Optimal path determination in a graph by hopfield neural network

Abstract Recurrent stable neural networks seems to represent an interesting alternative to classical algorithms for the search for optimal paths in a graph. In this paper a Hopfield neural network is adopted to solve the problem of finding the shortest path between two nodes of a graph. The results obtained point out the validity of the solution proposed and its capability to adapt itself dynamically to the variations in the costs of the graph, acquiring an “awareness” of its structure.

[1]  H.P. Graf,et al.  Analog Electronic Neural Networks , 1992, ESSCIRC '92: Eighteenth European Solid-State Circuits conference.

[2]  L.D. Jackel,et al.  Analog electronic neural network circuits , 1989, IEEE Circuits and Devices Magazine.

[3]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Mahesan Niranjan,et al.  A theoretical investigation into the performance of the Hopfield model , 1990, IEEE Trans. Neural Networks.

[6]  Alfred V. Aho,et al.  Data Structures and Algorithms , 1983 .

[7]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Salvatore Cavalieri,et al.  Hopfield Neural Network for Routing , 1993, IWANN.

[9]  David E. van den Bout,et al.  A traveling salesman objective function that works , 1988, IEEE 1988 International Conference on Neural Networks.

[10]  Philip D. Wasserman,et al.  Neural computing - theory and practice , 1989 .

[11]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.