GraphBU: MILP Instance Generation with Graph-Native Block Units

2026-07-07

AI Summary

Existing methods for generating mixed-integer linear programming (MILP) instances struggle to preserve the structural information relied upon by solvers and learning-based strategies, particularly due to the lack of explicit modeling of the coupling between local subproblems and the global instance. This work proposes GraphBU, a graph-native MILP instance generation framework that explicitly captures the interconnection between local subproblems and the overall structure by defining graph tile units enriched with interface information. By integrating an interface-augmentation mechanism and a compatibility-aware replacement strategy, GraphBU ensures structural plausibility and high feasibility while maintaining permutation invariance. Experimental results demonstrate that the generated instances achieve a graph statistical similarity of 0.934 and an average feasibility of 96.7%, leading to an average improvement of 8.0% in the primary metric of downstream Predict-and-Search approaches.

Abstract

Mixed-integer linear programming (MILP) instances used for solver development are hard to obtain when models come from private or application-specific pipelines. A generator must keep the structure that solvers and learned policies rely on. Existing general generators usually choose their generation unit from a formulation template, summary statistics, local graph edits, or blocks found after recombination. These units do not explicitly record how a local part of the MILP is coupled to the rest of the instance. We propose GraphBU, a graph-native generator whose basic unit is a local subproblem plus its interface. The method promotes coupling nodes into master constraints or boundary variables and uses the resulting block units for compatibility-checked replacement. The analysis focuses on the properties needed by this construction: promotion separates interfaces, replacement can preserve feasibility under an interface-slack condition, and the graph construction is invariant to row-column permutations. On MILP instances generation, this unit keeps graph statistics close to the source family, preserves feasibility on most datasets, and improves downstream Predict-and-Search training. Genrated by GraphBU, The average graph-statistical similarity was approximately 0.934, the average feasibility was approximately 96.7%, and the average increase in the main index of downstream PS was approximately 8.0%.

Problem

• MILP instance generation
• graph-native
• block units
• structure preservation
• coupling

Innovation

• GraphBU
• MILP instance generation
• graph-native block units
• interface-aware replacement
• feasibility preservation