GraphBU Generates Realistic MILP Instances with Block Units

Developing and testing efficient solvers for Mixed-Integer Linear Programming (MILP) problems requires a continuous supply of diverse and challenging instances. However, obtaining these instances can be difficult, especially when the original models are proprietary or application-specific. Existing general-purpose generators often struggle to replicate the intricate structural properties that MILP solvers and learning-based policies depend on, leading to less effective testing and development. A new method called GraphBU (Graph-Native Block Units) addresses this by introducing a novel approach to MILP instance generation. GraphBU's core idea is to use "graph-native block units," which consist of a local subproblem along with its interface—how it couples to the rest of the instance via master constraints or boundary variables. This allows the generator to perform compatibility-checked replacements, ensuring that the generated instances retain the structural integrity of the original problem family. Analysis shows that GraphBU effectively preserves key graph statistics, maintaining a high similarity to the source family. It also largely preserves feasibility across datasets and significantly improves the training of downstream Predict-and-Search algorithms. Empirical results demonstrate an average graph-statistical similarity of 0.934, approximately 96.7% feasibility, and an 8.0% increase in the main index for downstream Predict-and-Search, highlighting its effectiveness in creating high-quality, structurally sound MILP instances.