Empirical Evidence of the Chaotic Behavior of the Hopfield-Tank TSP Model

Since its introduction, the Hopfield-Tank model for the Traveling Salesman Problem (TSP) has been surrounded by controversial evidence regarding its viability as a model and its capabilities to produce good results to this hard optimization problem. In this paper we investigate the reasons behind the difficulty of obtaining verifiable results and the viability of the model, by investigating the behavior the Hopfield-Tank neural network for the TSP has in circumstances when it is expected to produce identical tours. Our investigations strongly suggest that, when it is expected from the network to converge in a predetermined tour, the neural network converges to almost all possible tours when an insignificant perturbation to the initial conditions is applied. The overall consequence of our findings regarding the viability of the Hopfield-Tank model and the cause of the controversy surrounding the Hopffield-Tank model for the TSP can be summarized by the following: The cause of the Hopfield-Tank neural network for the TSP controversy and the difficulties in reproducing results is the chaotic behavior of the model. The finding of useful results for the TSP using the Hopfield-Tank network are purely casual and not to be attributed to the viability of the model. In essence the Hopfield-Tank neural network for the TSP is as viable as chaotic systems can be