Solving TSP by dismantling cross paths

Abstract

Traveling salesman Problem (TSP) is a classical NP-hard problem and has been extensively studied in literature. Eliminating the cross paths, which commonly exist in approximate solutions to large scale TSP, can effectively improve the quality of the solutions. Through studying the impact of cross paths on the cost of a loop, in this paper we develop a method to detect and dismantle cross paths, and thus propose a novel greedy algorithm-based approach to the TSP. This approach has been evaluated on ten TSP data sets and compared to three classical optimization techniques, including the elastic network, ant colony algorithm and genetic algorithm. Our results show that the proposed approach can get approximate solution of high quality with far less computational cost and has an excellent performance in solving large-scale TSP.