Resumen
This paper investigates the systematic and complete usage of k-opt permutations with k=2…6" role="presentation">??=2?6k=2?6
k
=
2
?
6
in application to local optimization of symmetric two-dimensional instances up to 107" role="presentation">107107
10
7
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" role="presentation">105105
10
5
points and specifically 3.37% for the largest examined tour containing 107" role="presentation">107107
10
7
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.