## 4 Experimental Simulation and Results Analysis
### Performance Comparison Between MSEChoA and Other Algorithms
#### 4.3.1 Solution Accuracy Analysis  
As shown in Table 4, in the tests on unimodal functions (F1 to F5), the MSECHOA algorithm achieved the theoretical optimal value of 0 on F1 to F4. Although MSECHOA did not surpass MSGWO and AWChOA on the F5 function, its performance was still significantly better than the original ChOA and most other improved algorithms, indicating its robustness in handling complex functions. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Algorithm** & \begin{tabular}{c} **Standard** \\ **Function** \\ \end{tabular} & \begin{tabular}{c} **Best Fitness** \\ **Value** \\ \end{tabular} & \begin{tabular}{c} **Average** \\ **Fitness Value** \\ \end{tabular} & \
\begin{tabular}{c} **Worst Fitness** \\ **Value** \\ \end{tabular} &
\begin{tabular}{c} **Standard Deviation of** \\ **Fitness Value** \\ \end{tabular} \\ \hline GWO & & 2.7451 \(\times\) 10\({}^{61}\) & 2.0058 \(\times\) 10\({}^{59}\) & 8.0392 \(\times\) 10\({}^{69}\) & 3.4286 \(\times\) 10\({}^{59}\) \\ EO & & 8.1172 \(\times\) 10\({}^{69}\) & 7.6076 \(\times\) 10\({}^{67}\) & 2.7059 \(\times\) 10\({}^{66}\) & 1.1166 \(\times\) 10\({}^{66}\) \\ ALO & & 4.7580 \(\times\) 10\({}^{7}\) & 5.0654 \(\times\) 10\({}^{6}\) & 9.8827 \(\times\) 10\({}^{6}\) & 3.7870 \(\times\) 10\({}^{6}\) \\ MSGWO & & 0 & 0 & 0 & 0 \\ ChOA & F1 & 4.0154 \(\times\) 10\({}^{22}\) & 2.6677 \(\times\) 10\({}^{21}\) & 5.6054 \(\times\) 10\({}^{21}\) & 2.3480 \(\times\) 10\({}^{21}\) \\ IchOA & & 5.7817 \(\times\) 10\({}^{209}\) & 5.2753 \(\times\) 10\({}^{200}\) & 2.6309 \(\times\) 10\({}^{279}\) & 0 \\ WChOA & & 0 & 0 & 0 & 0 \\ AWChOA & & 0 & 0 & 0 & 0 \\ MSECHOA & & 0 & 0 & 0 & 0 \\ \hline GWO & & 5.9076 \(\times\) 10\({}^{49}\) & 2.0702 \(\times\) 10\({}^{13}\) & 4.1257 \(\times\) 10\({}^{12}\) & 9.2235 \(\times\) 10\({}^{13}\) \\ EO & & 4.1664 \(\times\) 10\({}^{27}\) & 1.0605 \(\times\) 10\({}^{20}\) & 2.0582 \(\times\) 10\({}^{19}\) & 4.5960 \(\times\) 10\({}^{20}\) \\ ALO & & 4.3682 \(\times\) 10\({}^{2}\) & 1.2297 \(\times\) 10\({}^{3}\) & 1.9752 \(\times\) 10\({}^{3}\) & 4.7699 \(\times\) 10\({}^{2}\) \\ MSGWO & & 0 & 0 & 0 & 0 \\ ChOA & F3 & 1.4114 \(\times\) 10\({}^{7}\) & 2.3789 \(\times\) 10\({}^{3}\) & 2.5539 \(\times\) 10\({}^{2}\) & 5.9865 \(\times\) 10\({}^{3}\) \\ IchOA & & 6.2521 & 6.3564 \(\times\) 10\({}^{3}\) & 2.0569 \(\times\) 10\({}^{4}\) & 5.9676 \(\times\) 10\({}^{3}\) \\ WChOA & & 0 & 0 & 0 & 0 \\ AWChOA & & 0 & 0 & 0 & 0 \\ MSECHOA & & 0 & 0 & 0 & 0 \\ \hline GWO & & 6.7639 \(\times\) 10\({}^{16}\) & 2.2771 \(\times\) 10\({}^{14}\) & 8.1989 \(\times\) 10\({}^{14}\) & 2.5581 \(\times\) 10\({}^{14}\) \\ EO & & 6.721 \(\times\) 10\({}^{3}\) & 2.0782 \(\times\) 10\({}^{21}\) & 1.215 \(\times\) 10\({}^{20}\) & 3.8011 \(\times\) 10\({}^{21}\) \\ ALO & & 9.3198 \(\times\) 10\({}^{23}\) & 4.9083 \(\times\) 10\({}^{23}\) & 4.8676 \(\times\) 10\({}^{22}\) & 1.5379 \(\times\) 10\({}^{22}\) \\ MSGWO & & 0 & 0 & 1.5379 \(\times\) 10\({}^{22}\) \\ ChOA & F4 & 8.3812 \(\times\) 10\({}^{4}\) & 2.5449 \(\times\) 10\({}^{2}\) & 1.1852 \(\times\) 10\({}^{1}\) & 4.0083 \(\times\) 10\({}^{2}\) \\ IchOA & & 1.1553 \(\times\) 10\({}^{60}\) & 1.9693 \(\times\) 10\({}^{44}\) & 1.3232 \(\times\) 10\({}^{43}\) & 4.4478 \(\times\) 10\({}^{44}\) \\ WChOA & & 5.4692 \(\times\) 10\({}^{53}\) & 1.1032 \(\times\) 10\({}^{249}\) & 1.0184 \(\times\) 10\({}^{248}\) & 0 \\ AWChOA & & 0 & 0 & 0 & 0 \\ MSECHOA & & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The experimental results of each algorithm on benchmark test functions.