Branch-and-bound for mixed‑integer linear programming (MILP) hinges on two tightly coupled decisions: branching and node selection. Most learning‑based approaches treat them separately, overlooking their interaction. Evo‑B&B introduces an LLM‑guided evolutionary framework that jointly evolves executable branching and node‑selection policies using end‑to‑end feedback from the SCIP solver. To improve search efficiency and avoid redundant evaluations of behaviorally similar policies, a behavior‑aware multi‑island evolutionary mechanism is employed. The mechanism records each policy’s branching actions $b_i(d)$ and node‑selection actions $n_i(d)$ on a fixed set of B&B decision states $D$, and computes similarity
$$ S(p_i,pj)=\frac{1}{|D|}\sum{d\in D}\mathbf{1}[b_i(d)=b_j(d)\land n_i(d)=n_j(d)] $$
to preserve diversity in the population. Experiments on four standard MILP benchmarks covering multiple instance scales show that Evo‑B&B achieves competitive solving performance and generalizes well to larger instances. Ablation studies confirm the benefit of joint evolution and behavior‑aware diversity management.
Review: This study highlights the synergy between large language models and evolutionary search, offering a promising direction for adaptive MILP solver design.