LEAP: LLM-Empowered Adaptive Portfolio Discovery for Instance-Aware MILP Configuration

We study instance-aware solver configuration for mixed-integer linear programs (MILPs). Modern MILP solvers expose numerous tunable parameters, and different instances within the same problem family can benefit from different configurations. Portfolio-based approaches exploit this variation by discovering a set of complementary configurations in advance and selecting an appropriate configuration from this portfolio for each new instance. However, portfolio discovery requires expensive solver evaluations over large configuration spaces, while conventional configurators primarily rely on numerical performance feedback without directly leveraging solver parameter semantics or problem-family knowledge. To address this limitation, we propose LEAP (LLM-Empowered Adaptive Portfolio Discovery), which integrates semantic guidance into numerical search. An LLM Initializer proposes starting configurations using problem descriptions and parameter semantics, while an LLM Refiner uses portfolio performance and search feedback to adaptively focus or expand a working subspace within a fixed base configuration space, guiding an existing model-based configurator to search for configurations that improve the current portfolio. At deployment, a lightweight GNN selector, with no LLM calls or configuration search, selects the configuration with the lowest predicted solving cost for each incoming instance. Experiments on MILP benchmarks demonstrate solving-time reductions of up to 43.2% and 94.7% over the default SCIP and Gurobi configurations, respectively. Ablations demonstrate the benefits of knowledge-guided initialization and adaptive working-subspace refinement for discovering higher-quality configuration portfolios.