Integrating data transformation techniques with Hopfield neural networks for solving travelling salesman problem

This study presents an improved artificial neural network (ANN) approach for solving travelling salesman problem (TSP). We employ Hopfield neural networks (HNN) and data transformation techniques (DTT) together to improve accuracy of the results and reach to the optimal tours with less total distances. To meet this purpose we integrate Z-score and logarithmic approaches with Hopfield neural networks, i.e., we prepare more appropriate inputs for the ANN training process. Then we evaluate the usefulness of our integrated approach by applying it on the 10-city problem which has been used for comparison by several authors. Results show that our integrated approach gives better results than basic Hopfield approach. In the other hand Z-score based approach gives the best results among all, logarithm based approach takes the second place and basic approach takes the third place. (C) 2010 Elsevier Ltd. All rights reserved.