Rotos puzzle theory

[Scigatt]

For the Rotos puzzle, I want to obtain and understand a 'fewest moves' solution to this puzzle. In particular, I want to solve the permutation below:

3 2 1
7 6 5 4
0 9 8

I did manage to solve it, but with a lot of turns(29 HTM, 70 QTM). How would I get a smaller solution? What about a general low move count solution for humans?

These are the algs I found to get the long solution:

R4 L2 R2 L4: Swaps at position pairs (2,9) and (4,7).

L3 R3 L3: Swaps at position pairs (1,3), (8,0) and (5,7).

R3 L' R3 L3 R: Places pieces at spots 1, 3, 8, and 0 on spots 6, 4, 7, and 5 respectively.

 

[jaap]

If you use the solver built into the javascript simulation on my page, you will get an optimal solution (in 'qtm'). The solution it finds is:
L-2 R' L2 R' L' R L R-2 L R L R L' R' L (15/18)
Like most optimal solutions, this does not really provide any insight.