Abstarct: In this thesis, the research and design of an optimized Brushless DC Motor (BLDC) with an external rotor, intended for in-wheel applications in electric vehicles, is addressed. The use of in-wheel motor technology enhances drive efficiency, dynamic stability control, and the safety of electric vehicles. One of the fundamental advantages of in-wheel motors is that they free up more space within the electric vehicle. This technology is extensively utilized in the automotive industry due to the compact size of the motor, high torque density, low noise levels, high reliability, good dynamic performance, and high efficiency. For decades, BLDC motors have been a suitable choice for this technology due to their valuable characteristics. This thesis explores BLDC motors with the aim of achieving high efficiency while adhering to nonlinear constraints (namely, flux density limits, current density, and physical dimensions). The common optimization objectives for BLDC motors include maximizing output efficiency, minimizing cogging torque, cost, and the volume of the motor structure for in-wheel applications in electric vehicles. In this study, a baxseline external rotor BLDC motor is considered, and a finite element method (FEM)-baxsed analysis process is conducted using the motor analysis software ANSYS RMxprt and ANSYS Maxwell. Subsequently, the optimization process is carried out using a bat algorithm, and the optimal dimensions are obtained through MATLAB. Finally, the optimized motor is re-simulated and subjected to finite element analysis, with the results compared to those of the initial structure.