## 4 The DABC Algorithm for an EAHFSP
### Scout Bee Phase
Thus, it is concluded that the DABC is significantly superior to the other four compared algorithms when used on the EAHFSP. The DABC algorithm performs better than the other four comparative algorithms on the EAHFSP, mainly depending on the diversified search strategies in the employed bee phase, the novel probability selection method in the onlooker bee phase, and the utilization of the diversity enhancement control strategy. These features help the DABC improve search efficiency, increase population diversity, and avoid falling stagnation. Therefore, the DABC algorithm obtains a better performance on the EAHFSP. ### A Real-Life Example

Roll is a very important tool in a steel rolling production line. In this study, we choose small and medium-sized rolls produced in a workshop to test the efficiency of the DABC. The processing of rolls includes turning, milling, grinding, and assembly. There are three machines for turning (\(M_{11}-M_{13}\)), three machines for milling (\(M_{21}-M_{23}\)), four machines for grinding (\(M_{31}-M_{34}\)), and one assembly machine (\(M_{a}\)). The manufacturing and assembly process is a typical AHFSP. There are 30 components that will be manufactured and assembled into 12 products. The DABC runs 10 times randomly for the real-life example. The non-dominated solutions generated using the DABC algorithm are given in Table 10. A Gantt chart for the optimal solution is illustrated in Figure 8. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Pair** & **Metric** & **R+** & **R–** & \(p\) & \(\alpha\) = 0.05** \\ \hline DABC vs. ABC & \(IGD\) & 0 & 44 & \(7.61\times 10^{-9}\) & Yes \\  & \(c\) & 44 & 0 & \(4.31\times 10^{-10}\) & Yes \\ DABC vs. TICA & \(IGD\) & 7 & 37 & \(1.10\times 10^{-5}\) & Yes \\  & \(c\) & 34 & 10 & \(8.41\times 10^{-4}\) & Yes \\ DABC vs. HPSO & \(IGD\) & 9 & 35 & \(5.80\times 10^{-5}\) & Yes \\  & \(c\) & 31 & 13 & \(2.05\times 10^{-3}\) & Yes \\ DABC vs. CCA & \(IGD\) & 0 & 44 & \(7.61\times 10^{-9}\) & Yes \\  & \(c\) & 44 & 0 & \(7.60\times 10^{-9}\) & Yes \\ \hline \end{tabular}
\end{table} 
Table 8: Results of the [PERSON] test. \begin{table}
\begin{tabular}{c c} \hline
**Algorithm** & **Mean Rank** \\ \hline DABC & 1.36 \\ ABC & 4.57 \\ TICA & 2.30 \\ HPSO & 2.50 \\ CCA & 4.27 \\ \hline \end{tabular}
\end{table} 
Table 9: Results of [PERSON]’s test. ## 6 Conclusions

In this study, a novel DABC algorithm is proposed to investigate an EAHFSP with makespan and TEC minimization. In the employed bee phase, diversified search strategies are designed, and the suitable search strategy for each food source is adaptively selected to improve the search quality. In the onlooker bee phase, a novel probability selection method is introduced to control the selection pressure, and a diversity control strategy is applied to increase the population and avoid the algorithm falling into stagnation. Finally, a series of comparative results demonstrate that the DABC owns excellent performance on the considered EAHFSP. Research using the DABC algorithm for EAHFSPs can assist in selecting the optimal scheduling plan and achieving a balance between economic efficiency and environmental effects. Thus, it is of great significance to managers and manufacturers. However, there are some limitations in this study, for example, some actual processing constraints and deteriorating effects are seldom considered. In the future, we will focus on an EAHFSP

Figure 8: A Gantt chart for the optimal solution. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Solutions** & **Makespan** & **TEC** \\ \hline
1 & 192.88 & 5555.96 \\
2 & 213.37 & 5391.84 \\
3 & 178.26 & 6021.80 \\
4 & 202.60 & 5449.45 \\
5 & 178.78 & 5610.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The non-dominated solutions generated using DABC. with more realistic constraints and a more complex processing environment, such as transportation time, preventive maintenance, uncertainty in processing, deteriorating effects, and multi-factory manufacturing.