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Minimum weight and high-efficiency gearboxes with the maximum service life are the prime necessity of today’s high-performance power transmission systems such as automotive and aerospace. Therefore, the problem to optimize the gearboxes is subjected to a considerable amount of interest. To accomplish these objectives, in this paper, two generalized objective functions for two stage spur-gearbox are formulated; first objective function aims to minimize the volume of gearbox material, while the second aims to maximize the power transmitted by the gearbox. For the optimization purpose, regular mechanical and critical tribological constraints (scuffing and wear) are considered. These objective functions are optimized to obtain a Pareto front for the two-stage gearbox using a specially formulated discrete version of non-dominated sorting genetic algorithm (NSGA-II) code written MATLAB. Two cases are considered, in the first with the regular mechanical constraints.