| 用Hopfield神经网络解哈密顿回路问题 |
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| 引用本文： | 陆生勋.用Hopfield神经网络解哈密顿回路问题[J].浙江大学学报(理学版),2010,37(2):180-184. |
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| 作者姓名： | 陆生勋 |
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| 作者单位： | 浙江大学信息与电子工程学系,浙江,杭州,310027 |
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| 摘 要： | 设PN是一个圆的内接正N边形,圆的直径为1.将一个N个顶点的简单图G的每条边赋权,权重为PN的边长;对于图G中不邻接的各对顶点,先求出这对顶点最短路的长度,再赋予PN中同样长度的路的两端点的距离.如此,将图G的哈密顿回路问题转变成旅行商问题:周游回路最优解的长度是否等于正N边形的周长.为了用Hopfield神经网络方法得到正确的判定,简化了初始状态,引用了动态消元算法.
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| 关 键 词： | 哈密顿回路问题 Hopfield神经网络 旅行商问题 |
Solving Hamilton cycle problem by using Hopfield neural network |
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| LU Sheng-xun.Solving Hamilton cycle problem by using Hopfield neural network[J].Journal of Zhejiang University(Sciences Edition),2010,37(2):180-184. |
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| Authors: | LU Sheng-xun |
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| Institution: | LU Sheng-xun(Department of Information and Electronic Engineering,Zhejiang University,Hangzhou 310027,China). |
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| Abstract: | Suppose that P_N is an inscribed regular N-side polygon of a circle which has unit diameter.Each edge of a simple graph G with the side length of PN is weighed.With respect to the pair of unadjacency vertices in G,the length of the shortest path between the pair is found and then this pair with the length of the distance of two points which link a path of P_N in the same length is weighed.Hence,the Hamilton cycle problem of G transforms to a traveling salesman problem to determine that whether there exists an optimal tour with the length of perimeter of P_N.In order to get correct result by Hopfield neural network method,the initial states are simplified and the dynamic elimination method is used. |
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| Keywords: | Hamilton cycle problem Hopfield neural network traveling salesman problem |
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