An Algorithm Framework for Traveling Salesman Problem Using Geometric Information

Abstract

Some traditional approaches of solving traveling salesman problem (TSP), such as: genetic algorithm, large neighborhood search algorithm, etc., aim to obtain a satisfactory solution of TSP through continuous search, and do not use the geometric characteristics of TSP. In this paper, by studying the path graph of the optimal solution of TSP, the authors find a special geometric characteristic of the best connections—points with closer distance between each other in the optimal connection form a path connected with the outside. Based on the geometric characteristic, a cluster first-insert second algorithm framework to solve TSP is proposed. The comparison between example algorithm and other algorithms shows that the algorithm framework has advantage in solution quality.