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Improving the Hopfield network through beam search

We propose a beam search mechanism to improve the performance of the Hopfield network for solving optimization problems. The beam search re-adjusts the top M (M>1) activated neurons to more similar activation levels in the early phase of relaxation, so that the network has the opportunity to explore more alternative, potentially better solutions. We evaluated this approach using a large number of simulations (20,000 for each parameter setting), based on 200 randomly generated city distributions of the 10-city travelling salesman problem. The results show that the beam search has the capability of significantly improving the network performance over the original Hopfield network, increasing the percentage of valid tours by 17.0% and reducing error rate by 24.3%.