A genetic algorithm approach is applied to the optimization of the potential energy of a wide range of binary metallic nanoclusters, Ag-Cu, Ag-Ni, Au-Cu, Ag-Pd, Ag-Au, and Pd-Pt, modeled by a semiempirical potential. The aim of this work is to single out the driving forces that make different structural motifs the most favorable at different sizes and chemical compositions. Paper I is devoted to the analysis of size-mismatched systems, namely, Ag-Cu, Ag-Ni, and Au-Cu clusters. In Ag-Cu and Ag-Ni clusters, the large size mismatch and the tendency of Ag to segregate at the surface of Cu and Ni lead to the location of core-shell polyicosahedral minimum structures. Particularly stable polyicosahedral clusters are located at size N = 34 (at the composition with 27 Ag atoms) and N = 38 (at the composition with 32 and 30 Ag atoms). In Ag-Ni clusters, Ag32Ni13 is also shown to be a good energetic configuration. For Au-Cu clusters, these core-shell polyicosahedra are less common, because size mismatch is not reinforced by a strong tendency to segregation of Au at the surface of Cu, and Au atoms are not well accommodated upon the strained polyicosahedral surface.