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 ,结果能够以很高的比率收敛于最优解 Aiming at the problem of minimum value and lacking of learning ability of Hopfield neural network (HNN), a learning algorithm is proposed. As the learning parameter, the coefficient which determines the weight value of the constraint condition is used to learn the parameter in the parameter space towards the direction of the fastest rising energy of HNN, so that the network state can escape effectively from the state of minimum value that may fall into. For the HNN which is in the minimum state in the state space, the parameter is first modified in the parameter space and then returned to the state space for state updating, and so on until the optimal solution or the satisfactory solution is found. The effectiveness of the algorithm is verified through simulation experiments. The algorithm is applied to the traveling salesman problem in 10 cities and 20 cities respectively, and the result can converge to the optimal solution at a very high rate