A direct neural approach for the traveling salesman problem

It is shown that a simple modification of the neural network as proposed by J.J. Hopfield and D.W. Tank (see Biological Cybernetics, vol.52, p.141-152 (1985)) can be used to find consistently valid solutions to the traveling salesman problem (TSP) for an arbitrarily large number of cities. This direct approach requires the selection of only one parameter which can be heuristically estimated, while the remaining parameters can be directly computed. Criticisms which claim that the TSP network cannot be easily scaled to large problems are shown to be inapplicable to this method. The quality of the solutions given by the direct method is comparable to those achieved by Hopfield, averaging in the top 99% of the solution space for small problems, and progressively poorer as the problem size increases. The reasons for the decline of solution quality are identified, and are shown to be fundamental problems with the neural representation of the problem