## 4 Comprehensive Experiments
### Workshop Example Simulation  
This paper took the instances in Tables A1 and A2 (refer to Appendix A) as the research object, and solved the green FJSP problem with the makespan, workshop energy consumption, and processing quality as the optimization goals. The transportation energy consumption of the AGV was generated randomly in [2.0, 2.5][47]. Furthermore, from a cost-saving perspective, we aimed to use the minimum number of AGVs under the premise of achieving multi-objective optimization. Therefore, in the given instances, the upper limit for the number of AGVs was set to 3 for Instance 5 \(\times\) 5 and 6 for Instance 15 \(\times\) 5. The transportation times between different machines are shown in Table 5.  
(1) Solution of the multi-objective model  
Figure 6 shows the feasible solutions for the Instance 5 \(\times\) 5, satisfaction \(\mu\geq\) 0.6. The number of feasible solutions obtained by IWOA was 10, and the feasible solutions of WOA(1), WOA(2), WOA-LEDE, and NSGA-II were 7, 8, 12, and 7. Table 6 shows the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Machine Number** & \(M_{0}\) & \(M_{1}\) & \(M_{2}\) & \(M_{3}\) & \(M_{4}\) & \(M_{5}\) & \(M_{6}\) \\ \hline \(M_{0}\) & 0 & 10 & 15 & 20 & 20 & 10 & 15 \\ \(M_{1}\) & 10 & 0 & 5 & 10 & 20 & 15 & 20 \\ \(M_{2}\) & 15 & 5 & 0 & 5 & 15 & 15 & 15 \\ \(M_{3}\) & 20 & 10 & 5 & 0 & 10 & 20 & 10 \\ \(M_{4}\) & 20 & 20 & 15 & 10 & 0 & 10 & 10 \\ \(M_{5}\) & 10 & 15 & 15 & 20 & 10 & 0 & 20 \\ \(M_{6}\) & 15 & 20 & 15 & 10 & 10 & 20 & 0 \\ \hline \hline \end{tabular} Note: \(M_{0}\) is the unprocessed job storage area, \(M_{1}\)–\(M_{5}\) are the machines, and \(M_{6}\) is the finished job storage area.  
\end{table} 
Table 5: The transportation times of AGVs between machines (unit: seconds). objective function value when the overall satisfaction of the above algorithm is optimal. Figure 7 is the comparison result of the membership degree \(\mu\) of each objective function. According to the calculation results, the optimal satisfaction value \(\mu\) = 0.749 was obtained by IWOA, the makespan of workshop \(Z1\) = 451, the energy consumption of workshop \(Z2\) = 3918, and the processing quality \(Z3\) = 0.834. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \(\mu\) & \(\mu\)**1** & \(\mu\)**2** & \(\mu\)**3** & **Z1** & **Z2** & **Z3** \\ \hline WOA(1) & 0.726 & 0.70 & 0.89 & 0.59 & 449 & 3784 & 0.827 \\ WOA(2) & 0.720 & 0.76 & 0.55 & 0.85 & 445 & 4004 & 0.836 \\ WOA-LEDE & 0.743 & 0.70 & 0.85 & 0.68 & 449 & 3808 & 0.830 \\ NSGA-II & 0.715 & 0.55 & 0.83 & 0.76 & 459 & 3823 & 0.833 \\ IWOA & 0.747 & 0.67 & 0.75 & 0.82 & 451 & 3918 & 0.834 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Maximum satisfaction value of the optimization results with different algorithms. Figure 6: Distribution of feasible solutions for Instance \(5\times 5\). Figure 7: Comparison of membership values. Compared to the optimal makespan goal Z1*, the actual makespan Z1 increased by 22 units, resulting in a \(-33\%\) degree of optimization. However, when measured against other optimal completion times \(Z2^{\star}\) and \(Z3^{\star}\), Z1 showed a reduction of 45 and 32 units, with optimization degrees of 48% and 67%, respectively. In relation to the optimal energy consumption goal Z2*, the observed energy consumption Z2 rose by 167 units, marking a \(-25\%\) degree of optimization. Conversely, it witnessed a decrease of 440 and 237 units compared to the energy consumptions of Z1* and Z3*. Compared with the optimal processing quality Z3*, the processing quality of Z3 was reduced by 0.0063 (optimization degree was \(-18\%\)). Nevertheless, Z3 was increased by 0.019 (optimization degree is 58%) and 0.027 (optimization degree is 82%) compared with the processing quality of Z1* and Z2*. The analysis clearly underscores the necessity and efficacy of a multi-objective model to enhance production quality while concurrently reducing energy consumption in the workshop setting.