We propose an approach to accelerate the computational exploration and the prediction of the preferred chemical ordering in alloy nanoparticles. This approach, named Grouping Global Optimization (GGO), is based on grouping atoms into equivalence sets constrained to be occupied by the same elemental species, with a consequent significant reduction in the compositional degrees of freedom of the system. The equivalence sets are defined on the basis of point group symmetry or in general of any given order parameter, thus leaving the user a great freedom in the implementation to each specific system. The GGO approach can be used within both systematic and stochastic sampling algorithms as demonstrated by tests conducted on prototypical nanoalloys, namely on Pd-Pt and Ag-Cu binary pairs, as representative of high- or low-miscibility alloys, respectively, and on particles of two different sizes, i.e., truncated octahedra composed of 586 and 4033 atoms. It is found that GGO enables an extremely quick scan of the chemical ordering in nanoalloys containing thousands of atoms and to predict low-energy chemical ordering patterns as a function of size and composition with a modest computational effort even for the larger and symmetry-broken particles. The strategy here proposed should be applicable equally well in other fields than that of nanoalloys.