Global Optimization for Combinatorial Geometry Problems Revisited in Era of LLMs

A January 2026 arXiv paper by Timo Berthold and co-authors reports that off-the-shelf global optimization solvers FICO Xpress and SCIP, applied to straightforward nonlinear programming (NLP) formulations, reproduced and in several cases improved on the best-known solutions from DeepMind's AlphaEvolve benchmark suite of combinatorial geometry problems. The authors ran both solvers without modification on a subset of the AlphaEvolve problems, matching or beating prior literature results including the LLM-driven discoveries. The paper argues generic NLP technology has matured enough to serve as a tool within LLM-driven algorithm discovery rather than being superseded by it.

Mathematics Optimization and Control Submitted on 9 Jan 2026 v1 https://arxiv.org/abs/2601.05943v1 , last revised 15 Jan 2026 this version, v2 Title:Global Optimization for Combinatorial Geometry Problems Revisited in the Era of LLMs View PDF https://arxiv.org/pdf/2601.05943 HTML experimental https://arxiv.org/html/2601.05943v2 Abstract:Recent progress in LLM-driven algorithm discovery, exemplified by DeepMind's AlphaEvolve, has produced new best-known solutions for a range of hard geometric and combinatorial problems. This raises a natural question: to what extent can modern off-the-shelf global optimization solvers match such results when the problems are formulated directly as nonlinear optimization problems NLPs ? We revisit a subset of problems from the AlphaEvolve benchmark suite and evaluate straightforward NLP formulations with two state-of-the-art solvers, the commercial FICO Xpress and the open-source SCIP. Without any solver modifications, both solvers reproduce, and in several cases improve upon, the best solutions previously reported in the literature, including the recent LLM-driven discoveries. Our results not only highlight the maturity of generic NLP technology and its ability to tackle nonlinear mathematical problems that were out of reach for general-purpose solvers only a decade ago, but also position global NLP solvers as powerful tools that may be exploited within LLM-driven algorithm discovery. Submission history From: Timo Berthold view email https://arxiv.org/show-email/2bc85032/2601.05943 Fri, 9 Jan 2026 16:59:52 UTC 927 KB \ v1\ https://arxiv.org/abs/2601.05943v1 v2 Thu, 15 Jan 2026 07:41:55 UTC 927 KB References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender 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 https://info.arxiv.org/labs/index.html .