arXiv:2605.25246v2 Announce Type: new 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. Existing benchmarks are limited to small or simplified examples far below real-world scale and complexity. We introduce FrontierOR, among the first benchmarks to systematically evaluate LLM-based efficient algorithm design for realistic large-scale optimization problems. FrontierOR includes 180 tasks derived from methodologically diverse papers published in top-tier operations research venues, each with standardized instances and a hidden, expert-verified evaluation suite. We evaluate seven LLMs spanning frontier, cost-effective, and open-source models both in one-shot and test-time evolution settings. The results reveal that frontier models still struggle to move from executable formulations to efficient optimization algorithms: the strongest one-shot model outperforms Gurobi in only 31% of cases in both solution quality and computational efficiency, and even strong coding agents with test-time evolution achieve only 50% on selected hard tasks. FrontierOR establishes a practical evaluation platform for LLM-based optimization algorithm design, which enables future LLMs and agents to be systematically tested on whether they can move beyond correct formulation toward a feasible, high-quality, and efficient algorithm.

arXiv:2510.18428v3 Announce Type: replace Abstract: Optimization modeling underlies critical decision-making across industries, yet remains difficult to automate: natural-language problem descriptions must be translated into precise mathematical formulations and executable solver code. Existing LLM-based approaches typically rely on brittle prompting or costly retraining, both of which offer limited generalization. Recent work suggests that large models can improve via experience reuse, but how to systematically acquire, refine, and reuse such experience in structurally constrained settings remains unclear. We present \textbf{AlphaOPT}, a self-improving experience library that enables LLMs to learn optimization modeling knowledge from limited supervision, including answer-only feedback without gold-standard programs, annotated reasoning traces, or parameter updates. AlphaOPT operates in a continual two-phase cycle: a \emph{Library Learning} phase that extracts solver-verified, structured insights from failed attempts, and a \emph{Library Evolution} phase that refines the applicability of stored insights based on aggregate evidence across tasks. This design allows the model to accumulate reusable modeling principles, improve transfer across problem instances, and maintain bounded library growth over time. Evaluated on multiple optimization benchmarks, AlphaOPT steadily improves as more training data become available (65\% $\rightarrow$ 72\% from 100 to 300 training items) and outperforms the strongest baseline by 9.1\% and 8.2\% on two out-of-distribution datasets. These results demonstrate that structured experience learning, grounded in solver feedback, provides a practical alternative to retraining for complex reasoning tasks requiring precise formulation and execution. All code and data are available at: https://github.com/Minw913/AlphaOPT.