## 4 Experiment
### IIPSO Algorithm Performance Test  
In order to verify the performance of the IIPSO algorithm, it was compared with the IPSO algorithm, the bald eagle search algorithm (BES) [33], the sparrow search algorithm (SSA) [34], the IIPSO-W [35] algorithm, and the IIPSO-L algorithm in the experiment. In a simulation experiment, five benchmark test functions were found for testing. The definition, value range, and theoretical optimal of the aforementioned test functions are listed in Table 5.  
The value of the mean and standard deviation of search results were recorded to evaluate the performance of different algorithms in terms of search accuracy and stability. The results of function verification testing are shown in Table 6. The mean value of IIPSO is the smallest among all algorithms compared, indicating that it has superior precision in seeking the optimal solution. With regard to stability, the standard deviation of IIPSO for the optimisation results of function \(f_{3}\) is slightly higher than that of IIPSO-L. However, IIPSO has the lowest standard deviation for optimising other functions. This indicates that IIPSO has a high degree of stability in the convergence path when solving unipolar and multipolar problems. Furthermore, the time complexity of the algorithm, that is to say, the response time, is also taken into account. The response time of IIPSO is demonstrably shorter than that of IPSO, thereby demonstrating that the enhancement of IPSO has effectively enhanced the efficiency of the algorithm. Concurrently, the response time of IIPSO is the shortest when compared with other algorithms. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Dataset** & **Index** & **Smote** & **Borderline-Smote** & **SVMSnote** & **ADASYN** & **Smote-IPF** & **RSnote** & **ISmote** \\ \hline \multirow{4}{*}{WIS} & F1 & 0.950 & 0.935 & 0.941 & 0.928 & 0.951 & 0.944 & 0.959 \\  & G-mean & 0.970 & 0.962 & 0.961 & 0.971 & 0.959 & 0.960 & 0.976 \\  & AUC & 0.971 & 0.970 & 0.969 & 0.964 & 0.959 & 0.961 & 0.979 \\  & F1 & 0.691 & 0.742 & 0.661 & 0.702 & 0.796 & 0.811 & 0.858 \\  & G-mean & 0.901 & 0.866 & 0.862 & 0.859 & 0.892 & 0.901 & 0.921 \\  & AUC & 0.919 & 0.881 & 0.871 & 0.879 & 0.920 & 0.912 & 0.931 \\  & F1 & 0.829 & 0.831 & 0.801 & 0.821 & 0.826 & 0.869 & 0.882 \\  & G-mean & 0.931 & 0.934 & 0.925 & 0.921 & 0.933 & 0.939 & 0.949 \\  & AUC & 0.939 & 0.942 & 0.929 & 0.931 & 0.921 & 0.940 & 0.951 \\  & F1 & 0.514 & 0.508 & 0.455 & 0.520 & 0.529 & 0.525 & 0.565 \\ YEA5 & G-mean & 0.931 & 0.933 & 0.896 & 0.938 & 0.911 & 0.939 & 0.922 \\  & AUC & 0.932 & 0.940 & 0.914 & 0.941 & 0.921 & 0.945 & 0.939 \\  & F1 & 0.442 & 0.435 & 0.392 & 0.329 & 0.407 & 0.436 & 0.527 \\ YEA6 & G-mean & 0.813 & 0.820 & 0.793 & 0.804 & 0.792 & 0.752 & 0.872 \\  & AUC & 0.839 & 0.822 & 0.841 & 0.822 & 0.791 & 0.841 & 0.852 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance of each algorithm on RF. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Functional Form** & **Value Range** & **Theoretical Optimal** \\ \hline \(f_{1}(x)=\sum\limits_{i=1}^{30}x_{i}^{2}\) & \([-100,100]\) & 0 \\ \hline \(f_{2}(x)=\sum\limits_{i=1}^{30}(x_{i}^{2}-10\cos(2\pi x_{i})+10)\) & \([-5.12,5.12]\) & 0 \\ \hline \(f_{3}(x_{1},x_{2})=\frac{\sin\sqrt{x_{1}^{2}+x_{2}^{2}}-0.5}{(1+0.001(x_{1}^{2}+x _{2}^{2}))^{2}}+0.5\) & \([-5,5]\) & 0 \\ \hline \(f_{4}(x)=-\sum\limits_{i=1}^{30}(x_{i}\sin(\sqrt{|x_{i}|}))\) & \([-500,500]\) & 0 \\ \hline \(f_{5}(x)=\frac{1}{4000\sum\limits_{i=1}^{n}x_{i}^{2}-\sum\limits_{i=1}^{n}\cos \frac{x_{i}}{\sqrt{i}}+1}\) & \([-600,600]\) & 0 \\ \hline \end{tabular}
\end{table} 
Table 5: Standard test functions. The simulation diagram and evolution process curves of five test functions are shown in Figure 12. It demonstrates that IIPSO significantly outperforms other algorithms with regard to convergence speed when testing functions \(f_{1}\)-\(f_{2}\). For the test function \(f_{3}\)-\(f_{5}\), IPSO, IIPSO-L, and IIPSO-W all have faster convergence speeds, but IIPSO still maintains high competitiveness.