We investigate the stability of the localization of a Bose-Einstein condensate in one-dimensional, two-dimensional and three-dimensional bichromatic optical lattices using a time-dependent variational approach. We derive the effective potential for the stability analysis of the system using the Gauss type trial wave function and give the stable criteria through this effective potential. It is demonstrated that the bichromatic optical lattice's intensities, two-body, three-body and high-order interactions play different roles in the stability of the system. The two-body and high-order have an important influence to the stability but the others play a regulatory role on the stability.
