We propose a method for the robust splitting of light between the two outer waveguides in a three-waveguide system by mode evolution. Arbitrary power splitting ratio is achieved by engineering the spacings between the middle waveguide and the outer waveguides. Coupling of light into the middle waveguide is suppressed by the adiabatic elimination scheme. To speed up the adiabatic passage in the effective two-mode system involving only the outer waveguides, we introduce the fast quasi-adiabatic dynamics protocol, leading to a shortcut to adiabaticity. Using the proposed fast quasi-adiabatic elimination scheme, power splitters with various power splitting ratios including, 10/90, 20/80, 30/70, 40/60, 50/50, 60/40, 70/30, 80/20, and 90/10, are designed. Simulations show that the splitters have good robustness against wavelength and fabrication variations.