Donato Maragno

Optimization with Constraint Learning

Defense date: 04-04-2025

Academic distinction: Cum Laude

Summary:

Mathematical optimization is a powerful decision-making tool used across diverse fields, with mixed-integer optimization (MIO) playing a key role in solving large-scale problems. However, optimization models often face challenges when constraints or objective functions are not explicit and difficult to design. This thesis introduces an Optimization with Constraint Learning (OCL) framework, integrating Machine Learning (ML) to infer and embed unknown constraints and objectives into MIO models.

This thesis applies OCL to supply chain optimization for humanitarian aid, demonstrating how learned food palatability constraints can be integrated to ensure that recipients enjoy the food and know how to prepare it. The thesis further demonstrates OCL’s versatility through two distinct applications: radiotherapy optimization and explainable artificial intelligence (XAI). In radiotherapy, OCL personalizes cancer treatment planning by integrating a predictive model for radiation-induced toxicity, optimizing treatment while minimizing patient risk. In XAI, given a fitted ML model, the OCL framework can be used to generate actionable counterfactual explanations that meet established quality criteria such as closeness, diversity, and robustness against environmental uncertainties.

The proposed OCL framework ensures computational efficiency and global optimality, facilitating its adoption by practitioners and researchers. By bridging optimization and ML, this work advances decision-making methodologies and lays the foundation for future research in data-driven optimization.