  We investigate the dynamics of interacting magnetic flux lines driven by an
external current in the presence of linear pinning centers, arranged either in
a periodic square lattice or placed randomly in space, by means of
three-dimensional Monte Carlo simulations. Compared to the non-interacting
case, the repulsive forces between the vortices reduce the critical current
J_c, as determined from the depinning threshold in the current-voltage (I-V)
characteristics. Near the depinning current J_c, the voltage power spectrum
S(w) reveals broad-band noise, characterized by a $1/w^a$ power law decay with
a <= 2. At larger currents the flux lines move with an average velocity v_{cm}.
For a periodic arrangement of columnar pins with a lattice constant $d$ and
just above J_c, distinct peaks appear in the voltage noise spectrum S(w) at w ~
v_{cm}/d which we interpret as the signature of stick-slip flux line motion.
