## 2 Literature Review  
Blending is an essential step in many industries [6; 9; 10; 11; 12; 13]. By determining an appropriate proportion, the optimized formulation strategy plays a crucial role in mitigating fluctuations in raw material supply, improving product quality, and reducing costs [10]. However, the primary challenge in optimizing formulation strategy lies in uncertainty, particularly the uncertainty of raw materials and their composition [6]. In recent years, scholars have proposed an increasing number of intelligent optimization algorithms, such as Genetic Algorithms [14], Particle Swarm Optimization (PSO) [15], and Human Learning Optimization (HLO) [7], etc. These optimization algorithms address these challenges with their excellent heuristic search capabilities and ability to find satisfactory solutions within a short time. [PERSON] et al. modeled the formulation process as a constrained scheduling problem, adopting a hybrid model combining PSO and linear programming to overcome its inherent nonlinearity and optimize raw material operations in steel production [16]. However, this method still needs manual modification and takes two minutes to solve. [PERSON] et al. proposed a multi-objective simulated annealing algorithm that enhanced the exploration of Pareto optimal solutions by introducing a decision space search strategy, thereby addressing the evaluation issues of coke quality and coal blending costs in complex coking-coal blending processes [17]. This study considered the cost, ash content, and sulfur content at the same time, but simplified the proportion range of each raw material. [PERSON] et al. developed a coal quality prediction model based on a PSO-enhanced feedforward neural network to tackle the issues of inaccurate coal quality calculations and overly simplistic coal formulation schemes in thermal power plants. This model does not consider any constraints, so it is difficult to apply in the actual scene [18]. [PERSON] et al. proposed a multi-metal multi-objective hybrid model optimization method that uses the Artificial Bee Colony algorithm to minimize grade fluctuation, mining transportation costs, and production capacity constraints, significantly improving the recovery rates of tungsten, molybdenum, and bismuth [19]. The model reduces the multi-objective problem to a single-objective one by assigningpredefined weights to the three objectives, thereby simplifying the computation; however, such a weighted-sum approach may fail to capture the full Pareto front and can bias solutions toward certain objectives. [PERSON] et al. implemented a closed-loop dynamic optimization of formulation parameters in the zinc smelting process using a variational Bayesian approach [20]. The model combines variable Bayesian, expert rules, and chance constrained programming, and achieves an increase in the compliance rate compared with manual mixing. [PERSON] et al. modeled the copper smelting process as a single objective function problem and obtained raw material formulation schemes using an improved PSO algorithm to assist decision-making [21]. For the multi-objective ore formulation problem involving ores of different grades, [PERSON] et al. suggested that, in addition to profit, the stability of the mixed product should also be considered. An improved GA based on non-dominated sorting was adopted to obtain satisfactory solutions [22]. [PERSON] et al. introduced a coal formulation optimization framework for coal-fired power plants by establishing a mathematical model aimed at cost minimization and employing a novel multi-strategy fusion multi-objective particle swarm optimization method, which achieved high-quality Pareto distributions under different weight combinations and significantly improved both economic and environmental benefits [23]. Although numerous algorithms have been successfully applied to coal blending, coking, and nonferrous ore blending, their process models and constraint sets differ significantly from those required for RHF operations.