In the present study, a novel technique, namely, evolutionary non-dominated sorting genetic algorithm-II (NSGA-II) was used in conjunction with developed artificial neural network (ANN) model to select optimal process parameters for achieving the better process performance in LBC. First, ANN with backpropagation algorithm was used to model the LBC of nickel based superalloy sheets. The input process parameters taken were oxygen pressure, pulse width, pulse frequency and cutting speed. The performance characteristics of interest in nickel based superalloy thin sheet cutting are average kerf taper and surface roughness. The ANN model was trained and tested using the experimental data obtained through experimentation on pulsed Nd-YAG laser beam machining system. The 4-10-11-2 backpropagation architecture was found more accurate and generalized for given problem with good prediction capability. The results show that the developed modelling and optimization tool is effective for process parameter optimization in LBC process. The optimization of the process suggests that for achieving high cut quality characteristics the pulse width, pulse frequency and cutting speed are set to lower limit within the available range and gas pressure is set to a level which is sufficient to remove the molten metal from the kerf.