Combining 2-opt, 3-opt and 4-opt with K-swap-kick Perturbations for the Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is a famous NP-hard problem typically solved using various heuristics. One of popular heuristics class is k-opt local search. Though these heuristics are quite simple, combined with other techniques in an iterated local search (ILS) framework they show promising results. In this paper, we propose to combine the 2-opt, 3-opt and 4-opt local search algorithms with so called k-swap-kick perturbations, which are a generalization of the well known double-bridge (random 4opt) move. To reduce the run time of our 2-opt, 3-opt and 4-opt implementations, we apply some enhancements like a candidate list (based on k-d tree), search cuts, greedy starts, two-level tree data structure and others. We provide experimental results of the implemented algorithms with the TSPLIB instances.