## 6 Results and Discussion
### Optimization Results of Energy Savings for Different Types of Batches  
The previous Section 6.1 has verified the validity of the model built in this paper, and the reheating method used is a mixture of cold- and hot-charging slabs. In this subsection, the energy savings will be considered for the case where the reheating furnace is completely loaded with hot-charging slabs or cold-charging slabs and discussed in comparison with the mixed situation. (1) Hot-charge mode  
In hot-charge mode (including HCR and DHCR), the energy consumption is referred to in Section 3.3. Similarly, taking 12 batches as an example, among them, batches 1-11 are the DHCR type, and batch 12 is the HCR type. Table 8 lists the castings included in each hot batch. In the reheating furnace, when HCR slabs are converted to DHCR slabs, more energy is wasted. Therefore, in the reheating process, priority is given to heating DHCR slabs and then HCR slabs. The Gantt chart obtained is shown in Figure 8. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Algorithms**} & \multirow{2}{*}{**Models**} & **Rated Gas** & **Gas Waste** & **Proportion** & **Completion Time** \\  & & **Consumption (GJ)** & **(GJ)** & **(\%)** & **(min)** \\ \hline \multirow{3}{*}{Ordered pair bat algorithm} & Minimum & 32,522.6 & 1855.6 & 5.71 & 3832 \\  & completion time & 32,522.6 & 549.3 & 1.69 & 4073 \\  & Minimum energy waste & 32,522.6 & 1066.9 & 3.28 & 3868 \\  & Minimum & 32,522.6 & 2066.3 & 6.35 & 3852 \\ Hamming distance & completion time & 32,522.6 & 549.3 & 1.69 & 4274 \\  & Minimum energy waste & 32,522.6 & 1071.2 & 3.29 & 4083 \\ Hamming distance & completion time & 32,522.6 & 2121.4 & 6.52 & 3856 \\  & Minimum energy waste & 32,522.6 & 549.3 & 1.69 & 4501 \\  & Mixed model & 32,522.6 & 1158.5 & 3.56 & 4239 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of three algorithms. The mixed scheduling consumes 323.7 GJ more gas resources, mainly due to the energy wasted during the conversion of DHCR to HCR batches. In comparison, using the minimum completion time objective function, the gas waste obtained is 633.4 GJ. The batch scheduling of hot-charge mode has a total rated consumption of 18,532.8 GJ. So, compared to the minimum time model, the model in this section saves 1.67% of the total consumption. (2) Cold-charge mode  
Referring to Section 3.4 for the energy consumption in cold-charge mode (CCR), Table 9 lists the castings included in each cold batch, and the Gantt chart obtained is shown in Figure 9.  
Because the slab needs to wait in the slab warehouse before being heated and rolled in cold mode, the front of the rolling line is in an idle state. The total rated consumption is 49,678.2 GJ, and the reheating furnace consumes 194.2 GJ more gas resources, accounting for 0.39%. At this time, if the minimized total time objective function is adopted, the total amount of over-consumption is 578.0 GJ, accounting for 1.16%. Therefore, 0.77% of the energy can be saved. Figure 8: Scheduling Gantt chart in hot-charge mode. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Batches**} & **Batch Types** & **Corresponding Castings** & **Batches** & **Batch Types** & **Corresponding Castings** \\ \hline
1 & DHRCR & 1, 2 & 7 & DHCR & 2, 3 \\
2 & DHCR & 7, 8 & 8 & DHCR & 19, 20 \\
3 & DHCR & 15, 16 & 9 & DHCR & 4, 5 \\
4 & DHCR & 11, 12 & 10 & DHCR & 9, 10 \\
5 & DHCR & 17, 18 & 11 & DHCR & 6, 7 \\
6 & DHCR & 13, 14 & 12 & HCR & 21, 22 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Castings schedule included in hot batch types. Based on the above analysis, the energy-saving effect on continuous casting-hot rolling scheduling varies under different batch types.