Chaotic simulated annealing with decaying chaotic noise

Area of Science:

• Artificial Intelligence
• Computational Neuroscience
• Optimization Algorithms

Background:

• Hopfield Neural Networks (HNN) are widely used for optimization but can get trapped in local minima.
• Traditional HNN dynamics are limited, hindering their ability to find global optima for complex problems.
• The Traveling Salesman Problem (TSP) is a classic NP-hard problem requiring efficient optimization strategies.

Purpose of the Study:

• To introduce a novel chaotic neural network (CNN) with enhanced dynamic properties.
• To investigate the application of this CNN to solve the Traveling Salesman Problem (TSP).
• To demonstrate the CNN's ability to escape local energy minima and find global or near-global optimal solutions.

Main Methods:

• A discrete-time, continuous-output Hopfield Neural Network (HNN) was modified by introducing and gradually reducing chaotic noise.
• The proposed chaotic neural network (CNN) was applied to instances of the Traveling Salesman Problem (TSP).
• Performance was evaluated based on the network's ability to find global minima and escape local energy wells.

Main Results:

• The chaotic neural network exhibited richer and more flexible dynamics compared to the standard HNN.
• The CNN successfully escaped local energy minima, leading to global solutions in 100% of simulations for small TSP instances (4 and 10 cities).
• For a larger 48-city TSP, the network consistently found near-optimal solutions across most simulation runs.

Conclusions:

• The proposed chaotic neural network effectively enhances optimization capabilities by leveraging transient chaos.
• The CNN provides a robust method for solving the Traveling Salesman Problem, outperforming traditional HNNs in escaping local optima.
• This approach offers a promising direction for developing more powerful neural network models for complex combinatorial optimization tasks.