey_{i}\ +0.5\times R\otimes stepsize_{i}\end{array} \right.\ \ \ \ i=1,2,3....,n.\ Iter<\frac{Max\_Iter}{3} \tag{4}\]  
where \(stepsize_{i}\) represents the step length of movement; \(R_{B}\) is a random vector of Brownian motion distributed normally; \(Elite_{i}\) is an elite matrix constructed by the top predator; \(Prey_{i}\) is a matrix of the same dimension as the elite matrix; \(R\) is a uniformly random vector within  
Figure 4: Principle of MPA.