## 1 Introduction  
Observing and controlling atoms at room temperature poses challenges because of their high energy states, but laser-cooled atoms serve as an advantageous experimental medium [1; 2; 3; 4; 5; 6; 7]. Cold atoms exhibit reduced motion speed and weak interaction forces, making them promising for applications in quantum optics, ultracold collisions, Bose-Einstein condensation, and precise measurements [8; 9; 10; 11]. To manipulate cold atoms effectively in experiments, a magneto-optical trap (MOT) is utilized, which converges atoms via a combination of light and magnetic fields on the basis of this principle [12; 13; 14; 15]. The fundamental concept of the MOT was initially introduced by [PERSON] and subsequently put into practice through collaboration with the research groups of [PERSON] and [PERSON] [16; 17]. The earliest MOT experiments involved the utilization of precooled sodium atomic beams. The original six-beam MOT setup necessitated a costly precooling apparatus and was relatively intricate [14]. In 1990, the [PERSON] team introduced the concept of background steam loading, simplifying the experimental procedure and facilitating the widespread adoption of MOT technology [18]. Currently, MOT technology is extensively employed in atomic physics research, encompassing various trapped atom types such as alkali metals, alkaline earth metals, inert gasses, and radioactive isotopes [19], with MOT configurations continuously evolving [20; 21; 22; 23; 24; 25; 26]. To enhance the spin polarization of cold atomic ensembles, [PERSON] et al. proposed a spin-polarized MOT [27]. To address the limitation of cold atom density due to radiation trapping, [PERSON] et al. introduced a dark MOT, which increased the atomic density within the trap center and extended the lifespan of cold atoms [28]. Various MOT schemes have been devised to streamline MOT structures, including single-beam MOTs, four-beam MOTs, and five-beam MOTs [11; 29; 30]. Two-dimensional MOTs, achieved by adjusting the axial beams of three-dimensional MOTs, have been widely adopted to convert trapped cold atomic ensembles into atomic beams [31; 32; 33]. Recent advancements in miniaturized cold atom sensor technology, particularly chip-level MOTs such as grating MOTs, have emerged as a prominent research focus [34; 35]. These chip-level MOTs offer reduced power consumption and compact size, opening new avenues for expanding the application scope of atomic MOTs. In addition to altering the structure, the optimization of the MOT can also be achieved by adjusting the control parameters. This process is referred to as parameter optimization. The primary aim of parameter optimization is to evaluate how the control parameters of the MOT affect its performance index, with the goal of identifying the most effective control parameters. This optimization procedure can improve MOT performance and is crucial for the progression of MOT technology. As a vital element of cold atom interferometers, factors such as the quantity of atoms captured by the MOT, the temperature of the cold-atom ensemble, and the duration of trapping significantly affect performance. For example, in optical lattice clocks, a greater number of atoms trapped in the MOT results in an increased signal-to-noise ratio in the data collected [36]. Conversely, in atomic gravimeters, the atomic diffusion effect caused by temperature variations can reduce the contrast of interference fringes and introduce systematic errors in measurements [37]. Furthermore, in atomic gyroscopes, the quest for improved measurement accuracy and bandwidth requires enhanced atom-loading efficiency [38]. Additionally, owing to the fundamental similarities in the principles underlying different types of MOTs, parameter optimization not only enhances the trapping efficiency of existing MOTs but also has substantial implications for the advancement of novel MOT technologies.