A laser beam machine is a non-traditional manufacturing technique that uses thermal energy to cut nearly all types of materials. The quality of laser cutting is significantly affected by process parameters. The purpose of this study is to use a genetic algorithm (GA) in conjunction with response surface approaches to improve surface roughness in laser beam cutting CO2 with a continuous wave of SS 304 stainless steel. The effects of the machining parameters, such as cutting speed, nitrogen gas pressure, and focal point location, were investigated quantitatively and optimized. The tests were carried out using the Taguchi L9 orthogonal mesh approach. Analysis of variance, main effect plots, and 3D surface plots were used to evaluate the impact of cutting settings on surface roughness. A multi-objective genetic algorithm in MATLAB was used to achieve a minimum surface roughness of 0.93746 μm, with the input parameters being 2028.712 mm/m cutting speed, 11.389 bar nitrogen pressure, and a focal point position of-2.499 mm. The optimum results of each method were compared, as the results the response surface approach is less promising than the genetic algorithm method.