Hybrid electrical vehicles involve two sources of energy, usually gasoline and electricity. The energy management determines the power sharing between the internal combustion engine and the electrical machine (EM). It is highly dependent on the driving cycle (i.e. the use of the vehicle). In this context, the optimal sizing of the EM is determined by: the driving cycle, the power-train characteristics (i.e. ratios and physical limitations e.g. maximum torque available) and the energy management. The key idea of this work is to involve the driving cycle and the environment of the electrical machine in a global multi-objective optimization process taking into account an optimal energy management and an accurate model of the EM based on magnetic circuit equivalent model.