Redesigning the Wheel for Systematic Travelling Salesmen

This paper investigates the systematic and complete usage of k-opt permutations with k=2…6 in application to local optimization of symmetric two-dimensional instances up to 107 points. The proposed method utilizes several techniques for accelerating the processing, such that good tours can be achieved in limited time: candidates selection based on Delaunay triangulation, precomputation of a sparse distance matrix, two-level data structure, and parallel processing based on multithreading. The proposed approach finds good tours (excess of 0.72–8.68% over best-known tour) in a single run within 30 min for instances with more than 105 points and specifically 3.37% for the largest examined tour containing 107 points. The new method proves to be competitive with a state-of-the-art approach based on the Lin–Kernigham–Helsgaun method (LKH) when applied to clustered instances.