## 5 Experimental Results and Cases Analysis
### Cases Analysis  
This section conducts a detailed analysis on two representative cases from 100 test cases in Section 5.2, evaluating algorithmic performance under typical real-world production conditions. Such analysis is particularly crucial for evaluating the performance of different optimization algorithms in practical applications, as it helps identify which algorithms can more effectively adapt to changes in raw materials, thereby maintaining the continuity and efficiency of the production process. In both of the two cases, the total raw material flow is 18t/h, and the proportion ranges for each bin as well as the elemental composition limits of the blended pellets specified by the production plan are shown in Table 4.  
In Table 5, Case I presents a resource-constrained scenario in which a specific raw material is approaching depletion, necessitating the formulation of a reasonable scheme. Among the multi-objective optimization solution sets provided by the four optimization algorithms, the final solution for each algorithm is chosen based on the weighted sum and normalized fitness values. This approach allows for the selection of a solution that comprehensively considers multiple objectives, with the goal balancing different performance metrics such as cost, efficiency, and quality. Facing the urgent scenario where the remaining materials in bin 6 and bin 8 were nearly exhausted, the IMOAHLO algorithm demonstrated a high degree of adaptability and intelligent decision-making by proactively deactivating bin 6, which contained an extremely low remaining material volume. The NSGA-II and MOHLO algorithms made similar decisions. The remaining material weight in bin 8 is relatively low, but since the current proportion is set at 0.4, the material in bin 8 will be quickly depleted if this proportion remains unchanged. The IMOAHLO algorithm preemptively adjusted the proportion from 0.4 to 0.07, effectively increasing the operation time of the formulation \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & \\ \hline Bin & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ Min & 0.01 & 0.01 & 0 & 0.10 & 0.05 & 0.01 & 0.02 & 0.03 & 0.02 & 0.02 & 0.01 \\ Max & 1 & 0.10 & 0 & 0.44 & 0.46 & 0.10 & 0.46 & 0.46 & 0.25 & 0.40 & 1 \\ \hline \hline \multicolumn{10}{c}{Element Content Limitations} \\ \hline Element & C & C & C1 & Zn & C/O & C1/Zn \\ Min & 0.08 & 0 & 0.01 & 0 & 0 & 0 \\ Max & 0.1 & 0.008 & 0.043 & 1.5 & 1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Proportion limitations and element content limitations. scheme from the original 1.28 h to 7.32 h, thereby providing sufficient time for subsequent material replenishment. Table 6 presents the fitness function results of the four optimization algorithms and the manual formulation scheme. The IMOAHLO algorithm exhibited the best performance. An element content value of 0 indicates that the elemental composition of the blended pellets met the required specifications. The similarity difference between the new scheme and the original one was 1.1. The operation time is \(-\)7.32 where the negative sign indicates that the system can continue to operate for 7.32 h under the current conditions. A start-stop switching value of 2 means that two bins were either deactivated or activated. In the table, the manual formulation scheme failed to consider the maximum operation time, which would lead to rapid material depletion and frequent updates of the formulation scheme. The MOHLO and SMPSO algorithms generated similar fitness function values and did not significantly extend the operation time. The IMOAHLO algorithm adjusted the proportion in bin 8 from the original scheme's 0.4 to 0.07 and triggered only two start-stop operations, achieving a longer operation time with minimal adjustments.