## 1 Introduction  
It is difficult to establish the mechanism model of the smelting process because of the complex furnace structure, various materials in the furnace, and rapid physical and chemical reactions in the furnace. Matte grade determines the amount of ISA furnace slag, which directly affects the heat loss of the ISA furnace and the heat supply of the converter. So, matte grade control is crucial in copper smelting. Meanwhile, the processing capacity of the converter blowing slag and the planned cold material determines the matte grade required for smelting and, finally, determines the production organization mode and smelting cost of the smelting furnace and converter. However, copper smelting system is a multidimensional, nonlinear, dynamic, and open complex system, and the matte grade is related to many factors, resulting in the prediction and modeling of matte grade is a NP-complete problem (Nondeterministic Polynomial complete problem). BP neural network [1, 2] is widely used in actual production prediction because of self-learning, self-organizing, self-adapting, and strong nonlinear function approximation abilities [3, 4]. [PERSON] et al. [5] proposed a hybrid model based on ladle thermal state and BP neural network to study actual steelmaking process characteristics. This helps to solve the problem that a single steelmaking process mechanism model is difficult to accurately predict the temperature of molten steel. The practical application shows that the model achieves a good prediction performance. [PERSON] et al. [6] developed a BP neural network model with a network structure of 3-2-2-1 to predict the rheological stresses in Al-Mg nanocomposites at high temperatures. The temperature, strain, and strain rate data during hot compression experiments were collected as model input. The model outputs the flow stress, which is compared with the Arrhenius hyperbolic and Johnson-Cook constitutive models. The results indicate that the BP neural network model had better prediction accuracy. [PERSON] et al. [7] used a BP neural network to predict the leaching rate of indium and optimize the acid leaching process of ITO (Indium Tin Oxide) waste target to recover indium. The results showed that the relative error between the output of the prediction model and the actual leaching rate was 1.0-1.3%. [PERSON] et al. [8] established a BP neural network prediction model for the content of variables that could not be detected in real time to predict the current (Si) content in the blast furnace smelting process. Combined with an expert system, the prediction model finally achieved an optimal control of the coal injection process. [PERSON] et al. [9] established a prediction model of end-point phosphorus content for BOF (Basic Oxygen Furnace) based on monotone-constrained backpropagation (BP) neural network, and 200 sets of data were used to verify the accuracy of the model. The hit ratios in the range of \(\pm\)0.005% and \(\pm\)0.003% are 94% and 74%, respectively; the results indicate predictive accuracy is better than that of an ordinary BP neural network. [PERSON] et al. [10] used the initial pH value, initial Pb\({}^{2+}\) concentration, adsorbent dosage, and contact time as the input layer of the BP neural network to predict the removal rate of Pb\({}^{2+}\) in the study of hydrometallurgical extraction of lead, and the actual results showed that the prediction results of the model were excellent. Although the BP neural network is used for model prediction with high generalization ability, it needs to be optimized by an optimization algorithm due to its slow learning speed and tendency to fall into local minima [11]. Genetic Algorithm (GA) [12,13] is a widely used optimization algorithm. In this algorithm, through iterative evolution of the population, the individuals with higher fitness in the current population are inherited by the next generation, and individuals with lower fitness are eliminated. Finally, the individual with the most increased fitness is found, and the optimization result is obtained.