Chaotic Simulated Annealing by A Neural Network Model with Transient Chaos

Abstract

We propose a neural network model with transient chaos, or a transiently chaotic neural network (TCNN) as an approximation method for combinatorial optimization problem, by introducing transiently chaotic dynamics into neural networks. Unlike conventional neural networks only with point attractors, the proposed neural network has richer and more flexible dynamics, so that it can be expected to have higher ability of searching for globally optimal or near-optimal solutions. A significant property of this model is that the chaotic neurodynamics is temporarily generated for searching and self-organizing, and eventually vanishes with autonomous decreasing of a bifurcation parameter corresponding to the "temperature" in usual annealing process. Therefore, the neural network gradually approaches, through the transient chaos, to dynamical structure similar to such conventional models as the Hopfield neural network which converges to a stable equilibrium point. Since the optimization process of the transiently chaotic neural network is similar to simulated annealing, not in a stochastic way but in a deterministically chaotic way, the new method is regarded as chaotic simulated annealing (CSA). Fundamental characteristics of the transiently chaotic neurodynamics are numerically investigated with examples of a single neuron model and the Traveling Salesman Problem (TSP). Moreover, a maintenance scheduling problem for generators in a practical power system is also analysed to verify practical efficiency of this new method.