Minimal number of moves for iPuzzle15 known? Solver algorithm known?

[Castorp]

Hello Puzzle15ers

I wrote a solver for the 15 puzzle that mimics what a human usually
does.
(For an illustration, see: http://www.youtube.com/watch?v=vFqTkyU3df8)
This dynamic programming algorithm solves,
row1 first, then row2 then row 3 and 4 together by separating
these rows in two squares. Most people do it this way.

However, there is most often a strategy which requires (many) fewer
moves to complete.
A human can easily concentrates on moving one tile at a time to the
right place,
but then disregards the rest of the puzzle.
A computer can optimize on this.

I wonder:
- if it has been proven that putting and leaving 1, 2, 3, 4 in row 1
does not disallow
the rest of the puzzle to be solved in general
- same for row 2
- if any results on minimal number of moves have been proven
http://mathworld.wolfram.com/15Puzzle.html
mentions some results on the 8 puzzle (without proof)
- if ever, an algorithm has been developed to do just that (for all
cases of course)

any comments welcome

thanks and best regards,

Peter