Optimal learning rate and neighborhood radius of Kohonen's self-organizing map for solving the travelling salesman problem

Abstract

The Travelling Salesman Problem (TSP) is one of the well-studied classic combinatorial optimization problems and proved to be a non-deterministic polynomial-time (NP) hard problem. Kohonen's self-organizing map (SOM) is a type of artificial neural network, which can be applied on the TSP. The purpose of the algorithm is to adapt a special network to a set of unorganized and unlabeled data so that it can be used for clustering and simple classification tasks. In this paper, we study the effect of changing the parameters in the SOM algorithm to solve the TSP. The focus of the parameter investigation lies on the influence of changes in the SOM learning rate and neighborhood radius as well as on the number of iterations in TSP problems with varying number of cities. Thus, the investigation is based on various problem instances as well as on different parameter settings of the SOM, which are compared with each other and discussed. The results are additionally compared with the nature inspired ant colony optimization (ACO) algorithm. As a result, it is proved that with the right parameter setting the SOM generated result is improved and that it is superior to the ACO algorithm.