用Hopfield-型神经网络解四色猜想问题

Hopfield-type Neural Network For Solving "Four-Coloring Map Problems

本文综合讨论了Ｈｏｐｆｉｅｌｄ－型神经网络的迭代算法，使其能保证能量函数单调下降；指出了文［１２］中的错误，并给出了原因；解决了用离散Ｈｏｐｆｉｅｌｄ－型二元神经网络不能求解带有负反馈的问题的难题，大大改进了文［１２］中的算法，能够成功地对任意多个国家的地图用四种颜色着色（使得任意相邻的两个国家着不同的颜色），并可对任意ｋ－可着色问题进行求解．

In this paper, we discussed the iteration algorithm of Hopfield-type Neural Network with which the Energy Function is always guaranteed to monotonically decrease; Pointed out the error in the proof and the drawbacks of the algorithm in cite [12], and analysed the reason; Settled the difficult problem of Neural Networks for solving optimization problem with negative feedback, impproved the algorithm in cite [12]; using our method, we can successfully dye 4 different colors for every map such that any adjecnt countries dying different colors; moreover , we can solving K-colorability problem respectivly.