Friction stir welding (FSW) is a process by which a joint can be made in a solid state. The complexity of the process due to metallurgical phenomena necessitates the use of models with the ability to accurately correlate the process parameters with the joint properties. In the present study, a multilayer perceptron (MLP) artificial neural network (ANN) was used to model and predict the ultimate tensile strength (UTS) of the joint between the AA2024 and AA7075 aluminum alloys. Three pin geometries, pyramidal, conical, and cylindrical, were used for welding. The rotation speed varied between 800 and 1200 rpm and the welding speed varied between 10 and 50 mm/min. The obtained ANN model was used in a simulated annealing algorithm (SA algorithm) to optimize the process to attain the maximum UTS. The SA algorithm yielded the cylindrical pin and rotational speed of 1110 rpm to achieve the maximum UTS (395 MPa), which agreed well with the experiment. Tensile testing and scanning electron microscopy (SEM) were used to assess the joint strength and the microstructure of the joints, respectively. Various defects were detected in the joints, such as a root kissing bond and unconsolidated banding structures, whose formations were dependent on the tool geometry and the rotation speed.