## 4 Discussion  
In this paper, a segmented mirror with a GRoC actuation system was designed. To solve the problem of insufficient approximation ability of existing surrogates, we proposed multiple surrogates to optimize the actuation point's position on the segmented mirror's back.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Surrogate** & **MS** & **PRS** & **RBFNN** & **KRG** \\ \hline \(Y_{\text{RMS}}\) & 0.92 & 0.87 & 0.90 & 0.90 \\ \(\delta_{\text{MAX}}\) & 0.91 & 0.85 & 0.85 & 0.64 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The determination coefficient of surrogates.  
Figure 11: Determination coefficient of multiple surrogates: (**a**) \(Y_{\text{RMS}}\) and (**b**) \(\delta_{\text{MAX}}\).  
Figure 12: Iterative process of optimization: (**a**) the optimization by numerical simulation and (**b**) the multiple-surrogate-based optimization.  
The comparison of approximation ability between the multiple surrogates and some existing surrogates (PRS, RBFNN, and KRG) in Figure 11 shows that the multiple surrogates' determination coefficient remained the highest during the iteration of the algorithm. It was the first to reach the decision condition (\(R^{2}>0.9\)) with 55 sampling points, and the determination coefficients of all surrogates at that time are shown in Table 4. The comparison of computational efficiency is shown in Figure 12, and it can be seen that the multiple surrogates needed 55 iterations of the numerical simulation to satisfy the convergence condition. In comparison, the direct optimization cannot fully converge after 200 iterations of numerical simulation. This might be because the numerical simulation is too complicated, and the optimum is affected by the local minima. The approximation of the numerical simulation is equivalent to smooth filtering, which reduces the local minima's influence and makes the optimization easier to converge. Some conclusions can be drawn:  
1. The optimization methodology used in this work provides a solution for designing a segmented mirror with a GRoC actuation system.
2. The proposed multiple surrogates have higher approximation ability than a single surrogate (PRS, RBFNN, and KRG), and at the same time, solve the problem of difficulty in choosing a reasonable surrogate in an approximation optimization.
3. The proposed multiple-surrogate-based optimization methodology effectively reduces the computational cost of optimization problems and makes the optimization problems easier to converge. In addition, this methodology is also suitable to be extended to other complex optimization problems.  
It should be noted that although our multiple surrogates achieved good results in this work, other surrogates such as deep learning could also be added to them. Hence, more surrogates will be added to our multiple-surrogate-based optimization methodology in the future.  
**Author Contributions:** Project administration, S.W.; methodology, J.D. and S.W.; software, Z.L.; writing--original draft, S.W.; writing--review and editing, S.X. and B.X. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National key research and development plan of China, grant number 2016 YFE020500 and the National Natural Science Foundation of China (NSFC), grant number 61905241.  
**Conflicts of Interest:** The authors declare no conflict of interest.