## 2 Materials and Methods  
This study utilizes the converter steelmaking production process of a steel mill (Shanxi Province, China) manufacturing Q235B-Z grade steel as a case study, with the process flow presented in Figure 1. The production process encompasses out-of-furnace batching, in-furnace blowing, and a single-stage deoxidizing alloying process, which is aimed at initially refining the molten steel. In the context of the industrial production process, dephosphorylation predominantly occurs during the furnace-blowing stage. During this stage, the analytical assessment and monitoring of detection data from the batching and blowing stages of the furnace are critical for achieving precise control over the dephosphorylation process. The test data encompass various parameters, including the composition of raw materials, temperature, and oxygen supply. Following the completion of the blowing process, a detailed evaluation of the process is conducted by measuring the steel composition data (i.e., endpoint composition). By meticulously adjusting the detection data to optimize the dephosphorylation reaction, it is possible to effectively mitigate the occurrence of phosphorus reversion, thereby enhancing dephosphorylation efficiency and reducing production costs [2]. Consequently, to tackle the optimization problem associated with the dephosphorylation process parameters during the furnace blowing stage, the optimization objectives are established based on numerical analysis of the smelting process, with the focus being on minimizing the endpoint phosphorus content (f\({}_{1}\)) and the steel production cost per ton (f\({}_{2}\)). The selected process parameters include the detection data of both the incoming batch and the furnace blowing stage. Through a comprehensive analysis of the physicochemical mechanism underlying the dephosphorylation reaction within the furnace, as documented in the literature [2], several critical factors that influence the endpoint phosphorus content in steel were identified. These factors encompass the carbon, silicon, and phosphorus content in the molten iron, the quantity and temperature of the molten iron, the quantity of scrap utilized, the amounts of lime and ore input, the initial pouring temperature, and the volume of oxygen blowing, among other experimental parameters. Consequently, the relationship function for the phosphorus content at the endpoint was derived as follows:  
\[f_{1}=f\big{(}w_{c0},w_{s0},w_{p0},W_{iron},T_{iron},W_{rested},W_{\text{ lime}},W_{ore},O,T\big{)}. \tag{1}\]  
Figure 1: Converter steelmaking process diagram. In the formula, f1 denotes the endpoint phosphorus content, while w,o, w,si0, and w,p0, respectively, represent the iron-carbon, silicon, and phosphorus content. Wiron, Wrestel, Wlime, and Wore, respectively, refer to the weight of iron, scrap, lime, and ore. Tiron represents the temperature of iron. O and T signify the amount of oxygen blowing and the temperature of a pour, and f signifies the function for calculating endpoint phosphorus content. The primary constituent of lime is calcium oxide. To decrease the production cost per tonne of steel, limestone and raw dolomite are partially substituted for lime in practical production processes. The production cost per ton of steel can be articulated as follows:  
\[\left\{ \begin{array}{l}C=\frac{C_{m}+C_{f}+C_{\rm{c}}}{W_{t}}\\ W_{t}=(W_{\rm{iron}}+W_{\rm{restel}})*\text{Qcover}\end{array} \right., \tag{2}\]  
\[\left\{ \begin{array}{l}C_{m}=k_{0}W_{iron}+k_{1}W_{restel}+k_{2}w_{si0}\\ C_{\rm{s}}=\frac{k_{3}W_{\rm{mm}}+k_{4}W_{\rm{s}}+k_{5}W_{\rm{s}}+k_{6}W_{\rm{ s}}}{100}\\ C_{\rm{f}}=k_{7}O+k_{8}T\end{array} \right.\,. \tag{3}\]  
In the formula, C represents the total cost of producing all tonnes of steel, Cm denotes the cost of raw materials, Cs signifies the cost of auxiliary materials, and Ct stands for the cost of process control. WIs, Wrd, and Wt represent the weights of limestone, raw dolomite, and molten steel respectively.