## 5 Simulation Experiment
### Example Application  
In order to better fit the actual operation of the factory workshop, and further expand the time components of the production cycle on the basis of considering the parallel mobile operation mode, this paper designs a FJSP test example, AT01, containing processing time, setup time and handling time for the production system with multi-equipment work centers, facing the requirements of multi-variety and small-batch job processing task orders. The data of the AT01 example are shown in Tables 7-9. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Example**} & \multirow{2}{*}{**Size**} & \multirow{2}{*}{\(B_{\text{KS}}\)} & \multirow{2}{*}{**Algorithm in This Paper**} & \multicolumn{2}{c}{**DPSO**} & \multicolumn{2}{c}{**Heuristic**} & \multicolumn{2}{c}{**IDMFO**} & \multicolumn{1}{c}{**HGWO**} \\  & & & & [25] & [30] & [31] & [32] \\ \cline{3-8}  & & & \(t_{B}\) & \(e\) & \(t_{B}\) & \(t_{B}\) & \(t_{B}\) & \(t_{B}\) \\ \hline Kacem01 & \(4\times 5\) & 11 & **11** & 0 & **11** & **11** & - & **11** \\ Kacem02 & \(8\times 8\) & 14 & **14** & 0 & 15 & 15 & 15 & **14** \\ Kacem03 & \(10\times 7\) & 11 & **11** & 0 & 12 & 13 & - & **11** \\ Kacem04 & \(10\times 10\) & 7 & **7** & 0 & **7** & **7** & **7** & **7** \\ Kacem05 & \(15\times 10\) & 11 & 12 & 9.09 & 11 & 12 & 13 & 13 \\ MK01 & \(10\times 6\) & 40 & **40** & 0 & 42 & 42 & **40** & **40** \\ MK02 & \(10\times 6\) & 26 & **26** & 0 & 32 & 28 & 27 & 29 \\ MK03 & \(15\times 8\) & 204 & **204** & 0 & **204** & **204** & **204** & **204** \\ MK04 & \(15\times 8\) & 60 & **60** & 0 & 80 & 75 & 62 & 65 \\ MK05 & \(15\times 4\) & 172 & 174 & 1.16 & 173 & 179 & 174 & 175 \\ MK06 & \(10\times 15\) & 57 & 61 & 7.02 & 66 & 69 & 67 & 79 \\ MK07 & \(20\times 5\) & 139 & 146 & 5.04 & 145 & 149 & 144 & 149 \\ MK08 & \(20\times 10\) & 523 & 535 & 2.48 & 524 & 555 & 523 & 523 \\ MK09 & \(20\times 10\) & 307 & 328 & 6.52 & 364 & 342 & 314 & 325 \\ MK10 & \(20\times 15\) & 198 & 238 & 20.2 & 252 & 242 & 235 & 253 \\ MRE & - & - & - & **3.43** & **9.01** & **8.39** & **5.83** & **7.95** \\ \(N_{B}\) & - & - & **7** & - & **4** & **3** & **4** & **7** \\ \hline \hline \end{tabular} Note: The bold is the preferred value for each instance run.  
\end{table} 
Table 6: Algorithm performance comparison. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Job Type**} & \multirow{2}{*}{**Job**} & \multirow{2}{*}{**Operation Number**} & \multirow{2}{*}{**OS**} & \multicolumn{4}{c}{**Machine and Processing Time/min**} \\ \cline{4-9}  & & & & **Work Center 1** & **Work Center 2** & **Work Center 3** & **Work Center 4** \\ \cline{4-9}  & & & & \(W\mathbf{C_{11}}\) & \(W\mathbf{C_{21}}\) & \(W\mathbf{C_{22}}\) & \(W\mathbf{C_{31}}\) & \(W\mathbf{C_{32}}\) & \(W\mathbf{C_{41}}\) \\ \hline \multirow{2}{*}{Type 1} & \multirow{2}{*}{Job 1} & 1 & 111 & 4 & 5 & 5 & - & - & 3 \\  & & 2 & 112 & 3 & - & - & 2 & 2 & 4 \\ \hline \multirow{4}{*}{Type 2} & \multirow{4}{*}{Job 1} & 1 & 211 & - & 3 & 3 & 4 & 4 & - \\  & & 2 & 212 & 2 & - & - & 2 & 2 & 3 \\  & & 3 & 213 & 4 & 3 & 3 & - & - & 5 \\ \cline{1-1} \cline{2-9}  & & 1 & 221 & - & 3 & 3 & 4 & 4 & - \\ \cline{1-1}  & & 2 & 222 & 2 & - & - & 2 & 2 & 3 \\ \cline{1-1}  & & 2 & 222 & 2 & - & - & 2 & 2 & 3 \\ \cline{1-1}  & & 3 & 223 & 4 & 3 & 3 & - & - & 5 \\ \hline \multirow{4}{*}{Type 3} & \multirow{4}{*}{Job 2} & 1 & 311 & - & 4 & 4 & 3 & 3 & 4 \\  & & 2 & 312 & 3 & 4 & 4 & 5 & 5 & 3 \\ \cline{1-1} \cline{2-9}  & & 1 & 321 & - & 4 & 4 & 3 & 3 & 4 \\ \cline{1-1}  & & 2 & 322 & 3 & 4 & 4 & 5 & 5 & 3 \\ \cline{1-1} \cline{2-9}  & & 1 & 331 & - & 4 & 4 & 3 & 3 & 4 \\ \cline{1-1} \cline{2-9}  & & 2 & 332 & 3 & 4 & 4 & 5 & 5 & 3 \\ \hline \hline \end{tabular} Note: The bold is the preferred value for each instance run.  
\end{table} 
Table 7: Job processing schedule of multi-equipment work centers.