Title: Large Language Model Guided Dynamic Branching Rule Scheduling in Branch-and-Bound
Primary area: applications to robotics, autonomy, planning
Keywords: branch and bound, mixed integer linear programming, large language model

Abstract: Branch-and-bound (B\&B) is a core technique in state-of-the-art mixed integer linear program (MILP) solvers. It reformulates an MILP into a systematic tree search and recursively partitions it into subproblems using various hard-coded heuristics, among which the branching rule plays a central role. Different branching rules yield distinct search trajectories and performance outcomes, making their selection a decisive factor in solver performance.
Traditionally, the configuration of the branching rule heavily relies on expert knowledge: a rule is manually configured for a given problem and applied throughout the entire B\&B process, or predefined to switch at certain depths. Such approaches fail to adapt to the evolving structure of the search tree, which often leads to suboptimal branching decisions and inefficient exploration of the search space. More recently, learning-based branching policies have been proposed to automate branching decisions using feature representations, but they often involve costly training pipelines and exhibit poor generalization across heterogeneous problem types.
In this work, we propose a large language models (LLMs)-guided approach to dynamically schedule the branching rule throughout the B\&B process. The term \emph{dynamic scheduling} refers to (i) identifying the problem type and scale at the initial stage to select an appropriate starting rule, and (ii) monitoring the evolving state of the search tree during solving to adaptively decide when and which branching rule to switch. By leveraging the extensive prior knowledge embedded in LLMs, our method eliminates dependence on human-crafted heuristics, removes the need for dedicated training, and achieves zero-shot generalization across diverse problem types.
Experiments on benchmark instances demonstrate that our method shows great potential and achieves competitive performance with state-of-the-art baselines in terms of solving efficiency.

TL;DR: We propose an LLM-guided dynamic branching rule scheduling framework for branch-and-bound MILP solvers.