The friction stir welding (FSW) process was applied to butt-weld AA5754 plates, and the joints of each weld case were identified by their tensile strength, hardness, and impact toughness. The combined effects of the process variables rotation speed, welding speed, and tilt angle have been evaluated in the present study using Taguchi's design of experiments approach and grey relational analysis (GRA). A multi-objective optimization approach (Taguchi method and GRA) was used to optimize and rank the process variables. The developed models are evaluated for sufficiency, and the most significant terms are found using the ANOVA approach. The results of the ANOVA showed that the rotational speed has a maximum contribution of 55.24%, 59%, and 46.27% in obtaining the optimal values of tensile strength, hardness, and impact toughness, respectively. Finding an optimal parameter that offers the maximum value of all replies requires the use of the GRA and Taguchi Technique by Similarity to Suitable Solution. The two methods provide the same results, and the optimal conditions are a rotational speed of 1000 rpm, a welding speed of 60 mm/min, and a tilt angle of 2.5 degrees. The optimal values for tensile strength, hardness, and impact toughness, respectively, were found to be 136 MPa, 85.25 HV, and 13 J.