基于Hopfield网络的极小值问题学习算法

Learning algorithm for solving local minimum problems based on Hopfield network

针对 Hopfield神经网络 (HNN )所存在的极小值问题及缺乏学习能力的问题 ,提出了一种学习算法。将决定约束条件权值大小的系数作为学习参数 ,在参数空间里使参数向着 HNN能量上升最快的方向学习 ,使网络状态能够有效地从可能陷入的极小值状态中逃脱出来。对于在状态空间里陷入极小值状态的 HNN,首先在参数空间里修正参数 ,然后再返回到状态空间里进行状态更新 ,如此反复 ,直至找到最优解或满意解。算法的有效性通过仿真实验进行了验证。该算法分别被应用于 10城市和 2 0城市的旅行商问题 。

A learning algorithm is proposed to solve the local minimum problem and the un-learnable problem for Hopfield neural networks. The learning algorithm defined the coefficients of the constraint weight degrees as the learning parameters, and increased the energy of the Hopfiled network by modifying its learning parameters in the parameter space, to enable the network to escape from a local minimum. The updating in state space and the learning in parameter space on the Hopfield network were repeated until the global minimum or a better solution was obtained. This learning algorithm was applied to the 10-city and 20-city traveling salesman problems. The network converges to the global minimum every time.