The challenge of distributing molten iron involves the optimal allocation of blast furnace output to various steelmaking furnaces, considering the blast furnace’s production capacity and the steelmaking converter’s consumption capacity. The primary objective is to prioritize the distribution from the blast furnace to achieve a balance between iron and steel production while ensuring that the volume of hot metal within the system remains within a safe range. To address this, a constrained multi-objective nonlinear programming model is abstracted. A linear weighting method combines multiple objectives into a single objective function, while the Lagrange multiplier method addresses constraints. The proposed hybrid Archimedes optimization algorithm effectively solves this problem, demonstrating significant improvements in time efficiency and precision compared to existing methods.