Perturbation: An Efficient Technique for the Solution of Very Large Instances of the Euclidean TSP

In this paper we introduce a technique for building eecient iterated local search procedures. This technique, that we call perturbation, uses global information on TSP instances to speed-up and improve the quality of the tours found by heuristic methods. The main idea is to escape from local optima by introducing perturbations in the problem instance rather than in the solution. The performance of our techniques has been tested and compared with known methods. To this end, we performed a number of experiments both on test instances, for which the optimal tour length is known, and on uniformly distributed instances, for which the comparison is done with the Held-Karp lower bound. The experimental results, done on up to 100,000 cities, show that our techniques outperform the known methods for iterating local search for very large instances.