How much can LLMs help solve MIPs?

Mixed-integer programming (MIP) is a core modeling tool for planning, scheduling, logistics, energy systems, and many real-world applications. However, MIPs are notoriously hard to solve even with state-of-the-art optimization solvers. We ask whether language models can help make progress by accelerating established solver-based workflows. Large language models (LLMs) have recently shown promise in advancing open problems in mathematics. An unresolved MIP instance can likewise be viewed as an "open problem": its variables, constraints, objective, and data define a verifiable computational open problem.

MIPLIB is a public library of real-world mixed-integer programming instances used to evaluate and compare optimization solvers.

We studied the complete set of 217 open MIPLIB instances in our benchmark snapshot with LLM-assisted workflows. LLM reasoning helped search for exploitable structure, primal heuristics, and dual certificates; optimization solvers and independent checks supplied numerical bounds and result verification.