The paper introduces the Weighted Variability Score (WVS), a metric that aggregates dispersion in runtime, optimality gap, LP iterations, and branch‑and‑bound nodes across repeated runs of MIP solvers. Experiments on 100 randomized runs of MIPLIB 2017 instances show a right‑skewed distribution, with many instances stable but some exhibiting large variability not explained by basic properties. A tree‑based predictor using static and root‑level features achieves a mean absolute error of 0.058 and Spearman rank correlation of 0.65, with root degeneracy, matrix structure, coefficient ranges, and presolve reductions identified as key drivers of high WVS.
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.
arXiv:2608. 19953v1 Announce Type: new Abstract: Mixed-Integer Linear Programming (MILP) is a fundamental problem class in operations research and combinatorial optimization, with broad applications to industrial decision-making.
arXiv:2605. 25246v3 Announce Type: replace Abstract: Large language models (LLMs) are increasingly used for optimization modeling and solver-code generation, yet practical operations research and optimization problems often require a harder capability: designing scalable algorithms that exploit problem structure and outperform direct formulation-and-solve baselines.
The paper introduces AutoMIP, a reusable agent skill designed to manage long‑horizon autoresearch for mixed‑integer linear and nonlinear programming problems. AutoMIP combines idea pooling with an algorithm tree search to maintain a persistent pool of complementary candidate ideas and organize experiments into a structured tree, allowing the agent to preserve unexplored hypotheses, refine promising algorithms, and switch methodological directions based on historical states. Experiments on MILP and MINLP benchmark cohorts show that AutoMIP achieves the highest final success rates, discovering new best solutions for 31 of 60 MIPLib instances and 52 of 60 MINLPLib instances, and ablation studies confirm the complementary contributions of idea pooling and algorithm tree search.
arXiv:2606. 23880v1 Announce Type: new Abstract: From climate teleconnections to gene regulation, modern time-series datasets encompass tens or hundreds of interacting variables, making causal discovery increasingly challenging.
arXiv:2608.23353v1 Announce Type: new Abstract: Mixed-integer programming (MIP) lies at the core of operations research and industrial optimization. While large language models (LLMs) have recently s...
The paper argues that partition-level scores used in decomposed algorithm selection overestimate what a deployable selector can achieve. It introduces the deployment‑fidelity gap, G(R), which measures the difference between partition‑level and end‑to‑end utility, and derives conditions under which a partition choice is truly deployment‑optimal. Experiments on five public benchmarks show that every decomposed pipeline has a positive gap, with some cases where the partition advantage disappears or reverses when evaluated end‑to‑end, highlighting the need to report both partition and end‑to‑end scores.
arXiv:2602. 07453v2 Announce Type: replace Abstract: Decision tree ensembles are widely used in critical domains, making robustness and sensitivity analysis essential to their trustworthiness.
StoSignSGD is a new sign‑based optimization algorithm that injects structural stochasticity into the sign operator, ensuring unbiased updates. It resolves the divergence issues of traditional SignSGD on non‑smooth objectives, achieving optimal convergence rates in convex settings and improved complexity bounds in non‑convex, non‑smooth problems. Empirical results show that StoSignSGD is stable and efficient across large language model training, outperforming AdamW and SignSGD in low‑precision regimes (FP8 and FP4) and delivering speedups and accuracy gains on models ranging from OLMo2‑370M to 7B LLMs.
Mixed-integer programming (MIP) lies at the core of operations research and industrial optimization. While large language models (LLMs) have recently shown promise in automated MIP modeling from natur...
GradSAT is a new framework that improves satisfiability solving for Quantifier-Free Floating-Point formulas by treating each SMT clause as an independent multi‑task learning problem. It uses dynamic gradient normalization (GradNorm) to balance gradient magnitudes across clauses, preventing a few difficult clauses from dominating the optimization trajectory. The approach combines a GPU‑accelerated PyTorch backend for continuous relaxation with a precise local search engine, yielding a robust, highly parallelizable solver.
FrugalEvo introduces a cost‑aware evolutionary framework that pairs a high‑cost, powerful LLM with a cheaper LLM to explore and refine program solutions, respectively. It incorporates a cache‑efficient evolution process that maximizes prefix reuse across steps and defines a Budget‑Aware Area Under the Curve (BA‑AUC) metric to evaluate solution quality within a fixed cost budget. Across ten mathematical and systems optimization tasks, FrugalEvo matches or surpasses state‑of‑the‑art baselines in final solution quality and achieves higher BA‑AUC on nine tasks, while delivering new state‑of‑the‑art performance on circle packing for costs as low as $0.55 to $1.68.