A "Cellular Neuronal" Approach to Optimization Problems

TL;DR

This paper introduces a cellular neural network model for solving optimization problems like the Traveling Salesman Problem, leveraging synchronization patterns of oscillators to represent solutions and discussing potential for global optimization through stochastic or chaotic methods.

Contribution

It generalizes the Hopfield-Tank neural network to a cellular architecture using oscillators, enabling simultaneous representation of multiple solutions and analytical insights into local optima.

Findings

Network converges to local optima including shortest tours

Synchronization patterns define solutions in the neural network

Potential for global optimization via stochastic or chaotic dynamics

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.