## 6 Conclusions and Future Work  
In addressing the practical engineering problem of RHF raw material blending, this paper constructs a multi-objective optimization mathematical model with two constraints and four objective functions, and proposes an IMOAHLO algorithm. Unlike prior studies' conventional focusing on singular objectives of economic cost minimization or metallurgical grade maximization, the mathematical model developed in Section 3 systematically incorporates the following multidimensional constraints. Elemental content constraints ensure the blended green pellets meet strict compositional requirements. Scheme similarity constraints limit the degree of change between successive formulation schemes to reduce operational disruptions. Continuous operation constraints and start-stop penalties reflect the real cost of opening or closing the valve. This model therefore fills a critical research gap by incorporating the full spectrum of practical engineering considerations encountered by operators in real-world scenarios. Building on the classical HLO framework, a novel mechanism was introduced in Section 4: a neighborhood search operator that intensifies local exploration around promising solutions, thereby improving the precision of fine-tuning each formulation scheme. IMOAHLO's hybrid search strategy is specifically tailored to the high-dimensional, continuous characteristics of RHF formulation schemes, achieving significantly superior Pareto-front coverage and convergence compared to other well-known algorithms. One hundred real production datasets collected from a steel-plant RHF line demonstrate that the proposed algorithm achieves a clear performance improvement: the average HV increases by 11.8%, while the average IGD and GD are only 36.6% and 33.6% of those of the other algorithms, respectively. Additionally, two typical case studies further demonstrate that the IMOAHLO algorithm can improve system stability, reduce operational fluctuations, and optimize the elemental composition of blended materials in scenarios with resource constraints and dynamic conflicts, proving its remarkable performance and decision robustness in practical applications. However, this study has some limitations that need further improvement. Firstly, the primary purpose of the RHF is to recover and reuse waste streams generated by other production units. The proposed scheme optimization model focuses on how to incorporate those external waste fractions in a stable, continuous manner to ensure the long-term unattended operation of the blending line. In evaluating the model's performance, this paper primarily examined relevant algorithmic performance metrics. However, different schemes significantly impact the drying and combustion processes in the rotary hearth furnace, ultimately impacting key production indicators such as fuel consumption rate, pelletizing yield, and metallization rate. Therefore, subsequent research will focus on using these industrial KPIs as evaluation benchmarks to conduct comprehensive and systematic assessments of formulation scheme performance, thereby establishing a more precise-process optimization model. Secondly, due to resource and time constraints, this study did not perform a full thermodynamic or detailed process simulation to validate the optimized formulation schemes. Without comprehensive process modeling, optimizing only the formulation schemes leaves uncertainties regarding practical performance. Therefore, future research will focus on coupling the scheme optimization model with drying and reduction process simulations to achieve whole-chain optimization, ensuring that the optimization model yields the desired results under actual operating conditions.