Automating Combinatorial Optimization Knowledge Transfer with LLMs

Developing combinatorial optimization algorithms is time-consuming and labor-intensive. While recent LLM-based methods enable automated algorithm design, they often overlook the transferable knowledge encoded in mature solvers. In this paper, we study Automated Knowledge Transfer (AutoKT), which asks: to what extent can LLMs automate knowledge transfer from a source solver to a target problem? To this end, we formalize the algorithmic knowledge space and transfer process, defining a comprehensive evaluation protocol across three tiers: same-domain, cross-domain, and new-domain transfer. We then develop a three-stage agentic framework: a local migration stage that incrementally constructs a scaffold from localized source knowledge, a global migration stage that coordinates the transferred knowledge, and a validation stage to ensure correctness. Extensive experiments demonstrate AutoKT's effectiveness across all three tiers, outperforming both strong domain heuristics and general-purpose coding agents. We further provide in-depth analyses revealing key insights into AutoKT's behavioral patterns and knowledge transferability, offering useful takeaways for the community.