## 1 Introduction  
Water pumps are important to vehicular cooling systems, directly affecting the efficiency, fuel consumption, and emissions of the vehicle. Traditionally, water pumps have been controlled through mechanical drag, using the belt connected to the crankshaft of the motor to control the flow rate, but this method can cause problems such as a poor cooling effect, low efficiency, and high vehicle energy consumption [1, 2, 3]. More recently, e-water pumps have been shown to effectively improve the cooling effect, thereby saving fuel and reducing emissions [4, 5, 6]. Thus, with the advent of the new energy era, the application of electronic water pumps in the field of passenger cars has been very popular; however, in heavy commercial vehicles, their motor efficiency is low, so they are rarely used. At present, permanent magnet synchronous motors have many advantages, such as their small size, high power density, and high efficiency [7, 8, 9], and they are widely used in the field of electronic water pumps. Compared with passenger cars, water pump motors in commercial vehicles need to have greater power, with limited installation space and higher output performance requirements, thus imposing stricter requirements for their design and optimization. In terms of motor design, the parameters are mainly determined according to the load requirements, and the design is completed with the help of simulation software [10; 11]. The authors of ref. [12] determined pump motor design parameters, according to the performance parameters of electronic water pumps on the market, and then completed the optimized design using Ansys Maxwell RMxprt 2022r2 software and a genetic algorithm. In ref. [13], a permanent magnet brushless DC motor was modified, and the stator and rotor of the motor were redesigned to meet the flow demand of the water pump. The aforementioned study used the performance parameters of the water pump itself to determine the design parameters of its motor, without considering the actual cooling needs of the engine, so the motor was large in size and its output capacity was excessive, properties which are not beneficial to reducing cost and layout space. Scholars studying motors both domestically and abroad have mainly achieved motor optimization through stator and rotor structure parameter optimization. The authors of ref. [14] used [PERSON]'s method to optimize the shape of the permanent magnet synchronous motor, and the results show that the optimized two-layer Machaon design has low torque pulsations. In ref. [15], the table-adhesive structure of bilateral-rotor permanent magnets was used to increase the air-gap magnetization, thus enhancing the output torque. The authors of ref. [16] studied the shape of surface-mounted rotor permanent magnets and used the pole-shaving method in order to generate effective magnetic density harmonics in the air gap and inject corresponding harmonic currents to enhance the output torque. The above studies predominantly focused on a single optimization objective, often overlooking the impacts on other aspects of the motor's performance. In order to simultaneously take into account multiple performance indices for the motor, multi-objective optimization strategies have been proposed. For example, in ref. [17], the NSGA-II algorithm was used to achieve significant reduction in cogging torque, using the cogging torque and output torque as the optimization objectives. In order to increase the average thrust of the motor and reduce its fluctuation, the researchers in ref. [18] used a neural network to establish a motor agent model, and the Pareto frontier method was used to determine the optimal parameter range with which to complete the multi-objective optimization of the permanent magnet synchronous motor. The authors of ref. [19] proposed a novel agent-assisted multi-objective optimization algorithm, with permanent magnet synchronous motor torque pulsation, torque amplitude, and a permanent magnet as optimization objectives.