Title: Structure-Aware Bipartite Representations for Efficient MILP Branching
Primary area: optimization
Keywords: Combinatorial optimization, Mixed Integer Linear Program, Branch And Bound, Block Structure, Graph Neural Networks

Abstract: Efficient branching variable selection is pivotal to the performance of Branch-and-Bound (B\&B) algorithms in Mixed Integer Linear Programming (MILP). Despite advances in traditional heuristics and graph-based learning methods, these approaches often fail to exploit the latent block structures inherent in many MILP problems. To address this limitation, we propose a novel graph representation that incorporates explicit block-structure annotations. By classifying variables and constraints according to their roles in block decompositions and augmenting edges with block identifiers, our method enables MILP solvers to better recognize localized patterns and global couplings. Through extensive experiments on six diverse MILP benchmarks, we demonstrate that our approach significantly improves upon state-of-the-art graph neural network baselines. Specifically, our method reduces search tree sizes by 2\%--4\% on standard instances and by 11\%--13\% on transfer instances, while decreasing solver runtime by 6\%--6.66\% on standard instances and by 5.5\%--6\% on transfer instances. Notably, these improvements are achieved without compromising solution quality. Our work highlights the importance of integrating structural priors into combinatorial optimization frameworks.