MIG welding is a modern part of advanced welding process. In this article, the mathematical modeling by ANN and parametric optimization of MIG welding joining process of cast iron has been propounded using soft computing hybrid-GAPSO. The article also shows the best model using NN basis of fittest with experimental result, computational time, convergence speed and finally RMSE obtained from cross-validation. In this research, the optimal value of the input variables obtained by hybrid-HGAPSO so that output variables hardness (HA) will be maximum & surface roughness (SR) and width of breadth thickness (WOBT) will be minimum, has been illustrated. In this experimental analysis minimized RMSE of 1.15%, 1.433%, and 1.6678% for HA, WOBT and SR are accomplished respectively by HGAPSO-ANN.