Title: Online Algorithm Configuration for MILP Re-Optimization with LLM Guidance
Primary area: optimization
Keywords: MILP re-optimization; sequential instances; algorithm configuration; large language models; multi-armed bandits

Abstract: In this work, we study the re-optimization setting for mixed-integer linear programs, where solving sequentially related instances can benefit from both adaptive solver parameter configuration and the reuse of historical information from previous solves. However, modern solvers expose hundreds of tunable parameters, yielding a large configuration space; and the effectiveness of re-optimization techniques (e.g., warm starts or branching statistics) varies substantially across problem families. To address these challenges, we formulate a generalized algorithm configuration problem that jointly determines solver built-in parameters and the selective use of historical information within a reduced configuration space. Given the sequential nature of re-optimization and the limited number of available instances, offline methods that require large datasets are impractical, so adaptive online configuration selection becomes essential. We therefore propose a two-stage framework: (i) configuration space reduction via large language models, which generate a compact portfolio of candidate configurations; and (ii) adaptive online selection using multi-armed bandit algorithms to minimize solving cost over the sequence. Empirical results on the MIP Workshop 2023 re-optimization benchmarks demonstrate that our method substantially outperforms default SCIP and Gurobi configurations as well as strong baselines, achieving solving time reductions of up to 54.18%, without requiring prior validation data or supervised training.