Chaotic Simulated Annealing by A Neural Network Model with Transient Chaos

摘要

We propose a neural network model with transient chaos, or a transientlychaotic neural network (TCNN) as an approximation method for combinatorialoptimization problem, by introducing transiently chaotic dynamics into neuralnetworks. Unlike conventional neural networks only with point attractors, theproposed neural network has richer and more flexible dynamics, so that it canbe expected to have higher ability of searching for globally optimal ornear-optimal solutions. A significant property of this model is that thechaotic neurodynamics is temporarily generated for searching andself-organizing, and eventually vanishes with autonomous decreasing of abifurcation parameter corresponding to the "temperature" in usual annealingprocess. Therefore, the neural network gradually approaches, through thetransient chaos, to dynamical structure similar to such conventional models asthe Hopfield neural network which converges to a stable equilibrium point.Since the optimization process of the transiently chaotic neural network issimilar to simulated annealing, not in a stochastic way but in adeterministically chaotic way, the new method is regarded as chaotic simulatedannealing (CSA). Fundamental characteristics of the transiently chaoticneurodynamics are numerically investigated with examples of a single neuronmodel and the Traveling Salesman Problem (TSP). Moreover, a maintenancescheduling problem for generators in a practical power system is also analysedto verify practical efficiency of this new method.