It is possible that Archelaus was a contemporary of Alexander, and perhaps accompanied him on his expeditions, but as his work is completely lost, nothing certain can be said about the matter. It is also uncertain whether this Archelaus is the same as the one whose "Euboeica" are quoted by Harpocration, and whose works on rivers and stones are mentioned by Plutarch and Stobaeus.
This article incorporates text from a publication now in the public domain: Schmitz, Leonhard (1870). "Archelaus". In Smith, William (ed.). Dictionary of Greek and Roman Biography and Mythology. 1. p. 261.