Algorithm for optimized sorting of boxen into a 4x4 rack

I'm looking to solve a problem regarding the optimal sorting of variable sized boxes into the confined space of a 4x4 sized rack. The algorithm should sort those boxes so that there is as little wasted rackspace as possible.

The rack I'm talking about looks like the typical IKEA rack "Expedit".

Perhaps somebody can point me to documentation on algorithms that could solve such a problem or to some implementation. Every programming language is welcome.

Thanks for your time, F开发者_如何学Gorank

What you are looking to do is solve the 2d bin-packing problem.

Here's a question with some pointers.

You want to look for the 1d bin-packing problem (and NOT the 2d bin-packing). This problem is very hard to solve. You want to read this: http://www.developerfusion.com/article/5540/bin-packing/. Here is a 2d version: Packing problem revisited