## 4 Optimization Results and Verification  
### BH-ACO\({}_{\rm R}\) Optimization Result  
Aiming at the optimization of energy consumption and surface roughness while turning on CNC lathes, an optimization program was written, which is based on the BH-ACO\({}_{\rm R}\) improved algorithm. It was realized in the Matlab2016a environment. The algorithm's parameters used in the program are shown in Table 4.  
In the case of setting the weight coefficient \(c\) of the multi-objective optimization function to 0.5, the variation in the optimized values of the specific turning energy and  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Iterations & 200 & \(v_{\rm cmax}\) & 60 \\ Initial population \(k\) & 10 & \(f_{\rm min}\) & 0.2 \\ Reinforcement factor & 0.5 & \(f_{\rm max}\) & 0.4 \\ \(q\) & 0.8 & \(a_{\rm pmax}\) & 0.3 \\ Offset distance ratio \(\zeta\) & 40 & \(a_{\rm pmin}\) & 0.7 \\ \hline \hline \end{tabular}
\end{table}
Table 4: BH-ACO\({}_{\rm R}\) algorithm parameter settings.  
Figure 6: BH-ACO\({}_{\rm R}\) algorithm flow chart.  
The optimization results regarding turning specific energy and material surface roughness obtained by optimizing the BH-ACO\({}_{\text{R}}\) and ACO\({}_{\text{R}}\) with different weight coefficients \(c\) are shown in Table 5.  
In order to demonstrate the performance of the algorithm more intuitively, the results yielded by the BH-ACO\({}_{\text{R}}\) and ACO\({}_{\text{R}}\) are shown in Figure 9. From Figure 9, it can be seen that the search result distribution of the ACO\({}_{\text{R}}\) is relatively concentrated. This is because when \(c\) takes different values, the distance difference between the solutions obtained by the ACO\({}_{\text{R}}\) algorithm is significant. The search results of the BH-ACO\({}_{\text{R}}\) algorithm are relatively evenly distributed, indicating that the BH-ACO\({}_{\text{R}}\) has to some extent avoided local optimization problems.  
In order to further verify the performance of the algorithm proposed in this paper, the BH-ACO\({}_{\text{R}}\) was applied to problems that were optimized in other studies. Table 6 lists the optimization results compared with the algorithms used in different studies. Compared with the results obtained using the orthogonal optimization method adopted by [PERSON] [19], it was found that the grinding specific energy (SEG) was reduced by 43.39%, and the surface roughness, Ra, was reduced by 4.29%. Although there was little improvement in Ra optimization, the SEG was significantly reduced, meaning that the BH-ACO\({}_{\text{R}}\) can further reduce grinding energy consumption while achieving the same processing quality. Compared with the GA algorithm adopted by [PERSON] [20], the algorithm proposed in this paper can optimize all three targets to a certain extent, especially the removal rate  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**BH-ACO\({}_{\text{R}}\)**} & \multicolumn{2}{c}{**ACO\({}_{\text{R}}\)**} \\ \cline{2-5} \cline{5-5} \(c\) & _SEC_ (/mm\({}^{3}\)) & _Ra_ (\(\upmu\)m) & _SEC_ (/mm\({}^{3}\)) & _Ra_ (\(\upmu\)m) \\ \hline
0.1 & 2.776 & 1.367 & 2.775 & 1.366 \\
0.2 & 2.682 & 1.525 & 2.776 & 1.367 \\
0.3 & 2.638 & 1.602 & 2.752 & 1.382 \\
0.4 & 2.579 & 1.778 & 2.615 & 1.792 \\
0.5 & 2.536 & 1.956 & 2.598 & 1.843 \\
0.6 & 2.458 & 2.282 & 2.431 & 2.491 \\
0.7 & 2.418 & 2.665 & 2.352 & 2.721 \\
0.8 & 2.370 & 2.892 & 2.332 & 3.101 \\
0.9 & 2.312 & 3.119 & 2.311 & 3.119 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Optimization results of turning under different weights.  
Figure 9: Comparison of optimization results between BH-ACO\({}_{\text{R}}\) and ACO\({}_{\text{R}}\).  
M\({}_{\text{R}}\), which reached 78.1%. Compared with the strengthening Pareto algorithm developed by [PERSON] [21], the BH-ACO\({}_{\text{R}}\) can acquire basically the same result in terms of surface roughness but can also improve the material removal rate (MRR) by 20.9%.