# Multi-Objective Parameter Optimization of Flexible Support System of Optical Mirror
## 1 Introduction  
With the development of information technology, modern optical mirrors are being enhanced rapidly toward large apertures and high precision [1, 2]. The increase in the requirements with regard to optical mirror aperture and precision has increased the difficulty of processing, as well as the requirements for processing equipment [3, 4]. At present, the processing of large optical mirrors depends mainly on robots and computer numerical control (CNC) machine tools. Manual grinding is rarely used [5, 6]. Furthermore, the optical mirror support systems used in processing are mostly traditional base supports, mechanical Whiffletree mechanism support systems, or hydraulic support systems [7]. Although these can meet the rigidity requirements of optical mirror processing, the rigiditycannot be adjusted. If the impact force of the polishing disc on the surface of an optical mirror being processed is excessive, it may damage the surface. This is particularly so for large, lightweight thin mirrors. The force may crush the mirror surface, and thereby, result in the consumption of a substantial amount of manpower and material resources [8; 9; 10]. Therefore, the performance parameters of the bottom support system are crucial for ensuring the surface forming accuracy of optical mirrors, in addition to the improvement of the motion accuracy of robot and machine tool [11; 12]. In recent years, many scholars have conducted a substantial amount of research on the support methods used in optical mirror processing, installation and posture adjustments. In addition, a few scholars optimized the structural parameters of support systems. [PERSON] et al. developed an active optics system based on a passive and whiffletree-supported mirror to compensate for the gravity-induced deformation and correct low-order aberrations caused by thermal variations and gravity relief during observing periods [13]. To counteract the effect of gravity deformations on the mirror surface of a space telescope's main mirror during installation, [PERSON] et al. improved the support system by using a flexure device with mechanical spacers instead of the traditional bipod flexure device [14]. To realize an ultra-light design of large-caliber splicing mirrors, [PERSON] et al. proposed a mirror support and drive integrated design method, combined with optical precision and surface accuracy of mirrors and position adjustment [15]. It was based on an analysis of the existing design schemes. [PERSON] et al. proposed a design scheme using carbon fiber-reinforced plastic truss rods for passive thermal compensation to improve the thermal effect of telescopes [16]. In addition, the function of thermal expansion coefficient and truss rod length was determined according to the principle of equal axial distance after deformation. [PERSON] et al. used a flexible mechanism with a cross spring pivot, in the fields of precision engineering and aerospace, and established its precise load rotation and center displacement model [17]. [PERSON] et al. applied the truss support structure to a space camera. They optimized the truss structure size through the weighting method to ensure good dynamic and static performance by large-area, off-axis three-mirror anastigmat space cameras [18]. Many of these scholars also use flexible support system (FSS) in the field of optical mirror support. To improve the fabrication efficiency and testing accuracy of meter-scale, [PERSON] et al. designed and manufactured a few hydraulic support units and tested these through a 4 m SiC mirror [19]. Therefore, the high accuracy of the designed support system was established. In order release the thermal stress of the optical primary mirror, [PERSON] et al. proposed a novel kinematic flexure mount, composed of three identical chains and analyzed the stiffness characteristics of its structure [20]. [PERSON] et al.