Mastering the smelting status and making the material adding strategy are important and challenging issue in the basic oxygen furnace (BOF) steelmaking process. Unfortunately, complex physicochemical reaction with multi-input and multi-output makes the first-principles models unusable. To this end, a black box operation optimization (BBOO) problem integrated black box data analytics modeling and optimization is abstracted from the BOF steelmaking process. Moreover, a derivative free optimization (DFO) method based on the trust region framework is developed to solve the operation optimization problem. In the proposed algorithm, we integrate quadratic interpolation and sparse modeling to construct the surrogate model. Wherein, $l_0$-norm optimization, which is solved through converting it into a convex optimization problem with introducing the slack variables, is used to determine the sparse surrogate model. Finally, we apply the proposed DFO algorithm and other DFO algorithms to solve the BBOO problem in BOF steelmaking process. The results demonstrate that the proposed method can be an alternative for providing solutions and insights of material addition in BOF process and the proposed algorithm is comparable.

掌握熔炼状态并制定材料添加策略是基本氧气炉（BOF）炼钢过程中重要且具有挑战性的问题。不幸的是，具有多输入多输出的复杂的物理化学反应使第一原理模型无法使用。为此，从转炉炼钢过程中提取了黑箱操作优化（BBOO）问题，将黑箱数据分析建模和优化集成在一起。此外，基于信任域框架开发了一种无导数优化（DFO）方法，以解决运营优化问题。在所提出的算法中，我们将二次插值和稀疏建模相结合以构建代理模型。其中，${升}_0$-norm优化通过引入松弛变量将其转化为凸优化问题而得以解决，用于确定稀疏替代模型。最后，我们将提出的DFO算法和其他DFO算法应用于转炉炼钢过程中的BBOO问题。结果表明，该方法可以为转炉过程中材料添加的解决方案和见解提供一种替代方法，并且该算法具有可比性。