## 5 Conclusions  
This study focuses on the zinc smelting workshop of a metallurgical plant in Shaanxi Province, China, using actual production data from the workshop. The objective is to reduce the melting point of mixed slag during the smelting process, thereby lowering production costs. This research holds significant practical importance for the metallurgical industry.  
This study demonstrates the effectiveness of using the CatBoost method with hyperparameter optimization to model slag melting points. Compared to the traditional phase diagram method used in the metallurgical industry, CatBoost provides higher accuracy, does not require specialized prior knowledge, and excels in handling complex problems. Unlike other ensemble learning models such as XGBoost and LightGBM, CatBoost autonomously handles categorical features, reducing the complexity of feature preprocessing, and is less affected by outliers and noise, resulting in a more stable and accurate model. Furthermore, we addressed the limitations of random initialization in the Snake Optimization (SO) algorithm by proposing the Halton sequence population initialization strategy. To counteract the tendency of SO to converge to local optima, we introduced the Elite Backward Learning strategy. Additionally, to improve the replacement of subsequent generations of individuals, a dynamic Cauchy-Gaussian mutation strategy that changes dynamically with the iteration number was incorporated. The performance of the Improved Snake Optimization (ISO) algorithm was evaluated using 10 classical test functions, encompassing unimodal, multimodal, and fixed-dimensional multimodal functions. Experimental and statistical results indicate that the ISO algorithm outperforms five existing state-of-the-art optimization algorithms in terms of accuracy, convergence speed, and stability. Finally, the ISO algorithm was applied to the optimization of zinc smelting slag melting point, where it achieved superior results to the five state-of-the-art algorithms, validating its effectiveness in real-world applications.  
In conclusion, the proposed method of TPE-Catboost modeling followed by optimization using the ISO algorithm demonstrates superior effectiveness. By comparing various evaluation metrics, it is demonstrated that TPE-Catboost achieves higher modeling accuracy. Through testing on various types of test functions and real-world engineering problems, the ISO algorithm has shown good performance across different optimization problems, validating its robustness and effectiveness. In future research, efforts will be focused on advancing this method further to address the larger context of energy conservation and emission reduction, aiming to accomplish more complex and meaningful tasks.  
Conceptualization, Z.L. and Y.K.; methodology, Z.L. and Y.K.; software, Z.L.; validation, Z.L.; formal analysis, Z.L. and Y.K.; investigation, Z.L.; resources, Z.L. and Y.K.; data curation, Z.L.; writing--original draft preparation, Z.L. and Y.K.; writing--review and editing, Z.L. and Y.K.; visualization, Z.L.; supervision, Y.K. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the data being part of ongoing research.  
The authors declare no conflicts of interest.