A "Cellular Neuronal" Approach to Optimization Problems
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.
Cite
@article{arxiv.0906.0115,
title = {A "Cellular Neuronal" Approach to Optimization Problems},
author = {Gregory S. Duane},
journal= {arXiv preprint arXiv:0906.0115},
year = {2015}
}
Comments
-2nd revised version submitted to Chaos (original version submitted 6/07)