A new local search heuristic based on nearest insertion into the convex hull for solving Euclidean TSP

Abstract

The travelling salesman problem (TSP) is probably the most famous and extensively studied problem in the field of combinatorial optimisation. This problem is in the fields of logistics, transportation, and distribution. Since the TSP is NP-hard, many heuristics for the TSP have been developed. In this paper, we developed a novel local search heuristic, based on nearest insertion into the convex hull construction heuristic for solving Euclidean TSP. The proposed method, nearest insertion into the convex hull local search (NICH-LS) is used to improve the initial tour, which is taken from a tour construction heuristic, multi-agent reinforcement learning (MARL) heuristic, by locally manipulating the order of nodes in the consecutive partial tours of the initial tour. Changing the order of nodes in a partial tour is done via constructing the NICH tour of these nodes and replacing the partial tour with the modified partial tour, if its length is reduced. The proposed novel local search heuristic is applied to 29 benchmark instances from TSPLIB. The computational results show the efficiency of the proposed local search compared with five state-of-the-art heuristics.