  We study numerically the evolution of the degree order and mobility of the
vortex lattice under steady and oscillating applied forces. We show that the
oscillatory motion of vortices can favor an ordered structure, even when the
motion of the vortices is plastic when the same force is applied in a constant
way. Our results relate the spatial order of the vortex lattice with its
mobility and they are in agreement with recent experiments. We predict that, in
oscillating applied forces, the lattice orients with a principal axis
perpendicular to the direction of motion.
