A study of the application of Kohonen-type neural networks to the Travelling Salesman Problem

Abstract

It is observed that animals often have to resolve difficult tasks of optimization and that this process can be studied by applying the formal framework of neural networks to a simple problem such as the Travelling Salesman Problem. Existing work is reviewed with particular emphasis on recent studies using "self-organizing networks". An algorithm is described in which general principles developed by Kohonen are applied to the Travelling Salesman Problem. Simulation results are given for problem sets of up to 10,000 cities. The routes generated are reported as being slightly longer than those produced by simulating annealing; compute time is lower and scales less than quadratically with problem size. It is suggested that the ability to perform optimization is an emergent computational property not just of the Kohonen model but of any mechanism capable of producing topology-preserving mappings, including mechanisms within the brain.