Improvement heuristics for the TSP like 2-Opt need construction heuristics (also called constructive heuristics) like the Nearest Neighbour to start. Intuitively, I would say that a better construction heuristic leads on average to better results for the improvement heuristic. I think this is difficult to prove because a worse initial solution could nevertheless lead to the global optimum. Is there a prove or anything else that makes a statement about the dependency of the quality of improvement heuristics and construction heuristics?
Or more generally speaking: Do better-starting solutions lead to better performances of improvement heuristics?