Using Hopfield networks to solve traveling salesman problems based on stable state analysis technique

We have elsewhere developed a general method called the stable state analysis technique to determine constraints that the weights in the Hopfield energy function must satisfy so that valid solutions of high quality can be always obtained. In this paper, the effectiveness of this method is demonstrated through a reinvestigation of the capability of the Hopfield neural net (HNN) to solve the traveling salesman problem (TSP). A large number of experiments on 10-city TSPs demonstrate the proposed method can obtain results comparable to those obtained using simulated annealing, while the mean error of achieved solutions to a 51-city TSP is about 15% longer than the optimal tour, which is much better than that of solutions obtained through other HNN-based methods.