## 5 Simulation Experiment
### Example Application
\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{6}{c}{**Machine and Processing Time/min**} \\ \cline{5-8}  & & & & **Work Center 1** & **Work Center 2** & **Work Center 3** & **Work Center 4** \\ \cline{5-8}  & & & \(\text{WC}_{\text{11}}\) & \(\text{WC}_{\text{21}}\) & \(\text{WC}_{\text{22}}\) & \(\text{WC}_{\text{31}}\) & \(\text{WC}_{\text{32}}\) & \(\text{WC}_{\text{41}}\) \\ \hline \multirow{5}{*}{Type 4} & \multirow{5}{*}{Job 1} & 1 & 411 & 1 & 1.5 & 1 & 3 & 2 & 2 \\  & & 2 & 412 & 1 & 2 & 2 & 3 & 1 & 2 \\  & & 3 & 413 & 1 & 1 & 1 & 1 & 3 & 2 \\ \cline{2-8}  & & 1 & 421 & 1 & 1.5 & 1 & 3 & 2 & 2 \\  & & 2 & 422 & 1 & 2 & 2 & 3 & 1 & 2 \\  & & 3 & 423 & 1 & 1 & 1 & 1 & 3 & 2 \\ \cline{2-8}  & & 1 & 431 & 1 & 1.5 & 1 & 3 & 2 & 2 \\ \cline{2-8}  & & 2 & 432 & 1 & 2 & 2 & 3 & 1 & 2 \\  & & 3 & 433 & 1 & 1 & 1 & 1 & 3 & 2 \\ \hline \multirow{5}{*}{Type 5} & \multirow{5}{*}{Job 2} & 1 & 511 & 1.5 & 3 & 2 & 1 & 3 & 2 \\  & & 2 & 512 & 2 & 1 & 2 & 1 & 1 & 2 \\  & & 3 & 513 & 3 & 1 & 1 & 2 & 2 & 2 \\ \cline{2-8}  & & 1 & 521 & 1.5 & 3 & 2 & 1 & 3 & 2 \\ \cline{2-8}  & & 2 & 522 & 2 & 1 & 2 & 1 & 1 & 2 \\  & & 3 & 523 & 3 & 1 & 1 & 2 & 2 & 2 \\ \hline \multirow{5}{*}{Type 5} & \multirow{5}{*}{Job 2} & 1 & 531 & 1.5 & 3 & 2 & 1 & 3 & 2 \\  & & 2 & 532 & 2 & 1 & 2 & 1 & 1 & 2 \\ \cline{1-1}  & & 3 & 533 & 3 & 1 & 1 & 2 & 2 & 2 \\ \hline \hline \end{tabular} Note: “-” indicates that the operation cannot be processed on the machine of the work center.  
\end{table} 
Table 8: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{5}{c}{**Handling Time of Different Equipment in the Work Center/min**} \\ \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Different Equipment** \\ **in the Work Center** \\ \end{tabular} } & \multirow{2}{*}{**Work Center 1**} & \multirow{2}{*}{**Work Center 2**} & \multirow{2}{*}{**Work Center 3**} & \multirow{2}{*}{**Work Center 4**} \\ \cline{3-3} \cline{5-8}  & & & \(\text{WC}_{\text{11}}\) & & & & \\ \hline Work Center 1 & \(\text{WC}_{\text{11}}\) & 0 & 1 & 1.5 & 1.5 & 2 \\ \hline Work Center 2 & \(\text{WC}_{\text{21}}\) & 1 & 0 & 0 & 0.5 & 0.5 & 1 \\  & \(\text{WC}_{\text{22}}\) & 1 & 0 & 0 & 0.5 & 0.5 & 1 \\ \hline Work Center 3 & \(\text{WC}_{\text{31}}\) & 1.5 & 0.5 & 0.5 & 0 & 0 & 1 \\  & \(\text{WC}_{\text{32}}\) & 1.5 & 0.5 & 0.5 & 0 & 0 & 1 \\ \hline Work Center 4 & \(\text{WC}_{\text{41}}\) & 2 & 1 & 1 & 1 & 1 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Jobs handling schedules between different equipment in the production system with multi-equipment work centers. As shown in Figure 12, with the increasing number of iterations, each scheduling objective is continuously optimized, and has good convergence; that is, the maximum completion time, the amount of machine downtime, the number of job handling times and the total load of the machine are constantly optimized, and they are nearly stable after 190 iterations. According to the Pareto optimal solution set and _gbest_ selection strategy in this paper, the job completion time is taken as the first priority of Pareto selection, and the fitness of other objectives evolves with the fitness of the job completion time. Therefore, it is reasonable that the fitness of other targets may decrease suddenly. The resulting optimal scheduling Gantt chart is shown in Figure 13, where the minimum maximum completion time is 16 min, the total number of machine adjustments is 7, the number of job handling times is 12 and the minimum total machine load is 83 min.