TITLE: How to pack 3D boxes into a bigger box?
QUESTION [9 upvotes]: Given a box of given size $L\times M\times N$ and a list of smaller boxes of given sizes $(l_i,m_i,n_i)$, decide whether the smaller boxes altogether fit into the big box (and produce such a packing if possible). 
The problem is NP-complete...so I am looking for a good heuristic algorithm...the algorithm should allow for (the obvious possible) rotations of the boxes.
What are currently good/best heuristic algorithms and codes? Links to papers or webpages are also welcome.

REPLY [5 votes]: It would probably take some work to turn this into an algorithm that can deal with rotations of the boxes, but you might be able to modify the three weight algorithm (a variation of ADMM) by Derbinsky, Bento, Elser, and Yedidia, which is a fairly simple algorithm that has recently beaten various records for circle and sphere packing in boxes.