Learning Implicit Feasibility Constraints for Real-World Routing and Scheduling: Application to Log Transportation

Abstract

Real-world vehicle routing and scheduling problems involve complex operational rules and feasibility constraints typically formulated as mixed-integer linear programs (MILP). However, optimization tools are built around a fixed set of hard-coded constraints, while in practice this set evolves as new rules or preferences emerge, seasonally or permanently. Updating it requires modeling and operations research skills that planners rarely have, so generated plans are routinely adjusted by hand based on practical knowledge. Building on recent work that uses machine learning to recover such hidden constraints, we propose a data-driven constraint-learning approach that trains three complementary predictors, a Graph Neural Network (GNN), a decision tree, and a linear regression, on historical execution data from a log-truck routing and scheduling problem ($\mathcal{LTRSP}$), and embeds each inside a MILP through linearized constraints. We further introduce a stacking mechanism that combines all three within a single augmented optimization problem (AOP), letting the solver endogenously select the most reliable predictor for each decision. On real-world industrial data, each predictor already improves feasibility, but the stacked embedding consistently achieves the lowest objective degradation: it (i)~satisfies the operational rules on unseen instances with smaller degradation than any single-model variant, (ii)~picks the most appropriate predictor per decision without prior knowledge of the rule's nature, and (iii)~reduces daily manual adjustment effort while remaining tractable for daily use. Beyond this application, the framework enables optimization tools that adapt to evolving practice without recurrent manual remodeling.