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Chaotic simulated annealing by a neural network with a variable delay: design and application.

Shyan-Shiou Chen1

  • 1Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan. sschen@ntnu.edu.tw

IEEE Transactions on Neural Networks
|August 17, 2011
PubMed
Summary

This study introduces a novel, intuitive Lyapunov function for delayed neural networks and designs a variably delayed neural network. This new model demonstrates superior searching ability compared to existing models.

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Area of Science:

  • Computational Neuroscience
  • Dynamical Systems Theory
  • Artificial Neural Networks

Background:

  • Delayed neural networks commonly use linear matrix inequality (LMI) for Lyapunov functions, which lack intuitiveness.
  • Designing effective neural networks for complex problems like the traveling salesman problem requires robust stability analysis.

Purpose of the Study:

  • To present advantages of variably delayed systems.
  • To develop an intuitive Lyapunov function for delayed neural networks, avoiding the LMI approach.
  • To design a delayed neural network tailored for quadratic cost functions.

Main Methods:

  • Proposed an alternative, intuitive Lyapunov function candidate for delayed neural networks.
  • Constructed a delayed neural network for a quadratic cost function by splitting second-order terms.

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  • Introduced a transiently chaotic neural network with variable delay for performance comparison.

    • Main Results:

    • The variably delayed neural network exhibited enhanced searching ability over established models (Chen-Aihara, Wang, Zhao).
    • Analysis of chaotic and convergent phases revealed stochastic properties and chaotic wandering in the variably delayed model.
    • A novel Lyapunov function, independent of LMI, was developed for delayed neural networks, correlating with the traveling salesman problem's objective function.

    Conclusions:

    • The proposed intuitive Lyapunov function offers a more accessible method for analyzing delayed neural networks.
    • Variably delayed neural networks show promise for improved performance in complex search tasks.
    • The study establishes a link between Lyapunov stability analysis and optimization problem objectives.