Learning to Allocate Solver Freedom: Adaptive Reoptimization for Mixed-Integer Programming

Can correction signals learned on smaller mixed-integer programs (MIPs) guide reoptimization at million-variable scale? Given a feasible anchor, we learn which integer decisions to release and adapt the amount of solver freedom to each instance. We study this question through anchor-conditioned reoptimization. A quality–freedom frontier characterizes the tradeoff between attainable solution quality and the number of anchor decisions left free. A lightweight gradient-boosted decision tree ranks variables using structural, root-LP, and anchor-conditioned features; a cumulative-score rule selects the free set, and a MIP solver jointly optimizes the released variables and continuous decisions. We derive a correction-coverage bound under marginal correction probabilities and show why high partial recall alone cannot guarantee objective improvement. Across three structurally distinct MIP families, our method improves gap–time tradeoffs and reduces mean optimality gaps by 14%-94% on larger instances relative to matched-budget unrestricted solving. On MILPBench, family-specific predictors trained using feasible references on 20,000-40,000-variable instances transfer to problems with up to two million variables without target-scale retraining or retuning, achieving competitive objective values in 175–397 seconds of measured online runtime. The framework operates entirely on CPUs without GPU acceleration, providing a practical and scalable interface between learning and MIP solving.