In this paper we propose a general recipe for calculating the automorphism
groups of semigroups consisting of partial endomorphisms of relational structures
with a single m-ary relation for any m in N over a finite set.
We use this recipe to determine the automorphism groups of the following semigroups:
the full transformation semigroup, the partial transformation semigroup, and
the symmetric inverse semigroup, and their wreath products, partial endomorphisms of
partially ordered sets, the full spectrum of semigroups of partial mappings preserving or
reversing a linear or circular order. We also determine the automorphism groups of the
so-called Madhaven semigroups as an application of the methods developed herein.