On chaotic simulated annealing

Abstract

Chen and Aihara recently proposed a chaotic simulated annealing approach to solving optimization problems. By adding a negative self-coupling to a network model proposed earlier by Aihara et al. and gradually removing this negative self-coupling, they used the transient chaos for searching and self-organizing, thereby achieving remarkable improvement over other neural-network approaches to optimization problems with or without simulated annealing. In this paper we suggest a new approach to chaotic simulated annealing with guaranteed convergence and minimization of the energy function by gradually reducing the time step in the Euler approximation of the differential equations that describe the continuous Hopfield neural network. This approach eliminates the need to carefully select other system parameters. We also generalize the convergence theorems of Chen and Aihara to arbitrarily increasing neuronal input-output functions and to less restrictive and yet more compact forms.