An Efficient Neighborhood Structure Generating Method for Large-scale Traveling Salesman Problem

Local search is a major methodology to address large-scale traveling salesman problems (TSPs). The key of local search in TSPs is to generate the neighborhood structure of a solution, i.e., a candidate set of edges connecting the cities. The main goal of this paper is to present an efficient neighborhood structure generation method called Euler neighborhood structure (ENS). It constructs a list of good candidate edge with a complexity lower than quadratic. With these candidate edges, local search is able to find high-quality solutions efficiently. To validate the effectiveness of the proposed approach, it has been integrated into the Lin-Kernighan-Helsgaun TSP solver. Experimental results show that the candidate set generated by ENS is more streamlined.