A regression based mathematical modeling and a heuristic based optimization technique in flux assisted TIG known as activated tungsten inert gas (A-TIG) welding process for AISI316L austenitic stainless steel parts is addressed in this paper using Grey-Taguchi approach and simulated annealing (SA) algorithm. Process input parameters considered, were welding current (I), torch speed (S) and welding gap (G). The most important quality characteristics have been taken in to account were depth of penetration (DOP) and weld bead width (WBW). To enhance the welding process performance, an activating flux (TiO2, nano-particle) has been used. To gather the required data for modeling purposes design of experiments (DOE) based on orthogonal array Taguchi (OA-Taguchi) method has been employed. Then, different regression equations have been employed to model the process. Moreover, grey relational analysis (GRA) has been used to model the process outputs as a multi criteria to achieve all considered output simultaneously. The most fitted models were selected based on the statistical analysis performed. Next, simulated annealing (SA) algorithm has been used for optimization of process parameters of the selected models (both single and multi-criteria) in such a way that WBW minimized and DOP and GRG (output of GRA) is maximized. Finally, experimental tests have been carried out to evaluate the performance of the proposed method. Moreover, results of the proposed technique has been compared with ones gained using Taguchi approach (signal to noise (S/N) analysis). Based on confirmation tests, the proposed procedure is quite efficient in modeling and optimization of A-TIG process.