Hierarchical Hopfield neural network in solving the puzzle problem

In this paper, two new approaches based on artificial neural networks for solving the puzzle problem are presented. To do this, a Hopfield neural network (HNN) is used in a certain constraint satisfaction problem of the puzzle so that the energy of a state can be interpreted as the extent to which a hypothesis fits the underlying neural formulation model. Thus, low energy values indicate a good level of constraint satisfaction. Then, inspired by the way a human being, as an intelligent system, solves a puzzle, two new hierarchical schemes are proposed. In these approaches, some intermediate stage puzzles are designed to guarantee reaching the answer. In addition, to increase the performance of the proposed algorithms and make them much more powerful, another criterion based on the Tree Search Algorithm is combined with them.