## 3 Experimental Testing of Search Performance on IABCBAS Algorithms
### Convergence and Stability Analysis  
Performance comparison experiments are conducted on five algorithms and each benchmark function is run independently 50 times. The evaluation metrics include the best value, average value, and standard deviation. The population size is set to 40 and the maximum number of iterations is 500. The experimental results are presented in Table 3.  
Among these functions, high-dimensional unimodal functions have only one global optimal point and no local extrema, which are mainly used to test convergence speed. Multimodal functions, which have multiple local extrema, are used to evaluate the performance of escaping local extrema across different dimensions (both high and low). For the three high-dimensional unimodal functions, the proposed IABCBAS algorithm achieves the theoretical optimal value of 0 when solving \(f_{1}\) and \(f_{3}\), with the corresponding standard deviation also being 0. In solving \(f_{4}\), the optimal value, average value, and standard deviation of the proposed IABCBAS algorithm are at least three orders of magnitude better than those of the other four algorithms. \begin{table}
**Type** & **Parameter** & **Basis Function** & **Function** & **Dimension** & **Corridor** & **Optimum Value** \\ \hline Higher & f\({}_{1}\) & Schwefel\({}^{\prime}\)s & f\({}_{1}(\mathrm{x})=\sum\limits_{i=1}^{\mathrm{N}}\left|\mathrm{x}_{i}+\prod \limits_{i=1}^{\mathrm{N}}\left|\mathrm{x}_{i}\right|\right.\) & 30 & \(\left[-\mathrm{10,10}\right]\) & 0 \\ \begin{tabular}{c} dimensional \\ unimodal \\ function \\ \end{tabular} & f\({}_{2}\) & Rosenbrock & f\({}_{2}(\mathrm{x})=\sum\limits_{i=1}^{\mathrm{N}-1}\left[100\left(\mathrm{x}_{i \mathrm{x}_{i}}-\mathrm{x}_{i}^{2}\right)+\left(\mathrm{x}_{i}-1\right)^{2} \right]\) & 30 & \(\left[-\mathrm{30,30}\right]\) & 0 \\ \begin{tabular}{c} function \\ \end{tabular} & f\({}_{3}\) & Sphere & f\({}_{3}(\mathrm{x})=\sum\limits_{i=1}^{\mathrm{N}}\mathrm{x}_{i}^{2}\) & 30 & \(\left[-\mathrm{100,100}\right]\) & 0 \\ \hline Higher & f\({}_{4}\) & Rastrigrin & f\({}_{4}(\mathrm{x})=\sum\limits_{i=1}^{\mathrm{N}-1}\left[\chi^{2}-10\cos\left( 2\pi\mathrm{x}_{i}\right)+10\right]\) & 30 & \(\left[-\mathrm{5.12,5.12}\right]\) & 0 \\ \begin{tabular}{c} dimensional \\ multimodal \\ function \\ \end{tabular} & f\({}_{5}\) & [PERSON] & f\({}_{6}(\mathrm{x})=\sum\limits_{i=1}^{\mathrm{N}}-\mathrm{x}\mathrm{sin} \left(\sqrt{\left|\mathrm{x}\right|}\right)\) & 30 & \(\left[-\mathrm{500,500}\right]\) & \(-\mathrm{418.98}\) \\ \begin{tabular}{c} function \\ \end{tabular} & f\({}_{6}\) & [PERSON] & f\({}_{6}(\mathrm{x})=\frac{1}{4000\mathrm{E}_{1}}\sum\limits_{i=1}^{\mathrm{N}-1} \mathrm{x}_{i}\left(\frac{\mathrm{x}_{i}}{\sqrt{1}}\right)+1\) & 30 & \(\left[-\mathrm{600,600}\right]\) & 0 \\ \hline \hline \end{tabular} \begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} Low-dimensional \\ multi-maximilian \\ function \\ \end{tabular} } & f\({}_{7}\) & Foxholes & f\({}_{7}(\mathrm{x})=\left(\frac{1}{500}+\frac{1}{\mathrm{E}_{1}^{2}}+\frac{1}{ \mathrm{E}_{1}^{2}+\sum\left(\mathrm{x}_{i}-\mathrm{x}_{i}\right)^{6}}\right)^{-1}\) & 2 & \(\left[-\mathrm{65,65}\right]\) & 1 \\ \
\begin{tabular}{c} Low-dimensional \\ multi-maximilian \\ function \\ \end{tabular} & f\({}_{8}\) & [PERSON] & f\({}_{8}(\mathrm{x})=-\sum\limits_{i=1}^{\mathrm{N}}\left[\left(\mathrm{X}- \mathrm{a}\right)\left(\mathrm{X}-\mathrm{a}\right)^{\mathrm{T}}+\mathrm{c}_{1} \right]^{-1}\) & 4 & \(\left[-\mathrm{10.54,10.54}\right]\) & \(-\mathrm{10.54}\) \\
\begin{tabular}{c} function \\ \end{tabular} & f\({}_{9}\) & Hartmann 6-D & f\({}_{9}(\mathrm{x})=-\sum\limits_{i=1}^{\mathrm{N}}\mathrm{c}\mathrm{exp}\left(- \frac{6}{\mathrm{N}}\mathrm{a}_{6}\left(\mathrm{x}_{i}-\mathrm{P}_{3}\right)^{2}\right)\) & 6 & \(\left[-\mathrm{3.52,0}\right]\) & \(-\mathrm{3.32}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The nine benchmark parameters for algorithm testing. Figure 3: Benchmark test function modeling. (**a**) Sphere function; (**b**) Foxholes function.