Most NP-complete problems have really good heuristics that come to within a hair of optimal on most useful real-world inputs, e.g. things like integer partitioning, bin packing, traveling salesman, etc. You need really unusual inputs to give an optimal solver a drastic advantage. Case in point, with real-world TSP the fact that the cities are embedded on a plane means their distances have constraints that don't exist in the general problem.
No, there aren't? The last time I checked, the best polynomial-time approximation algorithm to symmetric TSP (Christofides) could only guarantee finding a tour with no more than 3/2 of optimal length. Has something better been found since then?
