I am interested in learning about what methods are currently considered to be the "best" for approximately solving large instances of the Traveling Salesman Problem (TSP) in practice. However, as I began writing a question concerning this I was prompted that
The question you're asking appears subjective and is likely to be closed.
I understand why this is a dangerous question to ask. There are many heuristics and meta-heuristics that have been published claiming to efficiently find near-optimal solutions to TSPs, each with their own benefits and drawbacks, and no method is necessarily clearly the best.
However, this is precisely why I'm interested in asking this question: there are so many different methods that exist that it is hard for someone not experienced in the field to truly compare them. Certainly some methods are more highly cited then others, but these methods may have been supplanted more recently by better methods which are less well known.
While the question has no definitive answer, it is not merely a matter of opinion. There are various empirical and theoretical results that can be referenced to justify a particular answer. Even if there is no one definitive answer, I can imagine that answers to the question could be given that would be constructive and helpful to myself and others with an interest in the subject.
Would asking this question be considered on topic in this community? If not, would there be a way of modifying or changing the question to make it more on topic? (For instance, asking for some very good methods for solving the TSP rather than "the best"?)