Any standard heuristic to solve bin packing problem with irregular sheet?

Question

I have a non-convex region (may contain holes). I want to:

1. Fill region with rectangles
2. No restriction on size or number of rectangles
3. Maximize the area occupied by rectangles
4. Minimize number of rectangles
5. Avoid rectangle overlap

Are there standard heuristic approaches to solve this optimization? How would you formally classify this problem?

Read through various cutting stock problem literature, but didn't find something quite similar.