Clustering-Assisted Ant Colony Optimization for Large-Scale Travelling Salesman Problem

Ant Colony Optimization (ACO) has been proven to be very effective in solving Traveling Salesman Problems (TSP). However, its effectiveness encounters limitations when solving large-scale TSP involving a considerably large number of cities. To alleviate this issue, clustering algorithms have been popularly used to help ACO effectively solve large-scale TSP, leading to Clustering-Assisted ACO (CA-ACO). Though there are a few studies in this direction, no research has been done to explore in depth the influence of clustering algorithms on ACO in solving large-scale TSP. To fill this gap, this paper investigates the effectiveness of three classical clustering algorithms (k-means, mini-batch k-means, and fuzzy c-means) on five classical ACOs (ant system (AS), elite AS (EAS), rank-based AS (RAS), max-min AS (MMAS), and ant colony system (ACS)) in solving large-scale TSP. To further boost the optimization performance, this paper designs a new sub-route merging scheme and a new local search method to effectively combine sub-routes and refine the final global route. Experiments conducted on six ArtTSP instances have proved that K-means is the most effective among the three clustering algorithms to cooperate with the five ACOs and ACS is the most effective among the five variants to cooperate with the three clustering algorithms to solve large-scale TSP.