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Hopfield神经网络是求解组合优化问题的一种有效方法。将所求问题转化为能量函数是神经网络求解组合优化问题的难点。针对此问题给出了能量函数设计的一般方法和步骤,证明了网络稳定的充分必要条件是网络的解有界。讨论了网络的平衡态与能量函数的极小点的关系,进一步完善了能量函数的方法。作为应用,严格证明了Hopfield神经网络的收敛性,所获结果不仅推广了一些已有的结论,而且为该网络的应用提供了一定的理论基础。
Hopfield neural network is an effective method to solve combinatorial optimization problems. It is difficult for neural network to solve the combinatorial optimization problem by transforming the desired problem into an energy function. A general method and procedure of energy function design are given for this problem. It is proved that the necessary and sufficient condition of network stability is the solution of network. The relationship between the equilibrium state of the network and the minimum point of the energy function is discussed, and the method of energy function is further improved. As an application, the convergence of Hopfield neural network is strictly proved. The obtained results not only generalize some existing conclusions, but also provide some theoretical basis for the application of the network.