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arxiv: 2605.25246 · v3 · pith:EXWRIKPYnew · submitted 2026-05-24 · 💻 cs.AI

FrontierOR: Benchmarking LLMs' Capacity for Efficient Algorithm Design in Large-Scale Optimization

Minwei Kong , Chonghe Jiang , Ao Qu , Wenbin Ouyang , Zhaoming Zeng , Xiaotong Guo , Zhekai Li , Junyi Li
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Yi Fan Xinshou Zheng Xi Jing Yikai Zhang Zhiwei Liang Seonghoo Kim Runqing Yang Zijian Zhou Sirui Li Han Zheng Wangyang Ying Ou Zheng Chonghuan Wang Jinglong Zhao Hanzhang Qin Cathy Wu Paul Pu Liang Jinhua Zhao Hai Wang
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Pith reviewed 2026-06-30 00:24 UTC · model grok-4.3

classification 💻 cs.AI
keywords LLM evaluationoptimization algorithmsoperations researchbenchmarkingalgorithm designlarge-scale problemssolver comparison
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The pith

Current LLMs struggle to design efficient algorithms that outperform Gurobi on most large-scale optimization problems.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents FrontierOR, a benchmark with 180 tasks sourced from top operations research publications. Each task requires LLMs to generate algorithms that scale to large instances by exploiting problem structure, rather than relying on direct solver calls. Testing across multiple models shows that the best one-shot performance beats Gurobi in solution quality and speed for only 31 percent of cases. Even with test-time evolution, success on hard tasks reaches just 50 percent. This highlights a gap between producing correct optimization code and creating truly efficient custom algorithms for practical use.

Core claim

FrontierOR is introduced as a benchmark derived from 180 methodologically diverse papers in top-tier operations research venues. It supplies standardized instances and a hidden expert-verified evaluation suite. Evaluations of seven LLMs in one-shot and test-time evolution modes indicate that frontier models move from formulations to efficient algorithms in a minority of cases, with the strongest one-shot model succeeding in 31% against Gurobi on both metrics and evolution agents at 50% on selected hard tasks.

What carries the argument

The FrontierOR benchmark, which tests the transition from executable formulations to structure-exploiting scalable algorithms on realistic instances.

If this is right

  • LLMs currently cannot reliably replace expert algorithm design for large optimization problems.
  • Direct use of solvers like Gurobi remains more reliable for most tasks.
  • The benchmark provides a standardized way to measure future improvements in LLM algorithm design.
  • Test-time evolution improves results but does not close the gap to human-level performance.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Models may be limited by training data that emphasizes formulation over algorithmic innovation.
  • Adding problem structure hints or domain-specific fine-tuning could be tested as extensions.
  • Success here would imply broader capabilities for automated scientific discovery in optimization.

Load-bearing premise

That performance on these 180 tasks accurately reflects the capacity to design efficient algorithms that exploit problem structure at real-world scale.

What would settle it

A model that outperforms Gurobi in both quality and efficiency on more than half of the 180 tasks would indicate that the reported limitations have been overcome.

Figures

Figures reproduced from arXiv: 2605.25246 by Ao Qu, Cathy Wu, Chonghe Jiang, Chonghuan Wang, Hai Wang, Hanzhang Qin, Han Zheng, Jinglong Zhao, Jinhua Zhao, Junyi Li, Minwei Kong, Ou Zheng, Paul Pu Liang, Runqing Yang, Seonghoo Kim, Sirui Li, Wangyang Ying, Wenbin Ouyang, Xiaotong Guo, Xi Jing, Xinshou Zheng, Yi Fan, Yikai Zhang, Zhaoming Zeng, Zhekai Li, Zhiwei Liang, Zijian Zhou.

Figure 1
Figure 1. Figure 1: Overview of the FrontierOR benchmark. FrontierOR spans diverse problem domains, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Evaluation Protocol of a FrontierOR benchmark task. We feed the problem description [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Algorithm pattern distribution and failure mode across models. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Self-evolution trajectories on the hard tasks. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Pairwise comparison on shared feasible large instances of tasks. Each case at Model [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper introduces FrontierOR, a benchmark of 180 tasks derived from methodologically diverse top-tier OR papers, each with standardized instances and a hidden expert-verified evaluation suite. It evaluates seven LLMs (frontier, cost-effective, open-source) in one-shot and test-time evolution settings on their ability to design scalable algorithms that exploit problem structure and outperform Gurobi baselines in solution quality and computational efficiency. Key results: the strongest one-shot model succeeds in only 31% of cases on both metrics, while strong coding agents with evolution reach only 50% on selected hard tasks. The benchmark and public code/data release aim to shift evaluation from formulation correctness to efficient algorithm design at realistic scale.

