Hopfield nets with time-varying energy functions for solving the travelling salesman problem

A novel method to solve the travelling salesman problem (TSP) with the Hopfield model is introduced. The method uses a time-varying energy function to enhance performance, instead of the simulated annealing approach of adding a random noise to the input of each neuron. The proposed energy function represents the TSP precisely and controls the process of convergence strictly. The method has obtained 100% optimal solutions within 300 iterations to the ten city problem with same map as that of J.J. Hopfield and D.W. Tank (1985), and has been proven very efficient for other sets of ten city problems whose cities are randomly and uniformly distributed within a unit square. Furthermore, some near-optimal solutions have also been found for larger-scale problems under the same circumstances