Vortex ratchet effect is investigated experimentally in the frequency range between 0.5 MHz and 2 GHz. The ratchet potential is provided by an array of about a quarter of a million nanoengineered asymmetric antidots in a Pb film. A square vortex lattice is stabilized at the first matching field, when each asymmetric antidot is occupied by a single vortex. We have found that (1) the transition from adiabatic to nonadiabatic cases occurring at about 1 MHz, above which the ratchet windows shift upwards with the applied frequency due to the fact that the time for a vortex to escape from the pinning potential is comparable to the period of the applied rf driving current I-rf; (2) a sudden V-dc reversal at large I-rf, which can be attributed to inertia effect; (3) the collective step-motor behavior in the MHz region, i.e., the vortex lattice moves forward by an integer number of the period of pinning array at each cycle of I-rf; and (4) very weak ratchet effect at several GHz, indicating the possibility of stronger inertia effects in the vortex motion at such high frequencies. These results reveal rich physics information in the nonadiabatic ratchet system and are of particular importance for particle separation and molecular motor in biology.