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packing rectangles into a container rectangle with minimum overlap
I have a case where I have a container rectangle of fixed dimensions, say WXH and I want to fill it up with two kinds of rectangles, with dimensions say w1Xh1 and w2Xh2,we can assume that w1,w2,h1 and h2 are integers, and these filling rectangles can be rotated by 90 degrees only. I want to fill up the container rectangle completely, for which there will be overlaps between rectangles. So, I have two objectives, first to determine minimum overlap area possible, and second determining the tiling placement(s) of rectangles that results in this minimum overlap area. How do I approach this problem? I have gone through the packing problems, but none of the standard algo seems to fulfill my requirement. Thanks a lot!