This paper shows that the performance of the Hopfield network for solving optimization problems can be improved by a varied beam search algorithm. The algorithm varies the beam search size and beam intensity during the network relaxation process. It consists of two stages: increasing the beam search parameters in the flrst stage and then decreasing them in the second stage. The purpose of using such a scheme is to provide the network with a better chance to find more and better solutions. A large number of simulation results based on 200 randomly generated city distributions of the 10-city traveling salesman problem demonstrated that it is capable of increasing the percentage of valid tows by 28.3% and reducing the error rate by 40.8%, compared to the original Hopfield network.
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