We introduce the concept of decision-focused surrogate modeling for solving computationally challenging nonlinear optimization problems in real-time settings. The proposed data-driven framework seeks to learn a simpler, e.g. convex, surrogate optimization model that is trained to minimize the decision prediction error, which is defined as the difference between the optimal solutions of the original and the surrogate optimization models. The learning problem, formulated as a bilevel program, can be viewed as a data-driven inverse optimization problem to which we apply a decomposition-based solution algorithm from previous work. We validate our framework through numerical experiments involving the optimization of common nonlinear chemical processes such as chemical reactors, heat exchanger networks, and material blending systems. We also present a detailed comparison of decision-focused surrogate modeling with standard data-driven surrogate modeling methods and demonstrate that our approach is significantly more data-efficient while producing simple surrogate models with high decision prediction accuracy.

翻译：我们提出了决策聚焦替代建模的概念，用于在实时场景中解决计算具有挑战性的非线性优化问题。该数据驱动框架旨在学习一个更简单的（例如凸优化）替代优化模型，并通过最小化决策预测误差（定义为原始优化模型与替代优化模型最优解之间的差异）来训练该模型。这一学习问题被形式化为一个双层规划问题，可被视为数据驱动的逆优化问题，我们采用先前工作中的一种基于分解的求解算法进行处理。我们通过涉及常见非线性化工过程（如化学反应器、换热器网络和物料混合系统）优化的数值实验验证了该框架。此外，我们详细比较了决策聚焦替代建模与标准数据驱动替代建模方法，结果表明，我们的方法在生成具有高决策预测精度的简单替代模型时，数据效率显著更高。