In this paper, an analysis of the vulnerability of the Italian high-voltage (380 kV) electrical transmission network (HVIET) is carried out for the identification of the groups of links (or edges, or arcs) most critical considering the network structure and flow. Betweenness centrality and network connection efficiency variations are considered as measures of the importance of the network links. The search of the most critical ones is carried out within a multi-objective optimization problem aimed at the maximization of the importance of the groups and minimization of their dimension. The problem is solved using a genetic algorithm. The analysis is based only on information on the topology of the network and leads to the identification of the most important single component, couples of components, triplets and so forth. The comparison of the results obtained with those reported by previous analyses indicates that the proposed approach provides useful complementary information.