Nominate-then-Adjudicate: LLM-Assisted One-Pass and Per-Instance MIP Solver Tuning

Yifan Zhao, Qianyang Zhao, Xinyu Guan, Kai Wei, Yuming Deng

Mixed-integer programming solvers expose hundreds or even thousands of parameters whose best setting varies per instance, yet per-instance search is prohibitively expensive. We frame this as configuration for heterogeneous Big Data optimization workloads and propose a nominate-then-adjudicate pipeline built around two design choices. First, a fixed portfolio is sampled once and reused across instances, removing per-instance configuration search at inference; on the evaluated families, the resulting shortlist retains substantial oracle headroom, making selection within it the empirical focus. Second, the fixed 20-feature representation can map structurally different instances to the same vector, preventing a feature-only selector from distinguishing them even when they prefer different configurations. The foundation model receives no task-specific weight updates, and selection is one-pass: one model call and no solver calls at inference. The study represents structural Variety through distinct formulation families and decision Value through solver-performance outcomes; the one-call, zero-solve protocol specifies the decision interface and leaves end-to-end latency unmeasured.…