Modifications of discrete Hopfield neural optimization in maximum clique problem

The Hopfield neural optimization has been studied in maximum clique problem. Its drawback with this approach has the tendency to produce locally optimal solutions due to the descent convergence of the energy function. In order to solve maximum clique problems, the discrete Hopfield neural optimization is studied by combining heuristics such as annealing method and scheduled learning rate which can permit the ascent modification. Each neuron is updated in accordance with a hill-climbing modification. The modifications provide a mechanism for escaping local feasible solutions by varying the direction of motion equation of the neurons. The effectiveness of both modifications is shown through various tests on random graphs and DIMACS benchmark graphs in terms of clique size and computation time.