There was an competition on codechef.com (great site by the way, monthly programming competitions) where one was supposed to solve an unsolveable sudoku (one should come as close as possible with as few wrong collumns/rows/etc as possible).
What I would do, was to first generate a perfect sudoku and then override the fields, that have been given. From this pretty good basis on I used genetic programming to improve my solution.
I couldn't think of a deterministic approach in this case, because the sudoku was 300x300 and search would've taken too long.
