In order to obtain high-quality welding, it is required to maximize ultimate tensile strength and minimize bead width. Moreover, it is significant to limit the penetration to the desired length. These three-output data are affected by some input parameters such as the wire type, the shielding gas, the laser power, the laser focus, the travelling speed and the wire feed rate. Optimization of these input parameters is quite substantial to reach desired weld quality. Before optimization, it is required to develop suitable mathematical models for each output parameters. Thus, intermediate values outside the experimental data can be acquired. First objective of this study is to propose modified second-order polynomial to develop high-accurate mathematical models compared to first-order linear models. The modified model may be described as cancelling of some redundant interaction terms in second-order polynomial. If the number of experiments is restricted as in this study, it is impossible to use second-order polynomial model because number of unknowns should be lesser than number of experimental data in order to obtain well-posed numerical solution. The number of unknown constants in modified model is lesser than secondorder polynomial and it is more accurate than first-order polynomial. Proposed models were designed in Matlab software using data from the previous studies. The second aim of this study is optimization of input parameters using a genetic algorithm to get desired penetration, minimum bead width and maximum ultimate tensile strength. According to optimum data, 29.9 % of improvement on ultimate tensile strength was observed in addition to 36.7 % lesser bead width compared to Taguchi optimization in previous study. Finally, this study is to present open source Matlab codes to the users. It is very adaptable for different experimental data and different physical models by making very small changes in the given codes.