A new motion equation for the minimum vertex cover problem

Abstract The minimum vertex cover problem is a classic graph optimization problem. It is well known that it is an NP-complete problem. In this paper, a new motion equation with a special term of the Hopfield neural network is presented for the minimum vertex cover problem. Extensive simulations are performed, and the simulation results show that the Hopfield neural network with the new motion equation works much better than the original Hopfield network and a sequential ratio-2 algorithm on random graphs, and has higher convergence rate to optimal solutions for benchmark graphs.