## 1 Introduction
[15] studied the design optimization of electric machines for 48 V hybrid vehicles, focusing on rotor technologies and pole-slot combinations. While it provides insights into rotor design performance and efficiency, it may not address the broader impacts on overall vehicle performance or integration into hybrid systems. Exploring these areas could lead to further research in electric vehicle design and analysis. Reference [16] presents a novel modular bearingless permanent magnet synchronous motor (PMSM) designed for ultra-clean applications, highlighting gaps in the existing literature on advanced motor designs. It utilizes 2D and 3D finite element method (FEM) analyses to evaluate motor performance and suspension control via Model Predictive Control (MPC). Additionally, the focus on decoupling characteristics and structural parameters indicates a need for further research into optimizing these factors across various applications, which have not been thoroughly explored in prior studies. [PERSON] et al. [17] propose a two-step design process for permanent magnet synchronous motors (PMSMs) to boost efficiency and minimize harmonics in lightweight electric vehicles. This study presents practical methods for improving motor performance but does not consider the broader impact on vehicle efficiency and alternative technologies. It also indicates possible directions for future research to enhance electric vehicle systems. The study [18]presents the design and optimization of an outer-rotor BLDC for medical devices, which will also meet high torque, high efficiency, and small size requirements. Different techniques are used to increase power density and efficiency in applications where size and weight are essential. For example, the Halbach magnet array can improve power density and efficiency by concentrating the magnetic flux [19]. In [20], a rotor design with optimal step-skew angles and optimum step lengths to reduce the cogging moment was proposed to improve the torque. The step-skew method is frequently used as a practical approach to minimize cogging torque in PM machines. Reference [21] explores the adjustments of pole pitch and pole arc in rotor magnets to minimize cogging torque in brushless DC (BLDC) motors. Their analytical findings on cogging torque reduction are consistent with Finite Element Analysis (FEA), establishing a strong basis for assessing the impact of design modifications on cogging torque reduction. Reference [22] presents a design optimization method to reduce cogging torque in PMSMs, contributing to the literature on their performance and reliability issues. However, it may overlook the impact of manufacturing variability on robustness and lacks a comprehensive comparison with other optimization methods, highlighting the need for further research. Many research studies mainly focus on optimizing motor efficiency, power density, and torque using different multi-objective optimization methods. It is only possible to optimize some of the machine's sizing parameters to improve all performance values. This is a time-consuming and complex process. For example, many machine performance improvement studies were carried out in this research, but the thermal performance still needs to be studied. In this paper, multiphysics using the coupled electromagnetic-thermal analysis method is proposed. Compared to the literature's design, analysis, and optimization methods, the techniques used in this paper are different. When the studies are examined, the design, optimization, analysis, and verification studies have yet to be fully and comprehensively discussed. In this study, the analytical sizing process, multi-objective optimization, finite element method (FEM) analysis and validation of the in-wheel or outer-rotor BLDC motor for the propulsion system of a small-power and low-speed electric vehicle are presented, as shown in Figure 1. In the first step, basic sizing is provided within certain electromagnetic and thermal limits to achieve the specified motor performance.