Mixed-Integer Optimization with Constraint Learning
提出一个方法框架，允许将训练好的机器学习模型（如线性模型、决策树、神经网络）直接嵌入到混合整数优化问题中，并给出两种处理学习约束不确定性的策略，通过世界粮食计划署人道主义援助规划和化疗方案优化案例验证了其可扩展性和数据驱动的决策效果。
In today’s data-driven world, there is a growing opportunity for optimization models to more closely resemble real-world scenarios, namely through learning constraints or objective functions that are not explicitly known and must be estimated through data. In “Mixed-Integer Optimization with Constraint Learning,” the authors establish a novel methodological framework for data-driven decision making. Their approach enables constraints and objectives to be embedded directly from trained machine learning models that are mixed-integer optimization representable including linear models, decision trees, ensembles, and neural networks. The authors propose two different strategies to manage uncertainty in learned constraints. The first is based on the concept of trust region where the convex hull of data points is used to avoid extrapolation. Additionally, they present an ensemble learning method for enforcing constraints across multiple estimators, improving the robustness of the downstream prediction accuracy. Practitioners can access this framework through the “OptiCL” Python package. Case studies on World Food Programme humanitarian aid planning and chemotherapy regimen optimization demonstrate the methodology’s ability to produce scalable and data-informed prescriptions.