###### Abstract  
The regulation of the melting point of zinc smelting slag has an important impact on the subsequent smelting processes of the metal. In actual production, uncontrollable melting points may result in inconsistent product quality, which has a great negative impact on the smelter's efficiency and environmental protection. However, the regulation mechanism of the melting point of the smelting slag is complex, with many influencing factors, and there is no recognized high-precision calculation method. In response to these challenges, this study introduces an innovative approach for optimizing the melting point of zinc smelting slag based on the improved Snake Optimization (ISO) algorithm. The melting point of zinc smelting slag is modeled using the Catboost algorithm, and the model parameters are optimized using the Tree-structured Parzen Estimator (TPE) to improve the accuracy of the model. Next, the ISO algorithm is employed to conduct optimization calculations, determining the optimal values of various production process parameters that minimize the melting point. The effectiveness of this approach was evaluated using diverse modeling algorithms and test functions, subsequently applied to optimize and validate actual production data from a smelter in Shaanxi, China. Statistical analyses reveal that the TPE-optimized Catboost model exhibits an R\({}^{2}\) of 93.89%, an RMSE of 7.02 \({}^{\circ}\)C, an MAE of 6.19 \({}^{\circ}\)C, and an MRE of 7.88%, surpassing performance metrics of alternative algorithms. Regarding optimization efficacy, the proposed ISO algorithm achieves an average reduction of 65 \({}^{\circ}\)C in the melting point and demonstrates superior robustness compared to both actual production data and alternative algorithms. zinc smelting slag; melting point optimization; Catboost; improved snake optimization algorithm +
Footnote †: journal: Applied Sciences  
coal to ensure smooth subsequent processes. However, excessively high melting temperatures not only affect energy consumption but also increase the difficulty and equipment costs of the smelting process, which greatly influences the application and promotion of the smelting roasting method [12]. Among the factors affecting melting temperature, slag melting point is a key factor, and, therefore, reducing the slag melting point is of significant importance for controlling the melting temperature. Zinc smelting slag contains various elemental components, and it is generally believed that the slag melting point is determined by the mass fractions of oxides such as Fe\({}_{2}\)O\({}_{3}\), CaO, SiO\({}_{2}\), Al\({}_{2}\)O\({}_{3}\), and MgO [13]. The process of zinc smelting is a complex and variable physicochemical process, and the melting point is an important indicator affecting the smelting effect. However, there is no universally recognized and highly accurate calculation method for the relationship between melting point and slag composition, which poses great difficulties in modeling and controlling the melting point [14]. In the metallurgical industry, the advancement of related research often relies on the combination of production experience and phase diagrams of various factors. [PERSON] et al. based their research on the CaO-MoO\({}_{3}\)-La\({}_{2}\)O\({}_{3}\) ternary phase diagram, using the solid-state reaction method to design and synthesize two new types of microwave dielectric ceramics, laying the foundation for the scientific research and practical application of related ceramic systems [15]. [PERSON] et al. established the CaO-Al\({}_{2}\)O\({}_{3}\)-Vox ternary phase diagram, conducting in-depth research on the changes in the valence state of vanadium during vanadium steel smelting processes, also achieving good results [16]. However, experimental studies on phase diagrams require a significant amount of time and economic costs, and they are faced with challenges such as experimental difficulty and time consumption.