BiFE: Search-Efficient Discovery of CPU-Only Branching Policies via LLM-based Bi-Fidelity Evolution

2026-09-29

AI Summary

This study addresses the bottlenecks of high GPU inference costs, insufficient CPU symbolic expressiveness, and expensive LLM-based search in branching strategies for mixed-integer programming. To overcome these challenges, this work proposes a bi-fidelity evolutionary framework that leverages LLM code generation to synthesize lightweight CPU branching rules. By synergistically combining low-fidelity screening with high-fidelity elite evaluation, the method effectively mitigates distribution shift inherent in offline imitation learning while enabling efficient exploration of the search space. Experimental results demonstrate that the discovered CPU branching rules outperform the SCIP solver and several baseline methods, achieving performance competitive with certain GPU-based neural policies. Consequently, the proposed approach successfully balances computational efficiency with solution quality, offering a practical alternative for large-scale optimization tasks.

Abstract

In branch-and-bound (B&B) for mixed-integer linear programming (MILP), branching variable selection critically impacts efficiency. Existing neural branching policies often require GPU inference, while CPU-efficient symbolic expressions lack the representational capacity for complex logic. Large Language Model (LLM)-generated code provides a flexible search space for designing lightweight branching rules with diverse algorithmic logic. To discover effective rules within LLM-based evolutionary frameworks, a core challenge arises: full B&B evaluation on real instances is prohibitively expensive, whereas offline imitation learning suffers from distribution shift. To address this, we introduce a Bi-Fidelity Evolutionary framework (BiFE). It employs low-fidelity imitation scores as a rapid pre-screener and selectively applies high-fidelity on-instance evaluation only to elite candidates, effectively balancing search efficiency with performance reliability. Experiments validate both the search efficiency of BiFE and the competitiveness of its discovered rules, which outperform the SCIP solver and other baselines on CPUs, and even surpass certain GPU-based neural policies.

Problem

• Mixed-Integer Linear Programming
• Branch-and-Bound
• Branching Policy
• Large Language Model
• Evolutionary Search

Innovation

• Branch-and-Bound
• Large Language Model
• Bi-Fidelity Evolution
• Mixed-Integer Linear Programming
• Branching Policy