Convergence acceleration of the Hopfield neural network by optimizing integration step sizes

In our previous work we have clarified global convergence of the Hopfield neural network and showed, by computer simulations, improvement of solution quality by gradually decreasing the diagonal elements of the coefficient matrix. In this paper, to accelerate convergence of the Hopfield network, at each time step the integration step size is determined dynamically so that at least one component of a variable vector reaches the surface of the hypercube. The computer simulation for the traveling salesman problem and an LSI module placement problem shows that convergence is stabilized and accelerated compared to integration by a constant step size.