## 1 Introduction
[17] obtained VI values to represent the relative importance of the design variables based on the errors before and after performing variable substitution during random forest training. Ref. [18] considered the relative importance of the input variables as the default output when calling the random forest algorithm in the Python sklearn package, so it was directly adopted as the basis for selecting the key design variables. The main difference between the two approaches is that the statistically based analysis methods focused only on the significance of the effect of the design variables on the objective variables under statistical significance, while the machine learning-based analysis methods are more inclined to focus on the effect of the design variables on the predictive performance of the model. However, we note that few studies combining the two have been reported. Factors such as strong coupling between motor parameters and nonlinearity of the objective function cause multi-objective optimization to fall into local optimums and the optimization objectives are difficult to be weighed, so a variety of intelligent optimization algorithms have been introduced to solve the problem [19]. Ref. [20] built a surrogate model with a pyramidal neural network (PNN) and used the Quantum Bat Algorithm (QBA) to optimize IPMSMs, which obtained higher output power and lower loss. Ref. [7] built a surrogate model with the Kriging method and used the Non-dominated Sorting Genetic Algorithm II (NSGA-II) multi-objective optimization algorithm to optimize the efficiency and torque fluctuation of a permanent magnet-assisted synchronous reluctance motor (PMASRM). After optimization, the PMASRM gained higher efficiency and less torque fluctuation. The results were well verified. Swarm intelligent optimization algorithm has stronger robustness, simple structure, less overhead, and self-organization; thus, the multi-objective particle swarm optimization (MOPSO) algorithm is widely used. Based on PSO for the PMSM's electromagnetic performance of multi-objective optimization, the results of [21] show that the cogging torque has been effectively reduced, the magnitude of the reverse electromotive force has been reduced, the flux density is in a reasonable range, and the electromagnetic performance of the motor has been improved. Ref. [22] used the Taguchi method and PSO to optimize an 8-pole, 48-slot IPMSM's average output torque, torque fluctuation, and iron loss. The results show that the average output torque is improved, the torque fluctuation and iron loss are suppressed, and the effectiveness of the Taguchi method-PSO hybrid algorithm is verified. Ref. [23] improved the weight coefficients of the PSO algorithm and used it to carry out multi-objective optimization of the Yokeless And Segmented Armature (YASA) motor in order to optimize the average output torque, the torque fluctuation, and the motor output power. The results showed that the motor output power and average output torque are improved, while torque fluctuation is effectively suppressed, and the effectiveness of the optimization was proven through experiments. Ref. [24] used the PSO based on adaptive inertia weights to carry out multi-objective optimization of the rotor pole-parallel hybrid excitation synchronous marine motors, which results in the improvement of the motor's torque, suppression of torque fluctuation and optimization of the no-load electromotive force. The multi-objective optimization algorithm gives a series of Pareto non-dominant solutions in which the final optimization result will be selected. For the selection of the Pareto optimal solution, practical feasibility and cost-effectiveness need to be considered, and the selection in engineering often relies on practical experience and skills [25], which is somewhat subjective. However, the objective selection method of Pareto's optimal solution has also gained attention. In ref. [26], a Pareto optimal solution ranking approach based on the R-method is proposed.