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A “cellular neuronal” approach to optimization problems

Chaos 19, 033114 (2009); doi:10.1063/1.3184829

Published 30 July 2009

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Gregory S. Duane
National Center for Atmospheric Research, P.O. Box 3000, Boulder, Colorado 80307, USA and School of Mathematics, University of Minnesota, 206 Church St. S.E., Minneapolis, Minnesota 55455, USA
The Hopfield–Tank [J. J. Hopfield and D. W. Tank, Biol. Cybern. 52, 141 (1985)] recurrent neural network architecture for the traveling salesman problem is generalized to a fully interconnected “cellular” neural network of regular oscillators. Tours are defined by synchronization patterns, allowing the simultaneous representation of all cyclic permutations of a given tour. The network converges to local optima some of which correspond to shortest-distance tours, as can be shown analytically in a stationary phase approximation. Simulated annealing is required for global optimization, but the stochastic element might be replaced by chaotic intermittency in a further generalization of the architecture to a network of chaotic oscillators. ©2009 American Institute of Physics
History: Received 27 May 2009; accepted 2 July 2009; published 30 July 2009
Permalink: http://link.aip.org/link/?CHAOEH/19/033114/1
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KEYWORDS and PACS

Keywords
PACS
  • 05.45.Xt
    Synchronization; coupled oscillators (nonlinear dynamical systems)
  • 02.60.Pn
    Numerical optimization
  • 87.18.Sn
    Neural networks and synaptic communication (biological complexity)
  • 87.10.-e
    General theory and mathematical aspects (biological/medical physics)
  • 05.50.+q
    Lattice theory and statistics
  • YEAR: 2009

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PUBLICATION DATA

ISSN:
1054-1500 (print)   1089-7682 (online)
Publisher:
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