## 5 Experimental Results and Cases Analysis
### Cases Analysis
Benefiting from the neighborhood search operator's fine-tuning of local solutions and an adaptive mechanism that prioritizes the social learning operator in later iterations to accelerate convergence, the IMOAHLO algorithm can rapidly adjust its strategy to devise a reasonable formulation scheme in a resource-constrained production environment. Case II illustrates another multi-objective conflict scenario that demands a superior formulation scheme. Although the original scheme can achieve long-term operation, the C element content in the blended pellets reached 11.23%, exceeding the standard by 1.23%. This indicated that there was still room for optimization in terms of element composition. Table 7 shows the optimization results of the various algorithms. From the optimization \begin{table}
\begin{tabular}{c c c c c} \hline
**Scheme**Function & **Element** & **Scheme** & **Operation** & **Start-Stop** \\  & **Content** & **Similarity** & **Time** & **Switching** \\ \hline Original & 0.39 & 0.00 & \(-\)1.28 & 0 \\ IMOAHLO & 0.00 & 1.10 & \(-\)7.32 & 2 \\ NSGA-II & 0.00 & 1.14 & \(-\)7.17 & 3 \\ MOHLO & 0.00 & 1.24 & \(-\)4.71 & 2 \\ SMPSO & 0.04 & 0.90 & \(-\)5.12 & 2 \\ Manual & 0.00 & 0.22 & \(-\)1.19 & 0 \\ \hline \end{tabular}
\end{table} 
Table 6: The objective function results of different algorithms in Case I. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline
**Bin** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** \\ \hline Weight (t) & 27.7 & 52.0 & 51.3 & 34.7 & 21.9 & 1.1 & 58.2 & 9.2 & 31.8 & 23.5 & 23.5 \\ \hline C content & 8.458 & 84.400 & 0.000 & 4.214 & 4.724 & 4.724 & 4.724 & 19.607 & 3.530 & 8.458 \\ Cl content & 0.939 & 0.000 & 0.000 & 0.080 & 0.008 & 0.008 & 0.008 & 0.008 & 6.130 & 0.320 & 0.939 \\ Zn content & 3.162 & 0.000 & 0.000 & 0.252 & 4.008 & 4.008 & 4.008 & 4.008 & 3.409 & 12.069 & 3.162 \\ Fe content & 46.190 & 0.000 & 0.000 & 63.583 & 44.627 & 44.627 & 44.627 & 44.627 & 38.299 & 39.736 & 46.19 \\ FeO content & 29.370 & 0.000 & 0.000 & 13.943 & 39.791 & 39.791 & 39.791 & 39.791 & 6.642 & 17.818 & 29.370 \\ \hline Original & 0.00 & 0.02 & 0.00 & 0.15 & 0.20 & 0.03 & 0.00 & 0.40 & 0.20 & 0.00 & 1.00 \\ \hline IMOAHLO & 0.00 & 0.07 & 0.00 & 0.21 & 0.15 & 0.00 & 0.44 & 0.07 & 0.06 & 0.00 & 1.00 \\ NSGA-II & 0.00 & 0.08 & 0.00 & 0.12 & 0.17 & 0.00 & 0.42 & 0.06 & 0.06 & 0.09 & 1.00 \\ MOHLO & 0.00 & 0.08 & 0.00 & 0.41 & 0.06 & 0.00 & 0.07 & 0.10 & 0.05 & 0.23 & 1.00 \\ SMPSO & 0.00 & 0.06 & 0.00 & 0.23 & 0.21 & 0.01 & 0.10 & 0.10 & 0.07 & 0.22 & 1.00 \\ Manual & 0.00 & 0.10 & 0.00 & 0.15 & 0.20 & 0.03 & 0.00 & 0.43 & 0.09 & 0.00 & 1.00 \\ \hline \end{tabular}
\end{table} 
Table 5: Optimization results of different algorithms in Case I.  
results, it is evident that each algorithm conducted its search within the constraints based on the originally set values. Table 8 summarizes the fitness function results obtained by each algorithm under this case. Although the manually implemented formulation scheme significantly optimized the elemental content limits after adjustments, there remains room for improvement because it is challenging for humans to fully consider all factors. In contrast, the IMOAHLO algorithm, by leveraging its broader solution search space, successfully identified a solution that completely meets the elemental content requirements. Compared with the NSGA-II and MOHLO algorithms, which also satisfy the element ratio requirements, the IMOAHLO algorithm extended the operation time to a maximum of 10.30 h, thereby reducing workload and enhancing system stability. Moreover, the scheme similarity provided by the IMOAHLO algorithm is significantly lower than that of the SMPSO and MOHLO algorithms. These results indicate that the IMOAHLO algorithm can better balance solution diversity and convergence while satisfying the constraints.