Predicting hardness of travelling salesman problem instances

Abstract

Travelling Salesman Problem is a classical combinatorial problem which is used to check the performance of heuristics and metaheuristics. However, for fairly comparing the performance of these algorithms, it is necessary an in-depth understanding of the hardness of the Travelling Salesman Problem instances. This requires to recognize which attributes allow a correct prediction of the hardness of the instances of Travelling Salesman Problem. In this work, the hardness of the instances was predicted based on the statistical distribution of the distance between the cities, the areas arisen from the Dirichlet tessellation, and the areas from the Delaunay triangulation. As a consequence of this work, the attributes which separate the ease and difficult instances of the Travelling Salesman Problem are stated.