## 1 Introduction  
Converter steelmaking offers a series of advantages, including high efficiency and low cost, making it one of the mainstream steelmaking methods in the steel industry [1]. This method effectively reduces phosphorus content--a detrimental element in molten iron--through both physical heating and exothermic chemical reactions between components. The endpoint phosphorus content of molten steel serves as a critical indicator for assessing the quality of molten steel, which directly influences the steel's plasticity and toughness [2]. Consequently, the reasonable regulation of converter steelmaking process parameters, effectively reducing the endpoint phosphorus content of molten steel is one of the significant challenges that the steel industry needs to overcome to meet the growing market demand and achieve the goal of high-quality and low-cost steel production. Scholars globally have conducted extensive research on process optimization to improve steel quality. Early studies by [PERSON] [3] and [PERSON] [4] focused on adjusting slag-forming and scrap material ratios to reduce endpoint phosphorus content under fixed furnace temperature conditions. However, the inherent complexity of in-furnacechemical reactions limits the effectiveness of purely dosage-based control strategies. Subsequently, the literature [5] proposes a synergistic modeling strategy integrating principal component analysis (PCA) and neural networks (NNs) based on the characteristics of converter metallurgical processes and production data. This method employs PCA to perform linear orthogonal transformations on process parameters, thereby eliminating multicollinearity among variables. However, PCA--a linear projection technique rooted in variance maximization--fails to adequately address nonlinear coupling relationships inherent in metallurgical processes, resulting in the forced decoupling of critical nonlinear features. While the subsequently developed neural network prediction model enhances fitting capabilities through nonlinear activation functions, its fully connected architecture lacks embedded metallurgical thermodynamic constraints. Consequently, the weights of the hidden layer remain disconnected from actual physical processes, creating a fundamental disconnect between mechanistic principles and data-driven modeling. To enhance model performance, [PERSON] [6], [PERSON] [7], and [PERSON] [8], R. introduced optimization algorithms to refine neural networks and extreme learning machines (ELMs), aiming to improve prediction accuracy for endpoint phosphorus content in molten steel. Nevertheless, these approaches retain inherent limitations: neural networks remain prone to overfitting, while ELM suffers from random weight initialization defects. Furthermore, such methods rely on engineers to preset static combinations of process parameters for pre-production simulations, effectively reducing the dynamic smelting process to a discrete parameter search. This simplification inherently limits real-time responsiveness to raw material composition fluctuations and fails to capture time-varying couplings among process parameters. To address steel quality optimization challenges, researchers have adopted intelligent optimization algorithms such as particle swarm optimization [9; 10], genetic algorithm [11; 12], and grey wolf algorithm [13], among others. These algorithms iteratively adjust process parameters by holistically considering multiple influencing factors during smelting. However, conventional methods frequently converge to local optima, overlook critical process constraints, and struggle to balance model accuracy with industrial feasibility--particularly when simultaneously optimizing endpoint phosphorus content and production costs. In addressing the optimization problem in the dephosphorylation process paramters of the converter steelmaking production, this study employs the actual production data from an industrial steel plant as a case exemple.