Improving the Performance of the Hopfield Network By Using A Relaxation Rate

  • Xinchuan Zeng
  • Tony R. Martinez


In the Hopfield network a solution of an optimization problem is obtained after the network is relaxed to an equilibrium state. This paper shows that the performance of the Hopfield network can be improved by using a relaxation rate to control the relaxation process. Analysis suggests that the relaxation process has an important impact on the quality of a solution. A relaxation rate is then introduced to control the relaxation process in order to achieve solutions with better quality. Two types of relaxation rate (constant and dynamic) are proposed and evaluated through simulations based on 200 randomly generated city distributions of the 10-city traveling salesman problem. The result shows that using a relaxation rate can decrease the error rate by 9.87% and increase the percentage of valid tours by 14.0% as compared to those without using a relaxation rate. Using a dynamic relaxation rate can further decrease the error 3rate by 4.2% and increase the percentage of valid tours by 0.4% as compared to those using a constant relaxation rate.


Relaxation Process Relaxation Rate Travel Salesman Problem Ation Rate Tour Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Wien 1999

Authors and Affiliations

  • Xinchuan Zeng
    • 1
  • Tony R. Martinez
    • 1
  1. 1.Computer Science DepartmentBrigham Young UniversityProvoUSA

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