Compound semiconductors are expected to expand the possibilities of semiconductor applications. In particular, Ⅳ−Ⅳ compound semiconductors, such as silicon−germanium (Si−Ge) alloys, have received much attention over the past several decades. Although many scholars have conducted experiments on Si−Ge alloys, few scholars have conducted theoretical simulations on them. Thus, fundamental understanding of nanoscale phenomena in the Si−Ge alloys is still insufficient. To address this problem, we identified energetically stable structures of the Si−Ge alloys using density-functional-theory (DFT) first-principles calculations and genetic algorithm (GA) and evaluated various properties of the Si−Ge alloys. We confirmed that the formation energies of the stable structures identified by GA-combined DFT calculations were lower than those of other Si−Ge alloys registered in an existing crystal structure database. The lattice constants and electronic band gaps of these stable structures were evaluated using DFT calculations, and trends in their properties similar to those reported in previous experimental studies were verified. From the evaluation of coordination number according to the Boltzmann distribution, we found that homoelement bonds (Si–Si and Ge−Ge) are easier to form than heteroelement bonds (Si−Ge) in the stable structures of Si−Ge alloys at any composition.