## 4 Experiment
### Result of Defect Classification Prediction  
In order to verify that the framework in this paper has a better predictive efficacy with respect to strip steel defects, a simulation experiment was conducted. In the experiment, a total of ten prediction models were constructed, namely, SVM (version 1.0.2), RF (version 1.0.2), GBDT (version 1.0.2), XGBoost (version 2.1.0), CatBoost (version 1.2.5), LightGBM (version 4.4.0), Stacking, ISmote_Stacking, IPSO_ISmote_Stacking, and IIPSO_ISmote_Stacking. These were trained and evaluated independently under the same experimental conditions. As \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Function** & **Index** & **IIPSO** & **IPSO** & **BES** & **SSA** & **IIPSO-L** & **IIPSO-W** \\ \hline \multirow{3}{*}{\(f_{1}\)} & Mean & \(6.66\times 10^{-34}\) & \(3.30\times 10^{-2}\) & \(3.59\times 10^{-3}\) & \(1.31\times 10^{-8}\) & \(2.50\times 10^{-29}\) & \(1.57\times 10^{-1}\) \\  & Standard Deviation & \(1.34\times 10^{-33}\) & \(6.15\times 10^{-3}\) & \(4.36\times 10^{-3}\) & \(7.15\times 10^{-1}\) & \(7.46\times 10^{-29}\) & \(1.78\times 10^{-1}\) \\  & Response time/S & \(2.76\times 10^{-6}\) & \(2.97\times 10^{-6}\) & \(4.88\times 10^{-6}\) & \(4.24\times 10^{-6}\) & \(3.77\times 10^{-9}\) & \(3.97\times 10^{-6}\) \\  & Mean & \(8.88\times 10^{-16}\) & \(2.78\times 10^{-6}\) & \(1.72\times 10^{-2}\) & \(6.53\times 10^{-4}\) & \(2.40\times 10^{-6}\) & \(3.49\times 10^{-2}\) \\ \multirow{3}{*}{\(f_{2}\)} & Standard Deviation & \(1.63\times 10^{-10}\) & \(5.21\times 10^{-6}\) & \(1.93\times 10^{-2}\) & \(6.12\times 10^{-0}\) & \(8.69\times 10^{-1}\) & \(2.16\times 10^{-2}\) \\  & Response time/S & \(4.08\times 10^{-6}\) & \(5.23\times 10^{-6}\) & \(6.45\times 10^{-6}\) & \(8.98\times 10^{-6}\) & \(4.42\times 10^{-6}\) & \(4.94\times 10^{-6}\) \\ \multirow{3}{*}{\(f_{3}\)} & Mean & \(1.75\times 10^{-26}\) & \(3.00\times 10^{-12}\) & \(6.22\times 10^{-8}\) & \(9.75\times 10^{-12}\) & \(1.13\times 10^{-28}\) & \(5.42\times 10^{-15}\) \\  & Standard Deviation & \(2.43\times 10^{-26}\) & \(9.24\times 10^{-12}\) & \(8.40\times 10^{-8}\) & \(6.24\times 10^{-7}\) & \(7.55\times 10^{-27}\) & \(3.62\times 10^{-15}\) \\ \multirow{3}{*}{\(f_{4}\)} & Response time/S & \(1.87\times 10^{-6}\) & \(2.22\times 10^{-6}\) & \(3.44\times 10^{-6}\) & \(3.78\times 10^{-6}\) & \(2.01\times 10^{-0}\) & \(2.44\times 10^{-6}\) \\  & Mean & \(8.60\times 10^{-13}\) & \(5.20\times 10^{-1}\) & \(6.99\times 10^{-5}\) & \(4.58\times 10^{-6}\) & \(1.89\times 10^{-9}\) & \(4.94\times 10^{-7}\) \\ \multirow{3}{*}{\(f_{4}\)} & Standard Deviation & \(0.57\times 10^{-12}\) & \(4.90\times 10^{-6}\) & \(7.83\times 10^{-6}\) & \(4.28\times 10^{-6}\) & \(2.35\times 10^{-9}\) & \(3.92\times 10^{-7}\) \\  & Response time/S & \(7.61\times 10^{-6}\) & \(10.2\times 10^{-6}\) & \(8.41\times 10^{-6}\) & \(9.59\times 10^{-6}\) & \(8.01\times 10^{-6}\) & \(9.01\times 10^{-6}\) \\ \multirow{3}{*}{\(f_{5}\)} & Mean & \(1.74\times 10^{-18}\) & \(3.22\times 10^{-10}\) & \(1.32\times 10^{-5}\) & \(4.82\times 10^{-7}\) & \(2.66\times 10^{-15}\) & \(3.21\times 10^{-12}\) \\  & Standard Deviation & \(3.84\times 10^{-18}\) & \(5.06\times 10^{-10}\) & \(2.33\times 10^{-5}\) & \(2.09\times 10^{-7}\) & \(4.21\times 10^{-15}\) & \(3.47\times 10^{-12}\) \\ \multirow{3}{*}{\(f_{5}\)} & Response time/S & \(11.42\times 10^{-6}\) & \(13.88\times 10^{-6}\) & \(14.21\times 10^{-6}\) & \(14.88\times 10^{-6}\) & \(13.2\times 10^{-6}\) & \(12.59\times 10^{-6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Simulation results of standard function. Figure 12: Evolution curve of test functions: (**a**) fitness value of f\({}_{1}\) function; (**b**) fitness value of f\({}_{2}\) function; (c) fitness value of f\({}_{3}\) function; (d) fitness value of f\({}_{4}\) function; and (**e**) fitness value of f\({}_{5}\) function.