A New Heuristic for Traveling Salesman Problem Based on LCO

Abstract

The Traveling Salesman Problem (TSP) is one of the most well known combinatorial optimization problem and has wide range of application. Since the TSP is NP-hard, many heuristics for the TSP have been developed. This study proposes a new heuristic for the TSP based on one of these heuristics named Local Clustering Optimization (LCO). LCO is a metaheuristic proposed by Furukawa at el. to give an accurate solution for large scale problems in a reasonable time. However, conventional LCO-based heuristics for the TSP is not suited to solving asymmetric instances. The proposed method iteratively adopts tour construction heuristics such as nearest neighbor and random insertion to get an accurate solution more efficiently for the both asymmetric and symmetric TSP. The proposed method and other heuristics are applied to benchmark instances from TSPLIB and randomly generated instances. The experiment shows the proposed method is superior to conventional LCO in terms of accuracy of the solution. However, the proposed method is inefficient for instances which are not close to Euclidean due to the same property of insertion heuristic.