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. However, the second case, power loss and the tribological constraints (scuffing and wear constraints), are included to obtain a Pareto front. Finally, the two cases are compared and the results reveal that there is a high probability of wear failure of gear pairs if tribological constraints neglected. When considered power losses in the objective function along with the tribological constraints, the efficiency of the gearbox is improved. However, the volume of the gearbox is slightly increased.