An effective iterated two-stage heuristic algorithm for the multiple Traveling Salesmen Problem

The multiple Traveling Salesmen Problem (mTSP) is a general extension of the famous NP-hard (TSP), that there are m (m>1) salesmen to visit cities. In this paper, we address mTSP with both minsum objective and minmax objective, which aims at minimizing total length tours longest tour among all tours, respectively. We propose an iterated two-stage heuristic algorithm called ITSHA for mTSP. Each iteration consists initialization stage improvement stage. generate high-quality diverse initial solutions. mainly applies variable neighborhood search (VNS) approach based on our proposed effective local neighborhoods optimize solution. Moreover, some optima escaping approaches employed enhance ability algorithm. Extensive experimental results wide range public benchmark instances show significantly outperforms state-of-the-art algorithms in solving objectives.