###### Abstract  
Due to fabrication difficulties, separately-polished segmented mirrors cannot meet the co-phasing surface shape error requirements in the segmented telescope system. Applying the global radius of curvature (GRoC) actuation system for the individual segments has become an effective solution in space-based telescopes. In this paper, we designed a segmented mirror with a GRoC actuation system. The direct optimization by numerical simulations has low computational efficiency and is not easy to converge for optimizing the actuation point's position on the segmented mirror. For this problem, three common surrogates, including polynomial response surface (PRS), radial basis function neural network (RBFNN), and kriging (KRG), were summed to propose the multiple surrogates (MS) which have the higher approximate ability. The surrogates were then optimized through the multi-island genetic algorithm (MIGA), and the segmented mirror met the design requirement. Compared with direct optimization through numerical simulations, the results show that the proposed multiple-surrogate-based optimization (MSBO) methodology saves computational cost significantly. Besides, it can be deployed to solve other complex optimization problems. multiple-surrogate-based optimization; multi-island genetic algorithm; Latin hypercube sampling; segmented mirror with a GRoC actuation system +
Footnote †: journal: Accepted: 21 November 2020;  
1  
[PERSON], [PERSON], Y.  
target map for the finely-polished. The surface shape error root mean square (RMS) after the second polishing can reach 20 nm [4; 5]. (2) In the co-phasing process, the system performs micro-control on the GRoC. The first application has a broad adjustment range (\(\pm\) 5 mm), and the second application has a small adjustment range (\(\pm\)0.15 mm) [6]. Since the actuation point of the GRoC actuation system on the segmented mirror's back directly affects the curvature adjustment accuracy, the actuation point's position needs to be optimized. Complicated structural optimization through numerical simulations is unavailable since searching for the optimum typically requires thousands or even millions of simulations. To alleviate the computational burden, the surrogate-based optimization methodology (SBOM) becomes the right choice. It simplifies the relationship between output responses and design variables through surrogates, then directly optimizes the surrogates. [PERSON] et al. optimized the 2.8 m diameter circular mirror's main structural parameters based on the back propagation (BP) neural network surrogate. The error between the surrogate and the simulation was less than 7.09% [7]. [PERSON] et al. and [PERSON] et al. used the radial basis function neural network (RBFNN) for the design of the sealing structure and shelter location problem under uncertainty of road networks, respectively, which significantly improved optimization efficiency [8; 9]. [PERSON] et al. optimized the functionally-graded plates using an RBFNN surrogate [10]. [PERSON] et al. carried out a many-objective optimization for a deep-sea aquaculture vessel by RBFNN surrogate [11]. Based on the response surface method (RSM) surrogate, [PERSON] et al. carried out a multi-objective optimization design on the robot arm's size parameters, which improved the computational efficiency by 90% compared with optimization by numerical simulation [12]. [PERSON] et al. used an RSM surrogate to replace the 3-D finite element method models in the design of a transverse-flux permanent magnet linear synchronous motor [13]. With the help of an RSM surrogate, [PERSON] et al. and [PERSON] et al. achieved good results in designing an outer rotor permanent magnet motor and designing a new compliant planar spring, respectively [14; 15]. [PERSON] et al. used a Kriging surrogate to replace the complicated optimization problem of multiple wing sails considering the flow interaction effect, which effectively improved the computational efficiency [16]. [PERSON] et al.