Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2009-05-30
Nonlinear Sciences
Adaptation and Self-Organizing Systems
-2nd revised version submitted to Chaos (original version submitted 6/07)
Scientific paper
The Hopfield-Tank (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.
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