摘要
通过对弹性神经网络进行分析,给出了求解TSP问题的一个改进的弹性网络算法.弹性网络是一个梯度下降的方法,由于弹性网络的能量函数有很多局部极小值,在实际的计算仿真中,经常会遇到网络陷入局部极小值而无法逃逸的情况.本文介绍一个改进的弹性网络学习算法,当弹性网络陷入局部极小值时,通过参数在能量函数梯度增加的方向改变参数值,从而帮助网络跳出局部极小值,求出全局最优解或更好的结果.通过对6个TSP问题进行模拟仿真,得出结论:对所有的问题,这个算法能够逃逸出弹性网络的局部极小值,求得最优解或更好的解.
The modified elastic net algorithm for finding solutions to the traveling salesman problem （TSP） is introduced. The elastic net method is basicallya gradient descent algorithm that will attempt to take the best path to the nearest minimum, whether global or local, If a local minimum is reached,the network will fail to learn. This paper introduces a gradient ascent learning algorithm of the elastic net for TSP. The learning algorithm is that the elastic net minimizes the path through cities. The procedure is equivalent to gradient descent of an energy function; and lends to a local minimum of energy that represents a good solution to the problem. Once the elastic net gets stuck in local minima, the gradient ascent algorithm attempts to fill up the valley by modifying parameters in a gradient ascent direction of the energy function. These two phases are repeated until the elastic net gets out of local minima and produces the shorted or better tour through cities. We test the algorithm on a set of TSP. For all instances,the modified algorithm is showed to be capable of escaping from the elastic net local minima and producing optimal tours or more meaningful tours than the original elastic net.
出处
《华北工学院学报》
2005年第4期235-238,共4页
Journal of North China Institute of Technology
基金
山西省自然基金资助项目
关键词
旅行推销商问题
人工神经网络
弹性网络
能量函数
traveling salesman problem
artificial neural networks
elastic net
energy function
