## 1 Introduction  
An axial flux permanent magnet brushless DC motor (AFMBLDC) has the advantages of a short axial length, small size, light weight, and high power density [1, 2]. In the past two decades, the AFPMBLDCs have been widely researched throughout the world. In [3, 4], we found that the AFPMBLDC can provide a larger output torque compared with the radial flux brushless DC motor. However, the torque ripple cannot be neglected due to the highogging torque. Thus, some design methods, such as fractional slot winding, stator skewed slot, and best pole slot fit method, are adopted to optimize the output torque [5, 6]. However, the above methods are only aimed at a single design method, which only improves the output torque of AFPMBLDC, leaving the problems of low efficiency and large losses [7, 8]. In order to improve the comprehensive performance of permanent magnet motors, a variety of optimization design methods have been proposed [9, 10]. Generally, optimization design methods are divided into global optimization and local optimization [11, 12]. Global optimization algorithms include the particle swarm optimization algorithm, genetic algorithm, ant colony algorithm, and simulated annealing algorithm, etc. The literatures [13, 14, 15, 16, 17, 18] used particle swarm optimization algorithm to optimize the parameters so that the permanent magnet motor has the characteristics of small coupling and simple control. [PERSON] et al. used the particle swarm reduction algorithm to optimize the parameters, which greatly reduced the torque ripple and made the motor run more smoothly [19]. The authors of [20] optimized the surface-mounted permanent magnet synchronous motor using a genetic algorithm improved by combining pattern search method. [PERSON] and [PERSON] improved the accuracy and speed of the genetic and colony algorithm [21]. [PERSON] and [PERSON] et al. used the particle swarm optimization algorithm to improve the materials utilization of a permanent magnet motor [22]. In [23, 24], a hybrid genetic simulated annealing algorithm and conformal mapping approach were applied for multi-objective analysis to optimize the motor, respectively. In [25], the authors performed a multi-objective optimization of a permanent magnet motor based on a forbidden search algorithm and a finite element method. In [26], the efficiency, size, and quality of a PMG were optimally designed using a non-dominated ranking genetic algorithm technique, which allows an arbitrary selection of the number of optimization objectives[PERSON] The establishment of the objective function of these global optimization algorithms is complex and the solution cycle is generally long, which makes it difficult to achieve a fast and efficient search for the optimal combination of the parameters of the motor. The local optimization methods include the magnetic network method, gradient descent method, and finite element method [27][PERSON] [PERSON] et al. used the finite element method to make an analysis of the temperature field of the coreless disk motor to optimize the motor winding [28; 29; 30][PERSON] [PERSON] et al. used the equivalent magnetic network method to establish the equivalent network model considering the magnetic leakage coefficient and air-gap magnetic density to solve the time-consuming problem of AFPMBLDC [31]. [PERSON] and [PERSON] et al. used the gradient descent method to correct the motor setting value for the weak magnetic control [32; 33]. Although the above local optimization methods are simple to calculate and have good convergence, they can only optimize for a single objective and cannot achieve multi-objective optimizations. Compared with local optimization methods, the Taguchi optimization method has the merits of achieving multiple objectives simultaneously and finding the optimal combinations of multi-objective optimization by fewer experiments [34; 35; 36]. [PERSON] et al.