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Crystal structure prediction has been widely used to accelerate the discovery of new materials in recent years. Up to this day, it remains a challenge to predict the stable stoichiometries and structures of ternary or more complex systems due to the explosive increase of the size of the chemical and configurational space. Numerous novel materials with a series of unique characteristics are expected to be found in this virgin territory while new algorithms to predict crystal structures in complex systems are urgently called for. Inspired by co-evolution in biology, here we propose a co-evolutionary algorithm, which we name COPEX, and which is based on the well-known evolutionary algorithm USPEX. Within this proposed algorithm, a few USPEX calculations for ternary systems and multiple for energetically-favored pseudobinary or fixed-composition systems are carried out in parallel, and co-evolution is achieved by sharing structural information on the fittest individuals among different USPEX sub-processes during the joint evolution. We have applied the algorithm to W–Cr–B, Mg–Si–O, and Hf–Ta–C, three very different systems, and many ternary compounds have been identified. Our results clearly demonstrate that the COPEX algorithm combines efficiency and reliability even for complex systems.

COPEX: co-evolutionary crystal structure prediction algorithm for complex systems