组合优化神经网络的胞元设计及稳定性分析

以ＴＳＰ网络为例，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Ｈｏｐｆｉｅｌ网络，如果对神经元的特性函数进行个性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。

NEURON DESIGN AND STABILITY ANALYSIS OF NEURAL OPTIMIZATION NETWORK

he Hopfield network has been frequently used to resolve a variety of optimization problems. However, the convergence and globally optimal solution to the problems are not guaranteed when the network is implemented in digital computer. In this paper, we investigate the reasons which result in the unstability and locally optimal solution, and propose a modified algorithm. First, a lemma is proved which indicates that the rapid convergence of symmetric Hopfield network with nonpositive synapse can be guaranteed if the S function of neuron sa tisfies some constraints. Second, a S function is provided which obeys above lemma and is able to oblige the energy function to descend along the current maximum gradient direction. Finally, a method is also given which can control the solution to move from local optimum to global optimum by producing a new solution that satisfies the contraint items of energy function. The experimental results show that the performance of the proposed algorithm is improved compared with some other known methods.