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If true, what implications does this have for P = NP? My intuition for a long time has been that P = NP only in the limit of an "infinitely sophisticated" algorithm. Such that as we do more research (or I suppose train larger models), we get closer and closer to the polynomial ideal.

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Current best heuristics, Lin-Kernighan-Helsgaun arrive probabilistically at better percentages for TSP.

Definitely makes you wonder if P = NP is even relevant when all the interesting instances can be solved to optimality or very near to it extremely often.

Some NP-complete problems have provably bad approximations if P!=NP. You don't get the same polynomial reduction behavior if you are using approximation algorithms. So for some problems we may have utterly practical algorithms and for others we never will (assuming P!=NP).

Doesn't apply here because this algorithm is an approximate TSP.

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