Is there a way that I can take an adjacency matrix and sort the edges in terms of which edges are objectively most valuable (a best pick) for a TSP circuit?
You cannot do it via sorting by lowest weight, because a row of [5, 19, 22, 28, 300] would all be sorted before [2000, 9000, 50000, 51000, 52000], even though the 2000 is much more valuable for your path than any of the choices are in the other row.
I tried normalizing the rows to unit length, which gives a more accurate picture of each edge's value in terms of efficiency. It is still often incorrect, though, and will end up finding a path without having all of the true best edges in it's collection.
I think the key involves sorting by the difference from one element to the next of the same row, so you get value in terms of how much you lose by moving on to the nextedge.
Does anyone know anything about this?