Hopfield Neural Network with Hysteresis for Maximum Cut Problem

A model of neurons with hysteresis (or hysteresis binary neurons) for the Hopfield neural networks is studied. We prove theoretically that the emergent collective properties of the original Hopfield neural networks also are present in the Hopfield neural networks with hysteresis binary neurons. As an example, the networks are also applied to the maximum cut problem and results of computer simulations are presented and used to illustrate the computation power of the networks. The simulation results show that the Hopfield neural networks with hysteresis binary neurons are much better than other existing neural network methods for solving the maximum cut problem in terms of both the computation time and the solution quality. Keywords—maximum cut problem, Hopfield neural network, hysteresis, collective properties, NP-complete problem