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以ＴＳＰ问题为例，详细分析了Ｈｏｐｆｉｅｌｄ网络在求解组合优化问题时经常出现的不稳定性和局部最优性，提出了解决这２个问题的一个改进算法．证明了对于全负联接的Ｈｏｐｆｉｅｌｄ网络，如果对神经元的特性函数进行修改就可以控制系统在状态空间的运动方向，从而保证网络在当前能量函数下降最快的方向上迅速地收敛到局部最优解．当系统到达局部最优解以后，再根据模拟退火（ＳＡ）的思想，通过给局部最优解以足够大的扰动，迫使系统解由当前的局部最优沿约束超曲线面的极小点转向全局最优．由于系统局部最优解的得到非常迅速，而且系统的运动轨迹可以控制，因此文中提出的算法在时间上大大优于ＳＡ法
Taking TSP as an example, the instability and local optimality of Hopfield network in solving combinatorial optimization problems are analyzed in detail. An improved algorithm is proposed to solve these two problems. It is proved that the Hopfield neural network with all negative connections can control the moving direction of the system in the state space if the characteristic function of the neuron is modified so as to ensure that the network rapidly converges to the local optimum in the direction that the current energy function declines most rapidly solution. After the system reaches the local optimal solution, according to the idea of simulated annealing (SA), by perturbing the local optimal solution with sufficient perturbation, the system solution is forced to turn from the minimum point of the current local optimal constrained hypersurface Global optimal. Because the local optimal solution gets very fast and the system’s trajectory can be controlled, the proposed algorithm outperforms the SA method in time