Simple and fast TSP initialization by Delaunay graph

Abstract

Finding an initial solution for traveling salesman fast and with reasonable quality is needed both by the state-of-the-art local search and branch-and-bound optimal algorithms. Classical heuristics require O(n 2 ) and their quality may be insufficient to keep the efficiency of the local search high. In this paper, we present two fast variants that utilize a Delaunay neighborhood graph. The best methods achieve 2.66% gap for Dots datasets, and 15.04% gap for the selected TSPLIB datasets. However, these results were obtained with slower algorithms. The best of the fast methods achieved 5.76% gap for Dots datasets, and 19.07% gap for the selected TSPLIB datasets in 307 milliseconds, on average.