Optimizing Structural Parameters and Layout of Fiber Positioners with the Whale Optimization Algorithm for LAMOST

Abstract Robotic fiber positioner (RFP) arrays are essential for multiobject spectroscopic telescopes. To improve the survey efficiency, they are densely arranged on the focal planes with overlapped patrol areas, guaranteeing full coverage and increasing the number of RFPs. However, this does not guarantee a proportional increase in observable targets due to collisions. To achieve optimal performance of RFPs across various target distributions, an effective method is necessary for optimizing the parameter settings and array layouts. This study addresses this challenge by applying optimization algorithms to minimize collision risks while maximizing target coverage in different configurations. Initially, the whale optimization algorithm is used to optimize RFPs with mixed arm-length ratios (three distinct ratios). The design is then refined by jointly optimizing arm length, mixed arm ratios, and variable pitch. Simulations based on the Large Sky Area Multi-Object Fiber Spectroscopic Telescope system show that RFPs with equal arm lengths and a fixed pitch of 10.4 mm provide optimal performance for both uniform and positional targets. This method offers a practical solution for designing and arranging RFPs on focal planes, thereby enhancing the performance of fiber positioning systems. Additionally, it can be applied to other major astronomical instruments such as the Dark Energy Spectroscopic Instrument and the Multi-Object Optical and Near-infrared Spectrograph.