## 4 Simulation Experiments
### Performance Testing and Results Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**IMOGWO**} & \multicolumn{2}{c}{**MODGWO**} & \multicolumn{2}{c}{**MOGWO**} & \multicolumn{2}{c}{**NSGA-II**} \\ \cline{2-10}
**Test Example** & \multicolumn{2}{c}{**Avg**} & \multicolumn{2}{c}{**Min**} & \multicolumn{2}{c}{**Avg**} & \multicolumn{2}{c}{**Min**} & \multicolumn{2}{c}{**Avg**} & \multicolumn{2}{c}{**Min**} & \multicolumn{2}{c}{**Avg**} & \multicolumn{2}{c}{**Min**} \\  & & **(Max)** & & & **(Max)** & & **(Max)** & & **(Max)** \\ \hline Problem & _SP_ & **0.2202** & 0.0956 & 0.3595 & **0.0641** & 0.3246 & 0.1532 & 0.32 & 0.1056 \\
05-11 & _GD_ & **0.0881** & **0** & 0.1878 & 0.1201 & 0.128 & 0.0636 & 0.112 & 0.0509 \\  & _IGD_ & **0.208** & **0** & 0.4401 & 0.286 & 0.3161 & 0.2497 & 0.347 & 0.2215 \\  & \(\Omega\) & **74\%** & **100\%** & 16\% & 50\% & 0\% & 0\% & 10\% & 33\% \\ Problem & _SP_ & 0.2416 & 0.111 & 0.3661 & **0.0489** & **0.2225** & 0.1256 & 0.2472 & 0.145 \\
06-01 & _GD_ & 0.0554 & **0.0205** & 0.1597 & 0.0768 & **0.0523** & 0.0241 & 0.0765 & 0.0425 \\  & _IGD_ & **0.1913** & **0.1046** & 0.3793 & 0.2255 & 0.2173 & 0.1601 & 0.2471 & 0.1956 \\  & \(\Omega\) & **63\%** & **86\%** & 6\% & 25\% & 10\% & 13\% & 21\% & 43\% \\ Problem & _SP_ & **0.111** & 0.0707 & 0.3171 & 0.1402 & 0.1163 & 0.0745 & 0.1847 & **0.0703** \\
06-11 & _GD_ & **0.0166** & **0.0122** & 0.0851 & 0.0521 & 0.0279 & 0.0199 & 0.0495 & 0.0266 \\  & _IGD_ & **0.0836** & **0.0408** & 0.3089 & 0.1964 & 0.1482 & 0.1227 & 0.1917 & 0.1246 \\  & \(\Omega\) & **64\%** & 72\% & 7\% & 15\% & 13\% & 29\% & 30\% & **100\%** \\  & _SP_ & **0.2223** & **0.1133** & 0.4246 & 0.1723 & 0.241 & 0.1272 & 0.3091 & 0.1514 \\ Mean & _GD_ & **0.052** & **0.017** & 0.1813 & 0.0768 & 0.0777 & 0.0383 & 0.0944 & 0.0433 \\  & _IGD_ & **0.1446** & **0.045** & 0.4313 & 0.2444 & 0.2306 & 0.1493 & 0.2557 & 0.1371 \\  & \(\Omega\) & **62\%** & **81\%** & 8\% & 27\% & 15\% & 28\% & 17\% & 41\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._  
Figure 5: _Cont._It also can be seen from Table 8 that the IMOGWO algorithm is superior to the MODGWO, MOGWO, and NSGA-II algorithms in the uniformity, convergence, diversity, and dominance of the solutions on the Pareto front for 3 factories cases. In order to more clearly determine whether there are significant differences between algorithms, SPSS Statistics 17 was used in this paper to conduct the Wilcoxon symbolic rank test, and the results are shown in Table 9. Table 8 shows the experimental results of the test cases with three factories. For the dominant proportion of 'Avg' in the \(SP\) indicator, the IMOGWO algorithm is 67%, the MODGWO algorithm is 0%, the MOGWO algorithm is 16.5%, and the NSGA-II algorithm is 16.5%. For its dominant proportion of 'Min,' the IMOGWO algorithm is 42%, the MODGWO algorithm is 16.5%, the MOGWO algorithm is 16.5%, and the NSGA-II algorithm is 25%. For the dominant proportion of 'Avg' in the \(GD\) indicator, the IMOGWO algorithm is 100%, the MODGWO algorithm is 0%, the MOGWO algorithm is 0%, and the NSGA-II algorithm is 0%. For its dominant proportion of 'Min,' the IMOGWO algorithm is 83%, the MODGWO algorithm is 8.5%, the MOGWO algorithm is 8.5%, and the NSGA-II algorithm is 0%. For the dominant proportion of 'Avg' in the \(IGD\) indicator, the IMOGWO algorithm is 100%, the MODGWO algorithm is 0%, the MOGWO algorithm is 0%, and the NSGA-II algorithm is 0%. For its dominant proportion of 'Min,' the IMOGWO algorithm is 0%, the MOGWO algorithm is 0%, and the NSGA-II algorithm is 0%. For its dominant proportion of 'Min,' the IMOGWO algorithm is 0%. For the dominant proportion of 'Avg' in the \(\Omega\) indicator, the IMOGWO algorithm is 92%, the MODGWO algorithm is 8%, the MOGWO algorithm is 0%, and the NSGA-II algorithm is 0%. For its dominant proportion of 'Max,' the IMOGWO algorithm is 92%, the MODGWO algorithm is 0%, and the NSGA-II algorithm is 0%.