## 3 Proposed MISAO
### Results Comparisons and Analysis of CEC2017 Benchmark Functions
#### 3.4.1 Effectiveness Validation of Different Components  
This study incorporates three enhancement strategies, including cyclic chaotic mapping initialization, Gaussian diffusion, and random follower search, to enhance the optimization performance of the classic SAO algorithm. In order to validate the effectiveness of each component, six different MISAO-derived algorithms with one or more fusion strategies are designed, as shown in Table 2, where 1 represents that the strategy is embedded; instead, 0 indicates that the strategy is not embedded. The performance of SAO, MISAO, and multiple MISAO-derived variants in ablating was simultaneously evaluated using the CEC 2017 test set. Table 3 showcases the average values (AVG) and standard deviations (STD) obtained by these algorithms for each of the 30 test functions. The AVG serves as an indicator of the central tendency of the algorithmic performance, providing a summary measure of the typical outcome. Meanwhile, the STD quantifies the dispersion or volatility of the results, offering insights into the reliability and consistency of the algorithms' performance. The bold values in each column denote the most optimal performance among the compared algorithms for the corresponding test function. The average ranking results are documented in Table 4 for a more thorough analysis. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Strategy** & **MISAO-1** & **MISAO-2** & **MISAO-3** & **MISAO-4** & **MISAO-5** & **MISAO-6** & **MISAO** \\ \hline \
\begin{tabular}{l} Circle Chaotic Mapping \\ initialization \\ \end{tabular} & 1 & 0 & 0 & 1 & 1 & 0 & 1 \\
\begin{tabular}{l} Gaussian diffusion \\ Random follower search \\ \end{tabular} & 0 & 1 & 0 & 1 & 0 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Different MISAO-derived variants with three improvement strategies. \begin{table}
\begin{tabular}{l l l} \hline \hline  & **The Function Name** & \(f_{\text{min}}\) \\ \hline \multirow{8}{*}{Multimodal Functions} & F4 & Shifted and Rotated Rosenbrock’s Function & 400 \\  & F5 & Shifted and Rotated Rastrigin’s Function & 500 \\  & F6 & Shifted and Rotated Expanded Scaffer’s F6 Function & 600 \\  & F7 & Shifted and Rotated Lunacek Bi\_Rastrigin Function & 700 \\  & F8 & Shifted and Rotated Non-Continuous Rastrigin’s Function & 800 \\  & F9 & Shifted and Rotated Levy Function & 900 \\  & F10 & Shifted and Rotated Schwefel’s Function & 1000 \\ \hline \multirow{8}{*}{Hybrid Functions} & F11 & Hybrid Function 1 (N = 3) & 1100 \\  & F12 & Hybrid Function 2 (N = 3) & 1200 \\  & F13 & Hybrid Function 3 (N = 3) & 1300 \\  & F14 & Hybrid Function 4 (N = 4) & 1400 \\  & F15 & Hybrid Function 5 (N = 4) & 1500 \\  & F16 & Hybrid Function 6 (N = 4) & 1600 \\  & F17 & Hybrid Function 6 (N = 5) & 1700 \\  & F18 & Hybrid Function 6 (N = 5) & 1800 \\  & F19 & Hybrid Function 6 (N = 5) & 1900 \\  & F20 & Hybrid Function 6 (N = 6) & 2000 \\ \hline \multirow{8}{*}{Composition Functions} & F21 & Composition Function 1 (N = 3) & 2100 \\  & F22 & Composition Function 2 (N = 3) & 2200 \\  & F23 & Composition Function 3 (N = 4) & 2300 \\  & F24 & Composition Function 4 (N = 4) & 2400 \\  & F25 & Composition Function 5 (N = 5) & 2500 \\  & F26 & Composition Function 6 (N = 5) & 2600 \\  & F27 & Composition Function 7 (N = 6) & 2700 \\  & F28 & Composition Function 8 (N = 6) & 2800 \\  & F29 & Composition Function 9 (N = 3) & 2900 \\  & F30 & Composition Function 10 (N = 3) & 3000 \\ \hline \hline \end{tabular}
\end{table}