In this paper, we have experimentally demonstrated light focusing through strongly scattering media by performing binary amplitude optimization with a genetic algorithm. In the experiments, we control 160 000 mirrors of digital micromirror device to modulate and optimize the light transmission paths in the strongly scattering media. We replace the universal target-position-intensity (TPI) discriminant with signal-to-background ratio (SBR) discriminant in genetic algorithm. With 400 incident segments, a relative enhancement value of 17.5% with a ground glass diffuser is achieved, which is higher than the theoretical value of 1/(2 pi) approximate to 15.9% for binary amplitude optimization. According to our repetitive experiments, we conclude that, with the same segment number, the enhancement for the SBR discriminant is always higher than that for the TPI discriminant, which results from the background-weakening effect of SBR discriminant. In addition, with the SBR discriminant, the diameters of the focus can be changed ranging from 7 to 70 mu m at arbitrary positions. Besides, multiple foci with high enhancement are obtained. Our work provides a meaningful reference for the study of binary amplitude optimization in the wavefront shaping field.