DecompGym: Benchmarking LLM Agents on Designing Decomposition Algorithms

Authors: Sikai Cheng , Tinghan Ye , Arnaud Deza , Xiaonan Qi , Miao Li , Litong Liu , Changkun Guan

View a PDF of the paper titled DecompGym: Benchmarking LLM Agents on Designing Decomposition Algorithms, by Sikai Cheng and 6 other authors

View PDF

HTML (experimental)

Abstract: Benders decomposition and column generation solve large optimization problems by passing cuts, columns, and dual values between a master problem and subproblems, and are hard to implement correctly. Large language models now automate parts of algorithm design, which points toward agents that build decomposition solvers for new problems. As a first step toward such agents, we study how well current coding agents design and implement these two algorithms, and how they fail. We introduce DecompGym, 81 instances from nine problem families (five Benders, four column generation), in which an agent writes a solver for a prescribed method. Each solver must meet three criteria: execution within a 60-second time limit; numerical feasibility together with a method audit, in which an LLM judge reads the solver's code; and an objective within 1% of the stored optimal objective. We evaluate 12 GPT, Claude, and Gemini models running in coding-agent tools. Over up to ten attempts, we compare independent regeneration with reflection, which first diagnoses the failure. On the first attempt, two models solve every instance and seven solve more than 90%. Most Benders failures (48 of 62) are missing or suboptimal solutions. The most common column-generation failure is a method-audit rejection. Output checks alone would accept 93 of the 108 attempts that fail the method audit. The most common rejection, an optimalif, occurs 96 times, 92 of them in one this http URL turns 66% of retries into successes, compared with 39% for regeneration, and it repairs method-audit failures, for which the judge names the defecective gaps. Agents for decomposition therefore need checks on how a solver reaches its answer and feedback that locates the error. The benchmark is available at this https URL .

Subjects:

Artificial Intelligence (cs.AI) ; Optimization and Control (math.OC)

Cite as:

arXiv:2610.38175 [cs.AI]

(or

arXiv:2610.38175v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.38175

Focus to learn more

arXiv-issued DOI via DataCite

Submission history

From: Tinghan Ye [ view email ]

[v1]

Wed, 28 Oct 2026 02:23:34 UTC (392 KB)

Full-text links:

Access Paper:

View a PDF of the paper titled DecompGym: Benchmarking LLM Agents on Designing Decomposition Algorithms, by Sikai Cheng and 6 other authors

View PDF

HTML (experimental)

TeX Source

view license

Additional Features

Audio Summary

Current browse context:

cs.AI

< prev

next >

new

recent

| 2026-10

Change to browse by:

cs

math

math.OC

References & Citations

SciX

Google Scholar

Semantic Scholar

export BibTeX citation

Loading...

BibTeX formatted citation

loading...

Data provided by:

Bookmark

Bibliographic Tools

Bibliographic and Citation Tools

Bibliographic Explorer Toggle

Bibliographic Explorer ( What is the Explorer? )

Connected Papers Toggle

Connected Papers ( What is Connected Papers? )

Litmaps Toggle

Litmaps ( What is Litmaps? )

scite.ai Toggle

scite Smart Citations ( What are Smart Citations? )

Code, Data, Media

Code, Data and Media Associated with this Article

alphaXiv Toggle

alphaXiv ( What is alphaXiv? )

Links to Code Toggle

CatalyzeX Code Finder for Papers ( What is CatalyzeX? )

DagsHub Toggle

DagsHub ( What is DagsHub? )

GotitPub Toggle

Gotit.pub ( What is GotitPub? )

Huggingface Toggle

Hugging Face ( What is Huggingface? )

ScienceCast Toggle

ScienceCast ( What is ScienceCast? )

Demos

Demos

Replicate Toggle

Replicate ( What is Replicate? )

Spaces Toggle

Hugging Face Spaces ( What is Spaces? )

Spaces Toggle

TXYZ.AI ( What is TXYZ.AI? )

Related Papers

Recommenders and Search Tools

Link to Influence Flower

Influence Flower ( What are Influence Flowers? )

Core recommender toggle

CORE Recommender ( What is CORE? )

Author

Venue

Institution

Topic

About arXivLabs

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

Which authors of this paper are endorsers? |

Disable MathJax ( What is MathJax? )