I am using ArcGIS and I have a layer of polygons that has an attribute. I would like to overlay a circle (or other shapes in theory) of a specified size such that it would encompass the maximum amount of the attribute from the polygons. For example, placing a circle with a diameter of 5 miles over census tracts (that have a population density attribute) so that the circle will encompass the maximum population possible.
I understand that preferably the shape I'm overlaying will be large enough not to get stuck in the middle of a single polygon. I also realize that calculating a maximizing function might not be entirely straightforward as there will be partial overlaps.
I imagine that there is something already out there that does this but I'm not having any luck with searching. I don't know what this sort of analysis would be called either so that doesn't help.
If ArcGIS isn't the appropriate tool for this I'm open to other suggestions. Thanks in advance for any help you can provide!