# Travelling Salesperson Revisited

I have decided to come back to the TSP problem. I have optimized my approximation. So first of all, my nearest neighbor was not very good in the previous one. I have fixed it, and now we get really nice graphs to start with. One of the main flaws of what I have is we’re kind of forced to begin in a place for the nearest neighbor(depending where you start it may give you less or better beginning approximation). The other main issue with what I have, is I don’t know if what I have is really any good. It’s sort of a mix mash of heuristics from Wikipedia. I’ll post more some other day, but I have attached the approximations I have been able to create. These were all calculated in under 30 seconds, most of them in the 4-10 second range on a modern i7 2.9 Ghz CPU.

These graphs are incredibly tricky to solve. Technically for a 100 node graph there are, different solutions, that all would need to be checked to guarantee the optimal solution. A 40 node graph, is approximated in just 1-2 seconds on my computer with this heuristic, there are different graphs that would need to be checked to find the most optimal solution. This problem is also believed to be NP-Complete, so the best we can do are approximations.