AA2024 and AA6061 aluminum alloys were fabricated using the friction stir welding technique to improve the tensile properties such as ultimate tensile strength (UTS) and tensile elongation (TE). The BoxBehnken design matrix with four significant factors-rotational speed (X(1)), welding speed (X(2)), axial load (X(3)), and pin shape (X(4)), each having three levels-was used with response surface methodology to develop a mathematical model. The experiments yielded ultimate tensile strength of 141 MPa at 12% tensile elongation. The obtained tensile properties of fabricated weld joints were low when compared to those of base materials. Several voids and pinholes were found, these being the consequence of poor tensile properties on the fabricated weld joints. Therefore, to maximize the tensile properties, two computational approaches were employed: a genetic algorithm and a simulated annealing algorithm. The main objectives of applying these computational approaches were: (1) to maximize the UTS and TE compared to the welding performance value of the experimental data and regression modeling; (2) to estimate the optimal process parameter values that must be within the obtained range of the minimum and maximum values; and (3) to evaluate the number of iterations generated by the computational approaches. The results show that use of the computational approaches resulted in significant improvement in the tensile properties. Comparing the genetic algorithm with the simulated annealing algorithm, the latter maximizes the tensile properties of fabricated AA2024 and AA6061 aluminum alloy weld joints; however, a considerable number of iterations and substantial amount of time was required to achieve a global optimal solution.