Abstract Inconel-718 is a nickel-based super-alloy which is extensively used in various modern manufacturing industries like chemical, aerospace, nuclear, marine, automobile and medical due to its excellent mechanical behavior. The conventional cutting method faces some problems for the cutting of these materials due to better mechanical properties. The unconventional cutting methods may be alternative methods for the cutting of these difficult-to-cut materials. Among the different unconventional methods, the laser cutting may be applied with satisfactorily quality by operating the machine at optimum settings. The laser beam cutting process is one of the most suitable unconventional cutting processes to achieve the geometrical accuracy with high precision at the optimum parameter level. The main aim of this experimental work is to optimize the different quality characteristics viz. top kerf deviation (TKD) and bottom kerf deviation (BKD), during the pulsed Nd: YAG laser cutting of Inconel-718 sheet by using the hybrid approach methodology regression based genetic algorithm. The design of experiment based L27 orthogonal array has been applied for performing the experiments. By using the experimental data, second order regression models for all quality characteristics have been developed. The hybrid optimization technique regression based genetic algorithm has been used for optimizing the quality characteristics. The optimum results found by proposed methodology have been compared experimentally. The comparison of optimized results with the experimental results shows that considerable improvements have been observed in all quality characteristics individually as well as simultaneously.