I have a little doubt with respect to the two-opt improvement heuristic for TSP. I understand how it works, from the Wikipedia article on 2-opt and Heuristics for the Traveling Salesman Problem. However, from my understanding and subsequent experiments, it appears this heuristic does not give any guarantee to at least not lead to a worse tour. If this is so, I don't understand how a two-opt move is any better than a random swap of cities. I would really appreciate if this can be clarified for me. Thanks!
Is a two-opt move guaranteed to produce a non-worse tour?
heuristics;traveling salesman