  We present the results of a computer simulation study of the melting scenario
of two-dimensional soft-disk systems with potential
$U(r)=\varepsilon(\sigma/r)^n$, $n=12$ and $n=1024$, both in the presence of
random pinning and without it. The melting parameters have been determined from
analysis of the behavior of equations of state, correlation functions of the
orientational and translational order parameters, Young modulus and
renormalization group equations. The transition points obtained from these
criteria are in good agreement. We have shown that the systems melted in two
stages - first-order hexatic phase to liquid transition and the continuous
Berezinskii-Kosterlitz-Thouless type crystal-hexatic phase transition. Random
pinning widened the hexatic phase, but left the melting scenario unchanged.
