## 4 Simulation Experiment and Analysis
### Test Results and Analysis
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Table**} & \multirow{2}{*}{**Evaluation**} & \multicolumn{2}{c}{**MSSA**} & \multicolumn{2}{c}{**MOPSO**} & \multicolumn{2}{c}{**HMSSA**} \\ \cline{3-8}  & & **Avg** & **Std** & **Avg** & **Std** & **Avg** & **Std** \\ \hline \multirow{3}{*}{DFJSP 01 (10 \(\times\) 6 \(\times\) 3)} & SP & 0.0562 & 0.0154 & **0.0488** & **0.0150** & 0.0691 & 0.0223 \\  & IGD & 0.1912 & 0.0199 & 0.1882 & 0.0158 & **0.0940** & **0.0100** \\  & \(\Omega\) & 0.0025 & 0.0066 & 0.0025 & 0.0052 & **0.0449** & **0.0319** \\ \hline \multirow{3}{*}{DFJSP 02 (10 \(\times\) 6 \(\times\) 3)} & SP & 0.0650 & 0.0179 & 0.0647 & 0.0239 & **0.0609** & **0.0164** \\  & IGD & 0.1864 & 0.0168 & 0.1854 & 0.0237 & **0.1042** & **0.0155** \\  & \(\Omega\) & 0.0029 & 0.0063 & 0.0075 & 0.0101 & **0.0397** & **0.0355** \\ \hline \multirow{3}{*}{DFJSP 03 (15 \(\times\) 8 \(\times\) 3)} & SP & **0.0677** & **0.0169** & 0.0761 & 0.0297 & 0.0692 & 0.0150 \\  & IGD & 0.1971 & 0.0133 & 0.1947 & 0.0208 & **0.1178** & **0.0139** \\  & \(\Omega\) & 0.0038 & 0.0063 & 0.0091 & 0.0106 & **0.0371** & **0.0389** \\ \hline \multirow{3}{*}{DFJSP 04 (15 \(\times\) 8 \(\times\) 3)} & SP & **0.0619** & **0.0189** & 0.0708 & 0.0259 & 0.0649 & 0.0148 \\  & IGD & 0.1867 & 0.0204 & 0.1950 & 0.0146 & **0.1029** & **0.0121** \\  & \(\Omega\) & 0.0016 & 0.0039 & 0.0032 & 0.0061 & **0.0452** & **0.0303** \\ \hline \multirow{3}{*}{DFJSP 05 (15 \(\times\) 4 \(\times\) 3)} & SP & 0.0638 & 0.0202 & 0.0676 & 0.0316 & **0.0599** & **0.0121** \\  & IGD & 0.1398 & 0.0133 & 0.1382 & 0.0087 & **0.0755** & **0.0075** \\  & \(\Omega\) & 0.0058 & 0.0070 & 0.0065 & 0.0082 & **0.0377** & **0.0304** \\ \hline \multirow{3}{*}{DFJSP 06 (10 \(\times\) 15 \(\times\) 3)} & SP & 0.0603 & 0.0121 & **0.0570** & **0.0138** & 0.0678 & 0.0151 \\  & IGD & 0.1809 & 0.0208 & 0.1848 & 0.0184 & **0.1032** & **0.0072** \\  & \(\Omega\) & 0.0084 & 0.0126 & 0.0074 & 0.0084 & **0.0342** & **0.0285** \\ \hline \multirow{3}{*}{DFJSP 07 (20 \(\times\) 5 \(\times\) 3)} & SP & **0.0626** & **0.0174** & 0.0672 & 0.0275 & 0.0690 & 0.0144 \\  & IGD & 0.1800 & 0.0229 & 0.1809 & 0.0157 & **0.0951** & **0.0101** \\  & \(\Omega\) & 0.0052 & 0.0082 & 0.0057 & 0.0076 & **0.0391** & **0.0317** \\ \hline \multirow{3}{*}{DFJSP 08 (20 \(\times\) 10 \(\times\) 3)} & SP & 0.0590 & 0.0195 & 0.0618 & 0.0173 & **0.0566** & **0.0078** \\  & IGD & 0.1722 & 0.0151 & 0.1857 & 0.0161 & **0.0950** & **0.0104** \\  & \(\Omega\) & 0.0072 & 0.0104 & 0.0011 & 0.0026 & **0.0417** & **0.0375** \\ \hline \multirow{3}{*}{DFJSP 09 (20 \(\times\) 10 \(\times\) 3)} & SP & 0.0604 & 0.0110 & 0.0690 & 0.0226 & **0.0574** & **0.0148** \\  & IGD & 0.1777 & 0.0154 & 0.1801 & 0.0158 & **0.0975** & **0.0111** \\ \cline{1-1}  & IGD & 0.0038 & 0.0048 & 0.0053 & 0.0096 & **0.0409** & **0.0289** \\ \hline \multirow{3}{*}{Total} & SP & **0.0619** & **0.0034** & 0.0648 & 0.0081 & 0.0639 & 0.0052 \\ \cline{1-1}  & IGD & 0.1791 & 0.0165 & 0.1814 & 0.0170 & **0.0984** & **0.0113** \\ \cline{1-1}  & IGD & 0.0046 & 0.0023 & 0.0054 & 0.0026 & **0.0401** & **0.0036** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation test results of three algorithms. Furthermore, the significant differences between the algorithms were tested using the Wilcoxon signed-rank test for relevant samples. For the three evaluation indexes of the test problem, the three algorithms are compared in pairs. The test results are shown in Table 5. The MHSSA has significant differences from the comparison algorithm in IGD and \(\Omega\) indexes, and the effect is the best. For the SP index, the three algorithms have no significant difference. In conclusion, the MHBSA proposed in this paper can effectively solve the dual-flexible job shop green scheduling problem. On the whole, the MHBSA is obviously superior to the other two comparison algorithms in terms of diversity, convergence, and dominance of non-inferior solutions on the Pareto frontier.