One-shot Learning for MIPs with SOS1 Constraints (2403.09815v1)

Abstract: Efficient algorithms and solvers are required to provide optimal or near-optimal solutions quickly and enable organizations to react promptly to dynamic situations such as supply chain disruptions or changing customer demands. State-of-the-art mixed-integer programming (MIP) solvers are crafted to tackle a wide variety of problems, yet many real-world situations are characterized by problem instances that originate from a narrow distribution. This has inspired the creation of tailored approaches that exploit historical data to inform heuristic design. Deep learning (DL) methods are typically used in this context to extract patterns from data, but they require large datasets and comprehensive hyperparameter tuning for strong performance. This article describes a one-shot learning heuristic that leverages solutions discovered within the branch-and-bound tree to construct a model with minimal overhead. We evaluate our method on the locomotive assignment problem (LAP) and sets of MIPLIB instances that contain constraints based on special ordered sets of type 1. Experimental results include a comparison with multiple primal heuristics and state-of-the-art MIP solvers. We show that the method is most effective with CPLEX in terms of the average primal gap.