Right, I should have made that point more clear. The TSP problem is NP-complete, but it may be possible to come up with an 'incomplete' algorithm that works ef

Right, I should have made that point more clear. The TSP problem is NP-complete, but it may be possible to come up with an 'incomplete' algorithm that works efficiently for a large subset of the problem space, and it may be possible to find an approximate algorithm that efficiently finds guaranteed near-optimum solutions to all problems. Neither of those two things requires doing the truly difficult (perhaps impossible) work of coming up with a precise, complete, and efficient algorithm to an NP-complete problem.