A genetic algorithm based search method was used to identify the lowest energy structure of XenY (Y = Cl-, Br-, Cl, and Br) microclusters. The optimization was performed using an empirical potential constructed from pairwise interactions (for the neutral clusters) together with three-body terms in the case of ionic systems. The variation of the cluster energy and the electrostatic stabilization energy as a function of the cluster size, n = 1-16, was examined. The calculations indicate that for large n values both Cl and Cl- were located inside the Xe cluster, while Br and Br- adsorb onto the cluster surface. For most cluster sizes, the lowest energy structures of the lighter halogen seem to be independent of its charge state. However, markedly different structures were obtained in the case of Br- and Br. The stabilization energies, E-stab, for the charged clusters were estimated using the most stable structures found in the optimizations. Both halogens exhibit rapid linear increase of the stabilization energy with cluster size up to n = 6. For larger clusters E-stab continues to increase linearly as a function of n but with a much smaller rate. The time evolution of the XenY- clusters after photoionization was simulated using molecular dynamics. It was found that for Cl-, the loss of the stabilization energy did not lead to appreciable fragmentation of the parent cluster, while for bromine a high degree of fragmentation occurs in less than 100 ps.