Abstract: We consider the problem of global synchronization in a large random network of Kuramoto oscillators where some of them are subject to an external periodically driven force. We explore a recently proposed dimensional reduction approach and introduce an effective two-dimensional description for the problem. From the dimensionally reduced model, we obtain analytical predictions for some critical parameters necessary for the onset of a globally synchronized state in the system. Moreover, the low dimensional model also allows us to introduce an optimization scheme for the problem. Our main conclusion, which has been corroborated by exhaustive numerical simulations, is that for a given large random network of Kuramoto oscillators, with random natural frequencies ômegai, such that a fraction of them is subject to an external periodic force with frequency Ômega, the best global synchronization properties correspond to the case where the fraction of the forced oscillators is chosen to be those ones such that |ômegai-Ômega| is maximal. Our results might shed some light on the structure and evolution of natural systems for which the presence or the absence of global synchronization is a desired property. Some properties of the optimal forced networks and their relation to recent results in the literature are also discussed. We consider here the dynamics of a large number of interacting Kuramoto oscillators. Each oscillator has its own natural frequency ômegai, which is assumed to be a random variable, and the interactions among them are associated with the edges of a random network. Despite being essentially a random system, there are plenty of robust results obtained from this kind of model which have proven to be relevant in many different areas. This is the case, for instance, of synchronization phenomena; see Refs. 1 and 2 for comprehensive reviews on the subject. Here, we are concerned with one of the main variations of the network of Kuramoto oscillators, the case where some of the oscillators are subject to an external periodically driven force with frequency Ômega. By exploring a recently proposed analytical approach, we introduce an optimization scheme for the onset of the so-called global synchronization in the system, a regime where all oscillators rigidly rotate, forming a compact swarm, in the same pace of the external force, with frequency Ômega. We show that the best global synchronization properties correspond to the case where the set of forced oscillators is chosen to be those ones such that the value of |ômegai-Ômega| is maximal. Our results may help one to understand the evolution and structure of natural systems with many interacting agents for which global synchronization plays an important dynamical role Ver menos