A novel evolutionary algorithm is described for designing the topology of spanning tree-based communication networks. Two specific performance objectives are dealt with: the optimum communication spanning tree problem (OCSTP), and the quadratic minimum spanning tree problem (q-MST). Improved network performance is reliably obtained when using the proposed algorithm on accepted benchmark instances, in comparison with the previous best-known approaches. The same methodology can be applied straightforwardly to the design of communication networks with other objectives.