FrontierOR: Benchmarking LLMs' Capacity for Efficient Algorithm Design in Large-Scale Optimization
Authors: Minwei Kong, Chonghe Jiang, Ao Qu, Wenbin Ouyang, Zhaoming Zeng, Xiaotong Guo, Zhekai Li, Junyi Li, +19 more
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. Code and data are publicly released at https://github.com/Minw913/FrontierOR.
We ask whether large language models (LLMs) can design effective algorithms for well-specified operations research (OR) problems. We study inventory control, queueing network control, and assortment optimization. We evaluate two levels of LLM use: at level 1, the model receives one problem instance and returns a solution for that instance; at level 2, it receives only the problem class description and broad parameter ranges, and returns an algorithm that maps instance parameters to solutions. Human input is minimal: we give one untuned prompt that describes the problem, and the model has access to a Python sandbox tool with a fixed compute budget. The strongest model we test, gpt-5.6-sol, matches or outperforms the best existing method on almost all evaluated instances. This holds even at level 2, where the returned algorithm is fixed before seeing the evaluation instances. Performance also improves sharply across models released less than eight months apart, suggesting that this capability is moving quickly. Thus, for the well-specified operations problems we study, a single untuned LLM query can already produce algorithms competitive with specialized methods. These results suggest that frontier LLMs can be a serious empirical baseline for algorithm design in well-specified OR problems.
LLM-based agents are increasingly deployed to solve optimization problems, yet existing benchmarks evaluate them on pre-structured mathematical formulations that bypass the most critical challenge: translating complex business requirements into correct models and solve efficiently. We introduce Opti-Agent-Bench, an end-to-end benchmark that evaluates Large Language Models (LLMs) across the complete optimization R&D pipeline, from understanding business-language descriptions through mathematical modeling, algorithm selection, and code implementation, to solution report generation. Our design rests on three pillars: (1) businesssemantic authenticity with anti-template traps that defeat pattern matching; (2) modular evaluation with cross-module consistency checking across Problem Understanding, Formal Modeling, Implementation, and Reporting; and (3) the ORAC bi-level validity framework that simultaneously ensures task quality and scoring integrity. Across several industrialscale tasks spanning integer programming, robust optimization, stochastic programming, and non-convex optimization, we expose critical failure modes of current models, including constraint omission, model-code inconsistency, and report-implementation divergence, that remain invisible under conventional single-metric evaluation.
We present JOR-Bench, a collection of five Japanese-language benchmarks for evaluating the ability of large language models (LLMs) to formulate and solve operations research (OR) problems. Each benchmark is a Japanese translation of an existing English benchmark: IndustryOR, MAMO Complex LP, NL4OPT, OptiBench, and OptMATH, covering 1,319 problems spanning linear programming, mixed-integer programming, non-linear programming, and combinatorial optimization. JOR-Bench is a solver-independent benchmark that can be used with any solver or programming language, and consists of pairs of Japanese problem statements and expected numerical answers. We evaluate seven LLMs, including multilingual general-purpose models and Japanese-specialized models, on both the original English and the new Japanese versions, and compare performance across languages. For the main evaluation, we standardize execution with the Python interface to OR-Tools to make model outputs comparable and reproducible with open-source software. Our results show that OR formulation ability is largely language-neutral for strong multilingual models; the overall average accuracy difference between English and Japanese is only −0.3 pp. Yet error analysis reveals subtle cross-lingual differences, including a pragmatic disambiguation failure in some domains that causes models to output decision-variable values instead of the objective value when the prompt is in Japanese.