Accurate control of the gram weight of a single cigarette is of major significance for the improvement of product process quality and the reduction of production costs. This paper establishes a graph neural network (GNN) model to predict the equipment operation parameters and cigarette product weight indexes, based on data from the PROTOS1-8 fine cigarette rolling machine in a tobacco factory. Aiming at the lack of optimization ability of the GNNs model, using the excellent performance of the gradient boosting tree algorithm in nonlinear optimization ability and convergence speed, and using the cigarette gram weight index of the trained GNNs prediction model as the fitness function, we carry out the search for the optimal cigarette weight product indexes and come up with the set of operating parameters with the best cigarette weight indexes and optimize the cigarette equipment parameters in the reverse direction. Experiments and promotion tests have demonstrated that the method significantly enhances the optimization of fine cigarette equipment, with a prediction accuracy of 0.8942. Compared to the traditional multiple linear regression model of 0.8527, the prediction ability has improved by 4.15%. The method is useful for analyzing the parameters of different types of cigarette equipment and can meet practical needs.