This work focuses on improving the Hopfield network for solving optimization problems. Although much work has been done in this area, the performance of the Hopfield network is still not satisfactory in terms of valid convergence and quality of solutions. We address this issue in this work by combing a new activation function (EBA) and a new relaxation procedure (CR) in order to improve the performance of the Hopfield network. Each of EBA and CR has been individually demonstrated capable of substantially improving the performance. The combined approach has been evaluated through 20,000 simulations based on 200 randomly generated city distributions of the 10-city traveling salesman problem. The result shows that combining the two methods is able to further improve the performance. Compared to CR without combining with EBA, the combined approach increases the percentage of valid tours by 21.0% and decreases the error rate by 46.4%. As compared to the original Hopfield method (using neither EBA nor CR), the combined approach increases the percentage of valid tours by 245.7% and decreases the error rate by 64.1%.
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