Direct-band silicon materials have been a sought-after material for potential applications in silicon photonics and solar cells. Accordingly, methodologies like nanostructure engineering, alloy engineering and strain engineering have been developed. In this work, the particle swarm optimization (PSO) algorithm is used to design direct-band Si-Ge alloys. The findings of phonon computations demonstrate that all these structures are dynamically stable. In addition, ab initio molecular dynamics and elastic constant calculations are carried out, with results indicating these structures are thermodynamically stable at 300 K, as well as being mechanically stable. All of these materials exhibit semiconductor behavior with band gaps of 1.03, 0.68 and 1.37 eV for α, β and γ phases, respectively, at the HSE06 level. The results of effective mass and mobility of carriers that are important in applications show that holes are more easily transported in all structures, with higher concentration of holes accompanied by lower carrier mobility. Different concentrations of holes nh lead to different limits in the scattering process. When nh is lower than the value of around 1016 cm-3, deformation potential scattering is dominant, while the ionized impurity scattering process limits overall mobility when nh is higher than such a value. Finally, the absorption spectra shows that both α and β phases have isotropic optical properties in the X- and Y-directions while strong anisotropy can be seen in the Z-direction. However, the γ phase exhibits no notable isotropy. This investigation finds three direct-band and potentially CMOS compatible materials, a finding which will benefit the development of high efficiency emitters or solar cells.