Significance. If the tasks validly isolate structure-exploiting algorithm design (rather than formulation) and the hidden suite prevents overfitting, the reported performance gaps would establish a clear, scalable testbed for LLM progress in practical large-scale optimization, highlighting current limitations beyond small/simplified examples. The public release of code and data is a positive contribution for reproducibility in this empirical benchmark setting.

major comments (2)
  1. [Abstract] Abstract: the headline claims that the strongest one-shot model outperforms Gurobi in only 31% of cases (both quality and efficiency) and that agents reach 50% on hard tasks are presented without any information on task selection criteria, statistical testing of the percentages, or how the hidden evaluation suite is constructed to prevent overfitting; these details are load-bearing for interpreting the central empirical results.
  2. [Abstract] Abstract (and implied § on benchmark construction): the premise that the 180 tasks test the shift to 'efficient optimization algorithms that exploit problem structure' rather than merely correct formulations is invoked to justify relevance, but no concrete mechanism (e.g., instance standardization details or expert verification criteria) is supplied to show how the evaluation distinguishes the two capabilities.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful comments, which highlight the need for greater transparency in the abstract and benchmark details to support interpretation of the central results. We address each point below and will revise the manuscript to incorporate additional clarifications on task selection, statistical aspects, and evaluation mechanisms.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline claims that the strongest one-shot model outperforms Gurobi in only 31% of cases (both quality and efficiency) and that agents reach 50% on hard tasks are presented without any information on task selection criteria, statistical testing of the percentages, or how the hidden evaluation suite is constructed to prevent overfitting; these details are load-bearing for interpreting the central empirical results.

    Authors: We agree these details are important for interpreting the headline percentages. Task selection criteria (derivation from 180 methodologically diverse top-tier OR papers) and the hidden expert-verified suite are described in Section 3; statistical computation of the 31% and 50% success rates (across the full set and selected hard tasks) appears in Section 4. To address the concern directly in the abstract, we will add a concise clause noting the tasks are drawn from top-tier venues with a hidden evaluation suite designed to prevent overfitting, and we will include a brief parenthetical on the percentages being computed over the standardized instance set. revision: yes

  2. Referee: [Abstract] Abstract (and implied § on benchmark construction): the premise that the 180 tasks test the shift to 'efficient optimization algorithms that exploit problem structure' rather than merely correct formulations is invoked to justify relevance, but no concrete mechanism (e.g., instance standardization details or expert verification criteria) is supplied to show how the evaluation distinguishes the two capabilities.

    Authors: The distinction is operationalized by requiring models to produce algorithms that improve both solution quality and runtime over Gurobi on large-scale standardized instances; correct formulations alone are insufficient to meet both criteria at the scales used. Section 3 outlines the standardization process and expert verification, but we acknowledge the need for more explicit criteria. We will expand the benchmark construction section with concrete details on instance scaling, the expert verification rubric (focusing on scalability and structure exploitation), and how the hidden suite enforces evaluation of algorithmic efficiency rather than formulation correctness alone. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

This is an empirical benchmark paper introducing FrontierOR with 180 tasks and reporting LLM performance metrics (e.g., 31% one-shot outperformance of Gurobi) via direct external comparisons. No equations, parameter fits, predictions derived from inputs, or load-bearing self-citations appear in the provided text; the central claims rest on standardized instances and hidden expert-verified evaluation, which are independent of the reported results. The derivation chain is self-contained against external baselines with no reduction to self-definition or ansatz smuggling.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper introduces an empirical benchmark without fitted parameters or new postulated entities; it rests on one domain assumption about task representativeness.

axioms (1)
  • domain assumption Tasks derived from published top-tier OR papers with standardized instances represent realistic large-scale optimization problems that require structure-exploiting algorithms beyond direct formulation.
    This assumption underpins the claim that the benchmark measures the targeted capability.

pith-pipeline@v0.9.1-grok · 5875 in / 1311 out tokens · 44569 ms · 2026-06-30T00:24:38.183281+00:00 · methodology

discussion (0)

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Reference graph

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