http://en.wikipedia.org/wiki/Bin_packing_problem
Not something simple (a NP-complete problem is a problem with heuristic solutions, but no general, deterministic solution working in finite time...).
Your problem seems simpler, as the container has no finite size. Or we miss information...
A simplistic, but effective solution is just to put all the rectangles on the same line: no white space, compact shape. But a bit longer than wide...
To pack in a more compact shape (rectangular with a ration closer of 1), you probably have to pick first the biggest shapes, and aggregate them. Then try to fit the smaller shapes.
You can also look the forums for layout sketches, there are some trying to do that, to pack circles, or words (search Wordle, there is a Processing library emulating / re-creating its algorithm). They often proceed this way: placing big shapes, trying to fit smaller shapes in the holes.

Another approach would be to use a treemap layout algorithm as your starting point, and then place each rectangle inside its treemap rectangle preserving its aspect ratio at the expense of a small amount of whitespace.

thanks you both,

I wasn't suggesting you were looking for an AR of 1. My point was that the same algorithm that does aim for 1 could be adapted to instead aim for an AR of the rectangle you wish to display at that location.

Sorry, i had to read better. Let's call it a day :)