In the current study, laser cutting of Ti6Al4V was accomplished using Taguchi’s L9 orthogonal array (OA). Laser power, cutting speed, and gas pressure were selected as input process parameters, whereas surface roughness (SR), kerf width, dross height, and material removal rate (MRR) were considered as output variables. The effects of input variables were analyzed through the analysis of variance (ANOVA), main effect plots, residual plots, and contour plots. A heat transfer search algorithm was used to optimize the parameters for the single objective function including higher MRR, minimum SR, minimum dross, and minimum kerf. A multi-objective heat transfer search algorithm was used to create non-dominant optimal Pareto points, giving unique optimal solutions with the corresponding input parameters. For better understanding and ease of selection of input parameters in industry and by scientists, a Pareto graph (2D and 3D graph) is generated from the Pareto points.