After fighting a Vasari AI as Advent, I found a mine clearing tactic that wasn't very obvious.
The normal flow I had is to jump in, dodge the mines, nix the starbase and tactical structures, liberate and colonize the planet, and move on. This leaves lots of cloaked mines and logistics, but delaying my fleet means giving the enemy an advantage. Solution?
Three scouts and a starfish. The starfish, with it's huge range, structure damage, and many targets means that it cleans out structures and mines, all at the same time, quickly and cheaply. Defense frigates didn't really seem as effective, relatively.
This only works for Advent, though - the Ogrov isn't quite the same thing and the Vasari don't get one. Anyone come up with interesting strats for TEC/Vasari?