When Solvers Get Moody: Quantifying and Predicting Performance Variability in Mixed Integer Programming

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. Among comparisons exceeding a 20% practical-difference threshold, the complete adjudicator records 538 wins and 185 losses against the top nominee, while its win rate against the default rises from 84.9% to 90.2%. Against per-instance configuration baselines under a matched one-pass protocol it leads the cluster-level methods and the best-performing evaluated per-instance baseline, ISAC+.

Configuring the hyperparameters of Mixed-integer programming (MIP) solvers is a high-dimensional, instance-dependent optimization problem where suboptimal settings can degrade solving time by orders of magnitude. Default configurations are often suboptimal, while traditional tuning methods either suffer from the ``cold-start'' problem and inefficient search or heavily rely on expert experience. This paper introduces GRIMIP (General Reasoning for Instance-specific MIP configuration), a novel hybrid intelligence framework that synergistically integrates the semantic reasoning capabilities of Large Language Models (LLMs) with the sample-efficient search of Bayesian Optimization (BO). GRIMIP enables the LLM to function as a complete probabilistic surrogate within the BO loop, significantly improving performance and reducing sampling and evaluation costs. On seven benchmarks including MIPLIB, GRIMIP achieves over 40% reduction in Primal-Dual Integral on hard instances, outperforming SMAC and other LLM-assisted BO methods. By granting LLMs sufficient autonomy, GRIMIP combines the expert-level reasoning of LLMs with the efficient search of BO, achieving state-of-the-art performance.

Mixed-Integer Linear Programming (MILP) is a fundamental problem class in operations research and combinatorial optimization, with broad applications to industrial decision-making. Owing to their NP-hardness, however, modern solvers may struggle to find high-quality solutions for challenging MILP instances within practical time limits. Recent learning-based approaches seek to accelerate MILP solving by directly predicting high-quality solutions from static instance-level features, such as variable-constraint bipartite graphs. Yet accurate solution prediction from instance features alone is difficult, and these methods largely overlook the information revealed during the solver's search process. In this paper, we find that solutions produced at the early search stage of MILP solvers, which are computationally cheap to obtain, are often structurally close to the solutions found after full-budget search. Motivated by this observation, we propose a new solver-informed paradigm that shifts the learning target from variable assignment to early-to-final consistency: for each variable, we predict whether its early-stage assignment should persist in full-budget solutions. The predicted consistency naturally guides downstream search, for instance by fixing the assignments deemed consistent. At inference time, we further ensemble consistency predictions across multiple early-stage solutions to improve robustness. Experiments across four MILP benchmarks show our method improves prediction-guided search across diverse downstream pipelines. With Gurobi, our proposed method reduces the primal gap by 56.9% on average and closes it completely on combinatorial auction instances. Besides, we transferred the Gurobi-trained model zero-shot to SCIP without adaptation, achieving a 36.4% average gap reduction across benchmarks.