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An annealed chaotic maximum neural network for bipartite subgraph problem.

Jiahai Wang¹, Zheng Tang, Ronglong Wang

¹Faculty of Engineering, Toyama University, Toyama-shi 930-8555, Japan. wjiahai@hotmail.com

International Journal of Neural Systems

|April 28, 2004

Summary

This study introduces a novel parallel algorithm for the bipartite subgraph problem, enhancing neural networks to escape local minima using chaotic dynamics. The algorithm achieves superior optimum or near-optimum solutions compared to existing methods.

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Area of Science:

Computational neuroscience
Graph theory
Optimization algorithms

Background:

The bipartite subgraph problem is an NP-complete problem requiring minimal edge removal for graph bipartiteness.
Existing parallel algorithms using maximum neural networks can easily converge to local minima due to their steepest descent basis.

Purpose of the Study:

To propose a new parallel algorithm that enhances maximum neural networks to overcome local minima.
To introduce transient chaotic neurodynamics for improved solutions to the bipartite subgraph problem.

Main Methods:

A novel parallel algorithm is developed by incorporating transient chaotic neurodynamics into a maximum neural network.
Negative self-feedback is added to the maximum neural network to induce chaotic dynamics and prevent local minima entrapment.
After chaotic dynamics subside, gradient descent dynamics guide the algorithm to a stable equilibrium.

Main Results:

The proposed algorithm combines the strengths of maximum neural networks and chaotic neurodynamics.
Extensive simulations demonstrate the algorithm's effectiveness in solving the bipartite subgraph problem.
The algorithm consistently finds optimum or near-optimum solutions, outperforming existing parallel algorithms.

Conclusions:

The new parallel algorithm effectively prevents neural networks from getting stuck in local minima.
This approach offers a significant improvement for solving the bipartite subgraph problem, achieving better solution quality.