## 5 IICA-QL for EEMsMIAJSP
### Revolution Based on Hyper-Heuristic Variable Neighborhood Search
### The Effectiveness of the Adaptive Trigger Mechanism for the Energy-Efficient Strategy

To verify the effectiveness of the adaptive trigger mechanism for the energy-efficient strategy, IICA-QL (denoted as A) is compared with IICA-QL executing the energy-efficient strategy on Pareto solutions (IICA-QL-PFE, denoted as B) and IICA-QL executing the energy-efficient strategy on all individuals (IICA-QL-AE, denoted as C). Using the same computation time as the termination condition, each algorithm runs independently, 10 times on 18 test instances. The average values of C-metric, GD, and HV obtained are shown in Table 4, with the best value for each metric highlighted in bold. The runtime of each algorithm on each scale is recorded in Table 5. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Notation**} & \multicolumn{4}{c}{**Factor Level**} \\ \cline{3-6}  & & **1** & **2** & **3** \\ \hline \(P_{s}\) & population size & 50 & 100 & 150 \\ \(N_{im}\) & number of imperialists & 3 & 5 & 7 \\ \(P_{a}\) & assimilation probability & 0.7 & 0.8 & 0.9 \\ \(P_{r}\) & revolutionary probability & 0.1 & 0.2 & 0.3 \\ \(\alpha\) & learning rate & 0.1 & 0.2 & 0.3 \\ \(\gamma\) & discount factor & 0.7 & 0.8 & 0.9 \\ \(\varepsilon\) & greed factor & 0.3 & 0.6 & 0.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter levels. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Level** & \(P_{s}\) & \(N_{im}\) & \(P_{a}\) & \(P_{r}\) & \(\alpha\) & \(\gamma\) & \(\varepsilon\) \\ \hline
1 & 0.7855 & **0.7943** & 0.7786 & **0.7912** & 0.7868 & 0.7844 & 0.7851 \\
2 & **0.7986** & 0.7814 & **0.7923** & 0.7838 & **0.7926** & 0.7856 & **0.7974** \\
3 & 0.7786 & 0.7869 & 0.7917 & 0.7877 & 0.7832 & **0.7926** & 0.7801 \\ Delta & 0.0200 & 0.0130 & 0.0138 & 0.0074 & 0.0094 & 0.0083 & 0.0174 \\ Rank & 1 & 4 & 3 & 7 & 5 & 6 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average RVs and ranks of each parameter. Table 5 and Figure 8, where the execution time of IICA-QL is comparable to that of IICA-QL-PFE and significantly faster than that of IICA-QL-AE. This demonstrates that while IICA-QL-PFE also applies the energy-efficient strategy, the adaptive trigger mechanism in IICA-QL ensures that potential solutions are not lost while simultaneously speeding up the convergence process by avoiding unnecessary evaluations and making more efficient use of computational resources. The significantly longer time required by IICA-QL-AE suggests that applying the energy-efficient strategy indiscriminately to all individuals results in an inefficient search. By contrast, the adaptive trigger mechanism in IICA-QL ensures a balance between search efficiency and solution quality, optimizing both the computational cost and the effectiveness of the search. ### Effectiveness of Operator Parameter Adaptive Adjustment Based on Q-Learning

To verify the effectiveness of the dynamic adaptive adjustment of the operator parameter based on Q-learning, IICA-QL (denoted as A) is compared with IICA-QL without this strategy (IICA-nQL, denoted as B), where the UX parameter is set to 0.55. Using the same computation time as the termination condition, each algorithm runs independently 10 times on 18 test instances. The average values of C-metric, GD, and HV obtained are shown in Table 6, with the best value for each metric highlighted in bold. From the C-metric results in Table 6 and Figure 9, it can be seen that in 17 out of 18 test instances, C(A,B) is greater than C(B,A), and C(A,B) shows an increasing trend. This indicates that the non-dominated solutions obtained by IICA-QL generally dominate those obtained by IICA-nQL, and the advantage becomes more pronounced as the problem scale increases. From the GD and HV metrics, it is evident that in all test instances, the values for IICA-QL are better than those for IICA-nQL, indicating that IICA-QL has better convergence and diversity compared to IICA-nQL.