## 1 Introduction  
The high-speed permanent magnet motors have the advantages of large power density, small volume, high efficiency, low noise and vibration [1, 2, 3]. So, it has broad application prospects in the fields of high-speed motor tools, compressors, blowers, turbine power generation, and has been widely concerned and studied by scientific researchers [4, 5, 6]. Due to the high speed and small size of the HSPMM, the design needs to consider the physical field performance such as electromagnetic, loss, mechanical strength, temperature, cooling and heat dissipation, and there are nonlinear and strong coupling relationships between different physical fields [7, 8]. Therefore, how to comprehensively analyze and optimize the multiphysics coupling performance of HSPMM has become a challenge task in this field [9, 10, 11]. The performance of some HSPMMs has been optimized in existing studies. Some scholars take improving efficiency and torque as optimization objectives, and stator design parameters are set as optimization variables, including air gap, slot size, stator core inner and outer diameter and core length, to optimize a motor with rated power of 6 kW [12]. The effects of sleeve thickness, interference fit, rotor temperature and PM segmentation on rotor stress distribution are investigated in [13, 14], which demonstrated that it is reliable to improve the performance of HSPMM by changing key parameters within a small range. For conventional motor, literature [15] presents a multi-objective optimization method based on subspace optimization strategy. The optimization time is shortened effectively by hierarchical optimization of structural parameters through subspace optimization strategy. In literature [16], a multi-objective optimization method based on sequential optimization strategy is proposed to improve the calculation accuracy of multi-field coupling optimization. The coupling relationship between different physical fields is simplified by artificially specifying the optimal order between different physical fields. However, studies on optimization of the HSPMM based on subspace and sequential optimization strategies are rare. Specifically, the following problems exist in existing studies:  
1. In current research, scholars focus on the influence of rotor design parameters on motor performance. However, stator design also has a significant impact on the electromagnetic performance, losses, and temperature rise of the motor. Due to the large number of stator parameters, their involvement in optimization can lead to a geometric multiplier increase in optimization training points. 2. In motor design, the issues within multiple physical fields involve complex interactions and coupling relationships. For example, changes in the electromagnetic field can affect the thermal field distribution, and variations in temperature can, in turn, impact electromagnetic performance. Present optimization studies often consider each physical field independently, overlooking the coupling effects between them. This approach of optimizing a single physical field could yield local optimal solutions rather than global ones. 3. From the previous literature, the subspace optimization strategy can lower computational problems caused by multiparameter optimization, and the sequential optimization strategy can simplify multi-physics coupling problem. Applying these two optimization strategies to the optimization process of HSPMM may greatly reduce the workload multiplied by multiple optimization objectives. Therefore, it is necessary to explore how to effectively integrate two strategies within the multiphysics optimization of high-speed motors, thereby addressing the optimization challenges posed by multiple parameters and multi-physical fields in high-speed motors. Unfortunately, subspace and sequence optimization strategies are usually used alone in conventional motors, while their combined strategies are missing in the HSPMM.