## 1 Introduction  
The steel industry has long been regarded as the foundation of the global industrial system and plays an indispensable role in promoting the development of modern society. As the world's largest producer and consumer of steel, China contributes approximately 50% of the global steel production [1]. However, the rapid development of the steel industry also faces the dual challenges of environmental pollution and resource waste [2]. The large amounts of waste and pollutants generated during the steel production process significantly impacts the environment. Therefore, effectively recycling the solid waste containing hazardous metallic elements generated during steel production can not only greatly improve resource utilization efficiency but also reduce environmental pollution [3]. The RHF stands out among various technologies for processing iron-containing dust due to its low energy consumption and high metallization rate, and has been widely adopted [4,5]. In the process of treating iron-containing dust with the RHF, the raw material blending system serves as the crucial initial step, ensuring the supply of qualified mixed materials that meet the requirements of the production plan to the subsequent stages of production. The effectiveness of the blending system mainly depends on the formulating blending scheme which is a complex decision-making process influenced by various factors, such as the types of raw materials, elemental composition, bin levels, production schedules, and the operational status of the RHF, etc. Traditional formulation schemes based on manual experience are characterized by a high computational complexity and excessive reliance on individual expertise, making it difficult to achieve a balanced optimization of multiple objectives during the production process, which can easily lead to fluctuations in product quality and declines in production efficiency. The design of the formulation scheme for the blending system is regarded as a multi-objective optimization process, addressed using optimization algorithms to provide decision support for operators. Although traditional optimization algorithms, such as the Newton method, are theoretically well established, they typically rely on precise mathematical models and are prone to becoming trapped in local optima, making them difficult to solve complex multi-objective optimization problems [6]. Heuristic and metaheuristic algorithms are effective solutions for such problems. As a metaheuristic optimization algorithm, the Human Learning Optimization (HLO) algorithm is capable of effectively handling complex problems that are nonlinear, non-differentiable, and non-convex without relying on precise mathematical models [7]. The algorithm seeks optimal solutions by simulating human behaviors during the learning process, including random learning, individual learning, and social learning. With its rapid convergence capability and superior global search performance, HLO has demonstrated its effectiveness in solving multi-objective optimization problems [8]. Therefore, this paper develops an improved multi-objective adaptive HLO algorithm (IMOAHLO) specifically for the formulation scheme optimization problem in RHF blending systems. The primary goal is to ensure a long-term, stable operation of the blending line--minimizing manual interventions--while meeting production requirements for elemental composition and resource utilization. While this work is grounded in the steel industry's RHF blending context, the proposed modeling and algorithmic framework have a broader applicability. The same framework can be readily extended to other continuous blending processes, such as middling coal proportioning in thermal power plants, as well as blending optimization in copper, iron, and other metallurgical industries, thereby offering a significant engineering value across various manufacturing and energy-conversion sectors.