Also, there are lots of specific configurations of cities for which an optimial solution can be found in a tractable amount of time -- it's only the general case that is the problem, and there's some debate about how "degenerate" real world examples are. In "well-behaved" cases, a good approximate answer will be the answer; in almost all cases, the differences between a good estmate and the correct solution is small relative to the total path (and so the difference is of limited importance).
I often find that optimization problems suffer from trying to optimize the general problem rather than using the constraints present in the real world.
TSP is similar to Turing machines and the halting problem -- in practice, it really doesn't matter.
I often find that optimization problems suffer from trying to optimize the general problem rather than using the constraints present in the real world.
TSP is similar to Turing machines and the halting problem -- in practice, it really doesn't matter.