We present a universal method for the largescale prediction of the atomic structure of clusters. Our algorithm performs the joint evolutionary search for all clusters in a given area of the compositional space and takes advantage of structural similarities frequently observed in clusters of close compositions. The resulting speedup is up to 50 times compared to current methods. This enables the first-principles studies of multi-component clusters with full coverage of a wide range of compositions. As an example, we report an unprecedented firstprinciples global optimization of 315 Si n O m clusters with n ≤ 15 and m ≤ 20. The obtained map of Si-O cluster stability shows the existence of both expected (SiO 2 ) n and unexpected (e.g. Si 4 O 18 ) stable (magic) clusters, which can be important for miscellaneous applications.Graphical TOC Entry 1 arXiv:1812.06568v1 [cond-mat.mtrl-sci] 17 Dec 2018The unique properties of nanoparticles are extensively used in optoelectronics, photovoltaics, photocatalysis, biomedicine, etc. These properties are closely linked to the atomic structure of particles, what is more explicit in the small particles and nanoclusters. 1,2 Despite the importance of knowing the structure, its experimental determination remains very difficult. 3 For this reason the main body of structural information on clusters is obtained via first-principles calculations 4 which were mostly done either for monoatomic clusters or for binary clusters of stoichiometric composition corresponding to the bulk compounds, while clusters of general composition were studied only in few publications. 5,6 Such an accent in ab initio research ignores the fact that the chemistry of clusters is much richer than that of solids because of a large share of surface atoms. Multi-component clusters often have stable compositions, which are far from chemical compounds presented in the bulk x-T phase diagram. This is of interest not only for basic chemistry of clusters. It significantly increases the scope of candidate nanomaterials for practical applications such as: the development of efficient and affordable catalysts 7,8 and magnets, 9 the investigation of complex processes of nucleation and particle growth, 10-12 etc.The bottle-neck of first-principles activity in cluster studies is the computational cost of atomic structure determination, which is a global optimization of the total energy among all possible atomic configurations. There are several methods of structure prediction (basin and minima hopping, 13,14 simulated annealing, 15 evolutionary algorithm, 16 etc.), however they all involve thousands of local optimizations (relaxations) even for finding a structure of one cluster. In the applications mentioned above, the computation of atomic structure and the screening of stability and properties are required in wide regions including hundreds of cluster compositions, therefore such firstprinciples investigations turn out extremely exhausting. To reduce the computational cost, the global optimization is frequently performed ...