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Rescaling the energy function in Hopfield networks

In this paper we propose an approach that rescales the distance matrix of the energy function in the Hopfield network for solving optimization problems. We rescale the distance matrix by normalizing each row in the matrix and then adjusting the parameter for the distance term. This scheme has the capability of reducing the effects of clustering in data distributions, which is one of main reasons for the formation of invalid solutions. We evaluate this approach through a large number (20000) simulations based on 200 randomly generated city distributions of the 10-city traveling salesman problem. The result shows that, compared to those using the original Hopfield network, rescaling is capable of increasing the percentage of valid tours by 17.6%, reducing the error rate of tour length by 11.9%, and increasing the chance of finding optimal tears by 14.3%.