I am looking for a survey or an original article that discusses what is known about homogeneity in preordered (quasiordered) sets.

We know that in the case of posets (partially-ordered sets), the theory of automorphisms and homogeneity has reached a great extent.

Recall that, a poset P is called homogeneous, if for each two elements a, b of P there is at least one automorphism of P which maps a onto b.