This past summer, I met an interesting person named Bill (from Florida). His claim to fame: He had achieved a "county blackout."
That is, Bill had visited every single county within the United States. All 3141 counties and county-equivalents currently in the United States. See the Wikipedia page for elaboration.
To me this is an amazing achievement, but it seems to suggest a "fuzzy-logic" approach to this "fuzzy-version" of the traveling salesman problem.
That is, the locations to visit are now not cities (i.e. points) but large geographical areas. So, this allows greater flexability in planning the trip...and also perhaps increases the complexity of the problem.
As far as I know, Bill was not interested in efficiency and his visits were not done in one contiguous trip....nor are other "county-collectors," as I learned about a county-counting blog and a special website for county-counters working towards a blackout!