Fitting a square grid with non-overlapping rectangles

Question

Let R be a list of rectangles R_i with integer height h and width w.

What are all the possible positions of these rectangles and their 90 degree rotations on a NxN square grid (N <= 64) without overlaps? Every rectangle R_i can and must be placed only once, but there can be duplicates in the list R. (You could also say each rectangle has to be placed m_i times, where m_i is a natural number bigger than 0, so no duplicates in set R)

For example

Let R = {{1, 2}, {1, 1}}.

And a 2x2 square grid:

0 0
0 0

We can fit the rectangles in the following way, where 'a' represents the first rectangle and 'b' the second rectangle:

b a    0 b     a 0    a a    
0 a    a a     a b    0 b    

0 a    b 0     a b    a a    
b a    a a     a 0    b 0    

The bigger picture is finding the best tiling in respect to a metric. I'm still thinking about the exact metric, its about the distance between some of the edges of the rectangles. I thought spanning the solution space would be a good start for some algorithm, greedy search or neural net etc.