We have employed simple model potentials and an evolutionary algorithm to assess the low-energy landscape of clusters resulting from the self-assembling of oppositely charged particles in two-dimensions (2D). The global minimum structures were obtained by employing an evolutionary algorithm (EA), which has been adapted to deal with planar clusters. The present results show that various families of structures, including linear-and ring-type motifs, arise in a relatively small energy-window. (C) 2018 Elsevier B.V. All rights reserved.