## 2 System Model and Problem Formulation
### Proposed 6 DChOA  
The standard ChOA, while innovative in its approach to mimicking chimpanzee hunting behavior, faces certain drawbacks that limit its performance in more complex or high-dimensional problems. One of the primary weaknesses is its vulnerability to premature convergence, where the algorithm quickly settles on a solution that is not globally optimal. This issue is particularly problematic in multi-modal landscapes, where the algorithm can easily get trapped in local optima due to insufficient diversity in the search process. The roles of the attackers, barriers, chasers, and drivers, although well designed for coordinating the search, often fail to provide the necessary variation to explore the full search space effectively, especially during the later stages of the optimization. Another significant limitation of the standard ChOA is its imbalanced exploration and exploitation. The algorithm may either over-exploit certain promising regions of the search space, neglecting broader exploration, or over-explore without adequately refining the best solutions. This imbalance can result in slower convergence rates or even missed opportunities to find better solutions. Additionally, the deterministic nature of the movement strategies, particularly the lack of chaotic or random elements, reduces the algorithm's ability to escape from local optima once it has become trapped. These factors combined limit the adaptability and robustness of the ChOA when applied to more challenging optimization tasks, making it less competitive compared to other advanced metaheuristics [43]. To address these challenges, the improved version of the algorithm introduces two new roles: leader and ranger chimps. The leader chimp enhances exploitation by guiding the search more efficiently toward promising areas of the solution space, ensuring better convergence rates. Meanwhile, the ranger chimps introduces a chaotic and random search behavior, improving exploration by helping the algorithm escape local optima. The new dynamics improve the balance between exploration and exploitation, as the ranger adds randomness to avoid premature convergence, and the leader ensures convergence toward global optima. By including these two new roles, the enhanced 6 DChOA significantly improves its ability to handle more complex and multi-modal problems, thus outperforming the standard ChOA. In the improved 6 DChOA, Equations (22)-(24) reflect the updated dynamics of the system, incorporating the newly introduced leader and ranger chimps. \[\left\{ \begin{array}{l}d_{Attacker}=\left|c_{1}.X_{Attacker}-m_{1}.X\right| \\ d_{Barrier}=\left|c_{2}.X_{Barrier}-m_{2}.X\right|\\ d_{Chaser}=\left|c_{3}.X_{Chaser}-m_{3}.X\right|\\ d_{Drirer}=\left|c_{4}.X_{Drirer}-m_{4}.X\right|\\ d_{Lead}=\left|c_{5}.X_{Leader}-m_{5}.X\right|\\ d_{Range}=\left|c_{6}.X_{Range}-m_{6}.X\right|\\ \end{array} \right., \tag{22}\]  
\[\left\{ \begin{array}{l}X_{1}=X_{Attacker}-a_{1}(d_{Attacker})\\ X_{2}=X_{Barrier}-a_{2}(d_{Barrier})\\ X_{3}=X_{Chaser}-a_{3}(d_{Chaser})\\ X_{4}=X_{Drirer}-a_{4}(d_{Drirer})\\ X_{5}=X_{Leader}-a_{5}(d_{Leader})\\ X_{5}=X_{Range}-a_{6}(d_{Range})\\ \end{array} \right., \tag{23}\]  
\[X\left(t+1\right)=\frac{X_{1}+X_{2}+X_{3}+X_{4}+X_{5}+X_{6}}{6} \tag{24}\]  
Equation (22) defines the distance calculations for each chimp role, including the original attackers, barriers, chasers, and drivers, along with the new leaders and rangers. These distances dictate how each chimp approaches the prey (optimal solution), with the leader guiding the search towards the most promising areas and the ranger introducing randomness to explore less-explored regions. Equation (23) updates the position of each chimp role based on their respective distances, ensuring that the leader drives convergence while the ranger maintains diversity and chaotic behavior to avoid local optima. Finally, Equation (24) computes the new overall position by averaging the positions of all six roles,ensuring a balanced combination of exploration and exploitation.