Pathfinding with unrestricted movement

I hope this doesn't end up becoming too difficult of a question. Basically, I'm working on a RTS-like game engine, and I'm working on optimizing my pathfinding AI for speed.

Pathfinding would normally not be much of a problem for me, but for this engine I need to have unrestricted movement, not tile-restricted movement. (In other words, the actors can move to specific coordinates on the map, they don't just move to the center of the tile you clicked in.)

I am not quite sure how to go about doing this, seeing as all of the pathfinding I've done in the past has been in strictly tile-based worlds. Any advice on this would be helpful.

One thing that I think will make it much easier to figure out is that the game map IS tile-based. Any tile on the map is either completely completely walkable, or completely unenterable, so I won't be dealing with oddly shaped walls or anything.


Thank you so much in advance for any help!
-Zippy Dee
Ted Bewman


//Edit: I forgot to mention that I'm using AS2.