A NEW METHOD FOR SHORTEST PATHS COMPUTATION BY NEURAL NETWORKS
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    Abstract:

    A new kind of neural networks for continuously computing the shortest path problem is presented in this paper,and the stability of the network is proved.This kind of neural networks is composed of the minimum selecting networks and other usually used neurons.For any directed or undirected graph,the neural networks are always convergent to their single equilibrium,so that the shortest paths of all the node pairs are produced.This paper makes a new study on solving the optimization,but not NP—hard problems by neural networks.

    Reference
    1 Hopfield J J. Neural networks and physical systems with emetgent collective computational abilities.Proc.Nat.Acad.Sci.,1982,79:2554~2558. 2 Hopfield JJ,Tank D w. Neural cornputations of decisions in optimization problems.Biol.cybern.,1986,52:141~152. 3 Tank D w,Hopfield J J, Simple neural optimization metworks:an A/D converter,signal decision cireuit,and a linear programming circuit.IEEE Trans.Circuits.Syst.,1986, CAS—33(5):533~541. 4 Rauch H E,Winarske T. Neural networks for routing communication traffic.IEEE Cont.Syst.Mag.,1988,5:26—30. 5 Zhang L, Thomopoulos S C A.Neural network implementation of the shortest path algorithm for traffic routing in communication networks.In:Proc.Int.Joint Conf.Neural Networks,1989,Ⅱ.591. 6 Mehmet Ali M K,Kamoun F. Neural networks for shortest path computation and routing in computer networks. IEEE Trans.N.Networks,1993,4(6):941~954. 7 Shi P,Wafd R K.OSNet:a neural network impletation of order statistic filters.IEEE Trans. N. Networks. 1993,4(2):234~24l. 8 Cichocki A,Unbehauen R.Neural networks for solving systems of linear equations and related problems.IEEE Trans.Circuits Syst., 1992,39:124~138. 9 Hopfield J J,Tank D W.Simple neural optimization networks:an A/D converter,signal decision circuit,and a linear programming circuit.IEEE Trans.Circuits Syst., 1986,CAS—33:533~541. 10 Kennedy M P,Chua L O. Neural networks for nonlinear programming.IEEE Trans,Circuits Syst., 1988,35:554~562.
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朱大铭,马绍汉.神经网络求解图最短路径问题的一种新方法*.软件学报,1996,7(zk):191-198

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  • Received:April 12,1995
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