Generator of learning data for the TSPs based on the visiting order of the cities on convex hull

Abstract

The optimal tours of the traveling salesman problems( TSPs) in two dimensional Euclidean space have the characteristics in the visiting order of the cities on the convex hull. Based on this characteristics, the TSPs can be replaced into some shortest Hamiltonian path problems(SHPPs) of which solutions assemble a tour. This reduction is enabled by the calculation of convex hull and the classification of the cities not on the convex hull into the subsets of cities which construct SHPPs. This procedure means that the TSPs are equivalent to the classification problems, which leads to be able to apply existing methods of machine learning to the TSPs. We show that the teaching data for machine learning are available as the optimal classifications in the instances of which the optimal tour has been found.