A Stochastic Neuron Model for Finding a Near-Maximum Independent Set of a Circle Graph

In this paper, we present a novel binary neuron model called stochastic neuron model for the Hopfield neural network. In order to avoid the inherent local minima problem of the Hopfield neural network, in the proposed neuron model, a stochastic mechanism is introduced into the input/output function of the neuron model. By means of the stochastic neuron model, the neuron network is allowed to jump to configurations of higher energy, occasionally. As a result, it is probable that the neural network escape from the state of the local minimum to a better state or the state of global minimum. Then, the characteristic of the stochastic neuron model is presented theoretically. To test the effectiveness of the proposed neuron model, we applied the stochastic neuron model to the maximum independent problem. A large number of instances are simulated to verify the proposed method, and the simulation results show that the proposed method is superior to that of best existing parallel algorithm.