A "Cellular Neuronal" Approach to Optimization Problems

Gregory S. Duane

doi:10.1063/1.3184829

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arXiv · 0906.0115

A "Cellular Neuronal" Approach to Optimization Problems

Gregory S. Duane

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Abstract

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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Gregory S. Duane. 2009-05-30. A "Cellular Neuronal" Approach to Optimization Problems. https://doi.org/10.1063/1.3184829

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