On the Empirical Scaling Behaviour of State-of-the-art Local Search Algorithms for the Euclidean TSP

We present a thorough empirical investigation of the scaling behaviour of state-of-the-art local search algorithms for the TSP; in particular, we study the scaling of running time required for finding optimal solutions to Euclidean TSP instances. We use a recently introduced bootstrapping approach to assess the statistical significance of the scaling models thus obtained and contrast these models with those recently reported for the Concorde algorithm. In particular, we answer the question whether the scaling behaviour of state-of-the-art local search algorithms for the TSP differs by more than a constant from that required by Concorde to find the first optimal solution to a given TSP instance.