On the stability of the travelling salesman problem algorithm of Hopfield and Tank
Biological Cybernetics
IEEE Transactions on Neural Networks
An Efficient Multivalued Hopfield Network for the Traveling Salesman Problem
Neural Processing Letters
A saturation binary neural network for crossbar switching problem
AICI'11 Proceedings of the Third international conference on Artificial intelligence and computational intelligence - Volume Part III
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When solving an optimization problem with a Hopfield network, a solution is obtained after the network is relaxedto an equilibrium state. The relaxation process is an important step in achieving a solution. In this paper, a new procedure for the relaxation process is proposed. In the new procedure, the amplified signal received by a neuron from other neurons is treated as the target value for its activation (output) value. The activation of a neuron is updated directly based on the difference between its current activation and the received target value, without using the updating of the input value as an intermediate step. A relaxation rate is applied to control the updating scale for a smooth relaxation process. The new procedure is evaluated and compared with the original procedure in the Hopfield network through simulations based on 200 randomly generated instances of the 10-city traveling salesman problem. The new procedure reduces the error rate by 34.6% and increases the percentage of valid tours by 194.6% as compared with the original procedure.