## 1 Introduction
To save computation costs and ensure the reliability of the design method, this paper uses the Latin hypercube initialization method instead of random initialization. Then, the optimization results using different initialization methods are analyzed. Another key to applying the multi-objective particle swarm optimization algorithm to the optimal design of aerostatic bearings is calculating the static performance (bearing capacity and gas consumption) through the basic structural parameters of the bearings. The Reynolds equation of compressible fluid is the basic equation for calculating the performance of gas bearings. Therefore, the essence of calculating the static performance of aerostatic bearings is to solve the Reynolds equation. [PERSON] researched the pressure distribution of the gas-lubricated circular thrust bearing by assuming that the flow pattern near an inlet could be divided into the supersonic flow region, the subsonic flow region, and the viscous and isothermal flow region. He found that the pressure distribution at the orifice outlet was not consistent with the Reynolds equation [17]. [PERSON] used the spring and damping coefficients to study the dynamic performance and stability of gas bearings [18]. [PERSON] solved the continuity equation and the Reynolds equation using the finite difference method to analyze the steady-state characteristics of porous gas bearings [19]. Professor [PERSON] et al. simplified the two-dimensional Reynolds equation into a one-dimensional one using the linear gas source assumption, which greatly shortened the calculation time of the static characteristics of aerostatic bearings compared with the numerical calculation method [20]. [PERSON] and [PERSON] applied the differential quadrature method to solve steady-state oil and gas lubrication problems in self-acting hydrodynamic bearings [21]. [PERSON] et al. derived the non-linear dimensionless Reynolds equation of the gas flow within bearings and discretized it using the Newton method [22]. [PERSON] et al. analyzed the pressure distribution in the bearing clearance of circular aerostatic thrust bearings with a single air supply inlet using CFD technology. It was found that the airflow state will change in the rapid pressure recovery region [23]. [PERSON] et al. used the Ph-method to analyze the Reynolds equation and solved it using the finite difference method and numerical integration. They analyzed the influence of the number and locations of entry holes on the characteristics of aerostatic bearings [24]. [PERSON] et al. determined discharge coefficients for a small feed hole of an aerostatic thrust bearing by comparing the results of a CFD simulation and a mathematical calculation model. They investigated the static and dynamic characteristics of aerostatic thrust bearings using FDM to solve the Reynolds equation and obtain the pressure distribution. It was found that the orifice could improve the damping and stiffness coefficient [25]. [PERSON] et al. used the finite difference method (FDM) to analyze the pressure distribution of the multi-supply air cushion. According to the principle of mass conservation, the correction iteration route of the pressure boundary conditions of each supply hole was developed, and the pressure distribution and gas flow under eccentric load were calculated [26]. [PERSON] et al. used the linear perturbation method to solve the Reynolds equation. They found that the bearing capacity and the critical mass of hydrogen gas bearings were slightly lower than other lubricating mediums [27]. Although the numerical calculation method shows high accuracy, there are some problems, such as a large amount of calculation, complex calculation steps, and a large amount of result data. Therefore, it is unsuitable as a solution method for the objective function in the iterative process of the optimization algorithm. To decrease the calculation time of the static performance, the engineering calculation model is established.