Branch-and-bound (BnB) solves mixed-integer linear programs by constructing and exploring a search tree.
Node selection and branching are two recurrent decisions that directly determine the tree.
Learning-based approaches typically optimize either decision in isolation and condition on a mostly local view, leaving the coupled evolution of the search tree insufficiently modeled.
This paper proposes Seq-BnB
Seq-BnB, a sequence-structured framework that learns branching and node selection from a shared global representation of the evolving BnB process.
Seq-BnB serializes node creations, node updates, node-selection events, and branching events into typed tokens, producing a causal event sequence of the search trajectory.
A self-attention encoder summarizes this global search history, a bipartite graph neural network encodes the current LP relaxation, and context-conditioned decision heads score branching variables and open nodes.
To reduce distribution shift between expert demonstrations and learned policies
Seq-BnB is trained with DAgger-style data aggregation.
On four MILP benchmark families
Seq-BnB consistently processes fewer BnB nodes than heuristic and learning-based baselines, with strong solution times on both standard and larger transfer instances.
While this paper evaluates Seq-BnB instantiation for branching and node selection, it accommodates additional solver decisions, such as cut selection, by introducing new action tokens and decision heads.