  We investigate soliton mobility in the disordered Ablowitz-Ladik (AL) model
and the standard nonlinear Schr\"{o}dinger (NLS) lattice with the help of an
effective potential generalizing the Peierls-Nabarro potential. This potential
results from deviation from integrability, resulting of randomness for the AL
model, and of both randomness and lattice discreteness for the NLS lattice.
Statistical properties of such a potential are analyzed, and it is shown how
the soliton mobility is affected by its size. The usefulness of this effective
potential in studying soliton dynamics is demonstrated numerically. Further we
propose two ways the soliton transport in presence of disorder can be enhanced:
one is to use specific realizations of randomness, and the other one is to
consider a specific soliton pair.
