Some surrogate-assisted optimization techniques are applied in order to improve the performances of a 5-phase Permanent Magnet (PM) machine in the context of a complex model requiring computation time. An optimal control of four independent currents is proposed in order to minimize the total losses with the respect of functioning constraints. Moreover, some geometrical parameters are added to the optimization process allowing a co-design between control and dimensioning. The effectiveness of the method allows solving the challenge which consists in taking into account inside the control strategy the eddy-current losses in magnets and iron. In fact, magnet losses are a critical point to protect the machine from demagnetization in flux-weakening region. But these losses, which highly depend on magnetic state of the machine, must be calculated by Finite Element Method (FEM) to be accurate. The FEM has the drawback to be time consuming. It is why, a direct optimization using FEM is critical. The response surface method (RSM) and the Efficient Global Optimization (EGO) algorithm consist in approximating the FEM by a surrogate model used directly or indirectly in the optimization process. The optimal results proved the interest of the both methods in this context