Theoretical considerations on the dynamics of hysteresis binary Hopfield networks for combinatorial optimization

It has been reported that hysteresis binary Hopfield networks achieve good performance for many combinatorial optimization problems. The theoretical analysis of the network dynamics or this good performance, however, is not given yet. In this paper, conditions for the convergence to an energy minimum state, and for the stability of the feasible and infeasible solutions to combinatorial optimization problems are shown in terms of the hysteresis size. Then, a theoretical explanation of the good performance of hysteresis binary Hopfield networks is also given. Simulations illustrate these theoretical conclusions