## 4 Experimental Simulation and Results Analysis
### Performance Comparison Between MSEChoA and Other Algorithms  
To validate the practical effectiveness of MSEChoA, this paper conducts a comprehensive performance comparison with several state-of-the-art metaheuristic optimization algorithms. These include the Grey Wolf Optimizer (GWO), Equilibrium Optimizer (EO) [29], Ant Lion Optimizer (ALO) [30], Multi-Strategy Grey Wolf Optimizer (MSGWO) [31], Chimp Optimization Algorithm (ChoA), Improved Chimp Optimization Algorithm (IChoA) [32], Weighted Chimp Optimization Algorithm (WChOA), and Adaptive Weighted Chimp Optimization Algorithm (AWChOA), which applies adaptive convergence factors and dynamic weight strategies. The specific experimental settings and parameters are shown in Table 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Standard Function** & **Average Fitness Value** &
\begin{tabular}{c} **Standard Deviation of** \\ **Fitness Value** \\ \end{tabular} \\ \hline ChOA & & \(1.9962\times 10^{1}\) & \(1.2464\times 1^{3}\) \\ CChOA & & \(1.2967\times 10^{14}\) & \(5.327\times 10^{15}\) \\ GChOA & F10 & \(8.8818\times 10^{16}\) & 0 \\ EChOA & & \(0.097619\) & 0 \\ MSEChoA & & \(8.8818\times 10^{16}\) & 0 \\ \hline ChOA & & \(7.1037\times 10^{3}\) & \(1.3919\times 10^{3}\) \\ CChOA & & \(1.0514\times 10^{6}\) & \(3.1708\times 10^{6}\) \\ GChOA & F11 & 0 & 0 \\ EChOA & & 0 & 0 \\ MSEChoA & & 0 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Algorithm** & **Parameters** \\ \hline GWO & \(r_{1}=[0,1]\), \(r_{2}=[0,1]\), \(a=[0,2]\) \\ EO & \(r_{1}=[0,1]\), \(r_{2}=[0,1]\), \(a_{1}=2\), \(a_{2}=1\), \(GP=0.3\) \\ ALO & \(r_{1}=[0,1]\), \(r_{2}=[0,1]\), \(c>1\) \\ MSGWO & \(r_{1}=[0,1]\), \(r_{2}=[0,1]\), \(a=[0,2]\), \(h=0.3\) \\ ChOA & \(r_{1}=[0,1]\), \(r_{2}=[0,1]\), \(f=[0,2.5]\) \\ IChOA & \(r_{1}=[0,1]\), \(r_{2}=[0,1]\), \(f=[0,2.5]\) \\ WChOA & \(r_{1}=[0,1]\), \(r_{2}=[0,1]\), \(f=[0,2.5]\) \\ AWChOA & \(r_{1}=[0,1]\), \(r_{2}=[0,1]\), \(f=[0,2.5]\) \\ MSEChoA & \(r_{1}=[0,1]\), \(r_{2}=[0,1]\), \(f=[0,2.5]\), \(k=[0,1]\), \(\gamma_{1}=[0,2]\), \\  & \(\gamma_{2}=[0,1]\), \(\gamma_{3}=[-1,1]\), \(\gamma_{4}=[0,1]\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameter Settings of Each Algorithm in the Simulation Experiments.  
In MSECHOA, the parameter \(k\) is a dynamic opposition-based learning (DOBL) parameter with a value range of [0, 1]. Its design aims to control the generation range of opposition solutions to adapt to the search requirements of different optimization stages. In the early stages of optimization, k has a larger value (close to 1), resulting in a broader distribution of opposition solutions, which helps to cover the search space and enhance global search capabilities. In the later stages, k gradually decreases, leading to a more concentrated distribution of opposition solutions, facilitating the fine-tuning of the local search space. Parameters \(\gamma_{1}\), \(\gamma_{2}\), \(\gamma_{3}\), and \(\gamma_{4}\), respectively, represent the step size adjustment parameter, which controls the magnitude of the search step size; the variation range parameter, which limits the range of solution updates; the direction switching parameter, which enables switching between forward and reverse searches; and the random perturbation parameter, which introduces randomness during the solution update process.