## 3 Proposed MISAO
### Results Comparisons and Analysis of CEC2017 Benchmark Functions
#### 3.4.2 Comparison and Analysis of Algorithms  
The results of the experimental comparison of MISAO with other classical algorithms are shown in Table 5, where AVG and STD denote the mean and standard deviation of the algorithms after 30 independent runs, respectively, and the optimal values are shown in bold in each column. By comparing and observing the average values (AVG), it is initially clear that for most of the benchmark test functions, MISAO has the smallest average value, which indicates that MISAO obtains relatively high-quality solutions when using other algorithms to optimize the benchmark functions. It is particularly effective in two types of tests: hybrid and composite functions, which suggests that the MISAO algorithm will have a more vital ability to find an optimal solution when faced with complex problems. Also, the standard deviation (STD) of the optimal solution is slight, indicating that MISAO has a high degree of stability when optimizing the benchmark function. To verify the validity of the experimental results of MISAO and to improve the understanding of the experimental \begin{table}
\begin{tabular}{l l l} \hline  & **Mean Rank** & **Final Ranking** \\ \hline SAO & 7.08 & 8 \\ MISAO-1 & 5.42 & 6 \\ MISAO-2 & 4.83 & 5 \\ MISAO-3 & 5.43 & 7 \\ MISAO-4 & 4.67 & 4 \\ MISAO-5 & 3.10 & 2 \\ MISAO-6 & 3.52 & 3 \\ MISAO & 1.80 & 1 \\ \hline \end{tabular}
\end{table} 
Table 4: Average ranking of different MISAO-derived variants. results, we further analyzed the experimental data using the Wilcoxon signed-rank test, shown in Table 6, where '+' indicates that the performance of MISAO is better than that of other algorithms, '\(-\)' indicates that the performance of MISAO is poorer than that of other algorithms, and '=' indicates that MISAO performs as well as other algorithms. Mean denotes the average ranking after 30 iterations of parallelization, and Rank denotes the overall final ranking. According to the results in Table 6, MISAO outperforms its competitors in at least 21 out of 30 functional evaluation trials. The average ratings indicate that MISAO is far superior to its competitors' algorithms. In addition, the MISAO algorithm has a huge advantage over the algorithms that have been improved in recent years, such as CLACO, GBSMA, and MOFOA. Figure 4 illustrates some of the results of the different algorithms iterated under the benchmark functions. In order to analyze the iterative process of the algorithms as thoroughly as possible, the nine functions in the figure were selected from a set of 30 functions in the following order: single-peak, multi-peak, hybrid, and combined functions. Figure 4 illustrates how MISAO outperforms other algorithms in pre-searching functions F5, F7, and F21. For functions F16, F23, and F28, MISAO can be updated to a superior solution even later in the optimization search, which shows its strong development potential. In addition, MISAO outperforms competing algorithms in the exploration and development phases for functions F1, F12, and F26. The comparative tests show that MISAO is a very effective metaheuristic optimization algorithm with high robustness and adaptability in solving optimization problems.