Hopfield网络求解TSP的一种改进算法和理论证明

本文通过简化Ｈｏｐｆｉｌｅｄ神经网络求解问题的能量函数，提出了一种神经网络求解ＴＳＰ的改进算法，借助连接矩阵特征值的分析、从理论上证明了该算法保证获得ＴＳＰ有效解的原因。大量计算机模拟实验表明，该算法明显优于目前广泛应用的Ａｉｙｅｒ算法，具有收敛速度快、可避免无效解，易获得优化解等特点。

A Modified Algorithm and Theoretical Analysis for Hopfield Network Solving TSP

The Travelling Salesman problem(TSP) is studied using Hopfield neural network(HNN) in this paper.A new algorithm is proposed by simplifying energy function,and the feasibility of the algorithm is analyzed.The analysis is based on the geometry of the subspace set up by the degenerated eigenvalues of the connection matrix.A large number of simulation results show that the algorithm has the advantage of avoiding most local energy minima with the optimum or near-optimum solution and fast speed of convergence.