In this paper, a software framework is presented through an application that is able to jointly optimize an electric motor and a gearbox for the design of a drive system for electric vehicles. The framework employs a global optimization method and uses both analytical and finite element method (FEM) models to evaluate the objective functions. The optimization process is supported by a statistical surrogate model, which allows a large reduction of runtime. An earlier version of this framework was only suitable for electric motor optimization. In the application presented in a previous paper, the motor of a belt-driven electric drive system was optimized. In this paper, the optimization of the same drive system is shown, but now with a combined optimization of a gear drive and motor. The objective functions of optimization are minimizing the total loss energy and the weight of the drive system. The optimization results are compared with previous results to demonstrate the further potential of joint optimization.