The random satisfiability (RAN-SAT) is a problem that decides whether there exists a mapping of truth values to variables that makes a given random Boolean formula satisfiable. This paper gives a brief discussion on artificial neural network, Hopfield neural networks and logic programming integration. It proposed a method of optimizing random satisfiability in Hopfield neural networks based on the model energy minimization scheme. Computer simulation is carried out to demonstrate and verify the feasibility to carrying out random satisfiability in the Hopfield network.