Towards Better Branching Policies: Leveraging the Sequential Nature of Branch-and-Bound Tree

Ce Zhang, Bin Zhang, Guoliang Fan

Keywords: Mixed-Integer Linear Programming, Branch-and-Bound, Branching Variable Selection Policy, Generalization, Mamba

TL;DR: We propose a branching policy that utilizes the sequential branching path of the branch-and-bound tree to guide current decision.

Abstract: The branch-and-bound (B\&B) method is a dominant exact algorithm for solving Mixed-Integer Linear Programming problems (MILPs). While recent deep learning approaches have shown promise in learning branching policies using instance-independent features, they often struggle to capture the sequential decision-making nature of B\&B, particularly over long horizons with complex inter-step dependencies and intra-step variable interactions. To address these challenges, we propose Mamba-Branching, a novel learning-based branching policy that leverages the Mamba architecture for efficient long-sequence modeling, enabling effective capture of temporal dynamics across B\&B steps. Additionally, we introduce a contrastive learning strategy to pre-train discriminative embeddings for candidate branching variables, significantly enhancing Mamba's performance. Experimental results demonstrate that Mamba-Branching outperforms all previous neural branching policies on real-world MILP instances and achieves superior computational efficiency compared to the advanced open-source solver SCIP. The source code can be accessed via an anonymized repository at https://anonymous.4open.science/r/Mamba-Branching-B4B4/.

Primary Area: Optimization (e.g., convex and non-convex, stochastic, robust)

Submission Number: 7870