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We performed a global search for possible Au-Si crystal structures using a genetic algorithm (GA) combined with density functional theory (DFT) calculations. Two Au-Si structures, $\mathrm{A}{\mathrm{u}}_{8}\mathrm{S}{\mathrm{i}}_{8}$ and $\mathrm{A}{\mathrm{u}}_{16}\mathrm{S}{\mathrm{i}}_{8}$, were found to be energetically stable and have no imaginary frequencies by phonon calculations. The formation energies of all the studied structures gave a convex hull of the Au-Si system, showing that the most stable composition was $\mathrm{Au}\ensuremath{-}\mathrm{Si}=1:1$ and that the Si-rich structures were much less stable than the Au-rich ones.