This paper presents a global optimization method able to find gear profile modifications that minimize vibrations. A non linear dynamic model is used to study the vibrational behavior; the dynamic model is validated using data available in literature. The optimization method takes into account the influence of torque levels both on the static and the dynamic response. Therefore, two different objective functions are considered; the first one is based on static analysis and the second one is based on the dynamic behavior of a lumped mass system. The procedure can find the optimal profile modification that reduce the vibrations over a wide range of operating conditions. In order to reduce the computational cost, a Random-Simplex optimization algorithm is developed; the optimum reliability is also estimated using a Monte Carlo simulation. The approach shows good performances both for the computational efficiency and the reliability of results.