This work optimizes the current (I), voltage (V), flow rate (F), and arc gap (G) of the gas tungsten arc welding (GTAW) of the Ti40A titanium alloy to decrease the heat input (HI) and improve the ultimate tensile strength (TS) and micro-hardness (MH). The radial basis function network (RBFN) was utilized to present performance measures, while weighted principal component analysis (WPCA) and an adaptive non-dominated sorting genetic algorithm II (ANSGA-II) were applied to estimate the weights and generate optimal points. The evaluation via an area-based method of ranking (EAMR) was employed to determine the best solution. The results indicated that the optimal I, V, F, and G are 89 A, 23 V, 20 L/min, and 1.5 mm, respectively. The improvements in the TS and MH were 1.2 % and 19.8 %, respectively, while the HI was saved by 18.4 %. The RBFN models provided acceptable accuracy for prediction purposes. The ANSGA-II provides better optimality than the conventional NSGA-II. The HI, TS, and MH of the practical GTAW Ti40A could be enhanced using optimality. The optimization method could be utilized to deal with optimization problems for not only other GTAW operations but also other machining processes.