Mixed-Integer Optimization with Constraint Learning

Abstract

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.