I'm interested in a particular case of this problem: fitting odd-shaped polygons/shapes within the bounds of a rectangle.
Say you have 10 sticker designs and you want to fit them all on a sheet of A4 paper for printing. You can rotate and translate each sticker at will to fit the shapes around each other.
My goal is to find the layout that allows me to maximise the size ("area"?) of each sticker. A harder problem would allow weightings that would allow some stickers to be larger than average and some smaller but I'm more interested in the simpler problem.
Is there any method or software for optimising the fit of the stickers within the bounding rectangle? I'm not expecting a perfect solution, just some way to get significantly better than random would be great.