## 5 IICA-QL for EEMsMIAJSP
### Revolution Based on Hyper-Heuristic Variable Neighborhood Search
This clearly shows that the dynamic adaptive adjustment strategy for the operator parameter based on Q-learning significantly improves the algorithm's performance, especially in larger and more complex problem instances. Additionally, this strategy ensures that the algorithm can maintain a robust balance between exploration and exploitation, further enhancing the quality of the Pareto front. Figure 8: Box and line plots of CPU time between IICA-QL and IICA-QL-PFE/IICA-QL-AE. Figure 7: Box plots of three metrics between IICA-QL and IICA-QL-PFE/IICA-QL-AE. ### Comparison with Other Algorithms

Since no existing research has been conducted on solving the EEMsMIAJPSP, to verify the effectiveness of the algorithm, IICA-QL is compared with the algorithms BPBMO [31], PSO-GA [35], and KBOA [28], which solve similar problems to the EEMsMIAJPSP. The parameters for BPBMO, PSO-GA, and KBOA are chosen as specified in their respective references. Each of the four algorithms is independently run 10 times for the runtime determined by the problem scale, and the average values of the evaluation metrics are calculated. The C-metric, GD, and HV values for each algorithm across 18 problem scales are shown in Table 7, with the best value for each metric highlighted in bold. As seen in Table 7 and Figure 10, the GD and HV values obtained by IICA-QL are superior to those of BPBMO, PSO-GA, and KBOA in all test instances. Specifically, the performance of IICA-QL in terms of the GD metric, demonstrating its ability to find solutions that are very close to the Pareto optimal front in the solution space, highlights its significant advantage in convergence. From the HV metric, it is evident that the values obtained by IICA-QL are much higher than those of the other three algorithms, indicating that IICA-QL not only finds high-quality solutions but also maintains solution diversity, covering a broader Pareto front region. These results clearly validate the effectiveness of IICA-QL in solving the EEMsMIAJPSP, showcasing its superiority in both convergence and diversity compared to existing approaches. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**C-Metric**} & \multicolumn{2}{c}{**GD**} & \multicolumn{2}{c}{**HV**} \\ \cline{2-7} O/J/A\_MT/IK & **IICA-QL(A)** & **IICA-nQL (B)** & **IICA-QL** & **IICA-nQL** & **IICA-QL** & **IICA-nQL** \\ \cline{2-7}  & **C(A,B)** & **C(B,A)** & & & & \\ \hline
25/13/22.2 & 2/2/2 & **



To further illustrate the performance of the compared algorithms, Figure 11 presents the Pareto results obtained by four algorithms on small-scale (25/13/22_2/2/2), medium-scale (82/42/71_3/3/3), and large-scale (202/104/175_4/3/4) instances. As shown in the figure, the Pareto front obtained by IICA-QL outperforms those of the other three algorithms across different instances, indicating that IICA-QL is able to achieve non-dominated solutions with lower makespan (\(C_{\text{max}}\)) and total energy consumption (\(TEC\)) compared to BPBMO, PSO-GA, and KBOA. This further validates the effectiveness of IICA-QL in both convergence and diversity across different problem scales, as it consistently generates higher quality solutions with a broader coverage of the Pareto front. ### Discussion

This paper presents a solution to the energy-efficient multi-stage multi-level assembly job shop scheduling problem (EEMsMIAJSP), a highly complex scheduling problem that arises in the manufacturing of multi-level products like ball valves and bogies. The multi-stage, multi-level structure of the EEMsMIAJSP involves not only the processing and assembly of various components but also intricate interdependencies between stages. These interdependencies often result in idle times, which contribute significantly to unnecessary energy consumption. The need to optimize both production efficiency and energy consumption makes the EEMsMIAJSP a challenging, yet important, problem in the manufacturing industry.