Self-organizing neural networks and various euclidean traveling salesman problems

By using competitive learning, which causes just one or a group of a small number of neurons to respond to a given input, self-organization of entire neural networks can be achieved. When this self-organization process is applied to various kinds of travelling salesman problems in a Euclidean space, a good approximation or the true solution is obtained. We use a sequential update which looks at the position vector of each city one at a time as the training method for a neural network arranged as a closed loop. In this case, we use symmetrical connections between neurons. The number of neurons required is approximately linear in the number of cities. In the first experiment, we carried out a quantitative comparison with the simulated annealing method using 500 sets of 30 cities and demonstrated this method's superiority. Next, we obtained a good approximation on a set of 532 U.S. cities and demonstrate its superiority with respect to the increase in the number of cities in actual (realistic) data. Further, for a generalized constrained multiple-salesman problem, we explain this method's compactness and efficiency and give an experimental example. The computation can be adequately performed by a common workstation with a serial processor.