{"slug": "global-optimization-for-combinatorial-geometry-problems-revisited-in-era-of-llms", "title": "Global Optimization for Combinatorial Geometry Problems Revisited in Era of LLMs", "summary": "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generic NLP technology has matured enough to serve as a tool within LLM-driven algorithm discovery rather than being superseded by it.", "body_md": "# Mathematics > Optimization and Control\n\n  [Submitted on 9 Jan 2026 (\n\n[v1](https://arxiv.org/abs/2601.05943v1)), last revised 15 Jan 2026 (this version, v2)]\n# Title:Global Optimization for Combinatorial Geometry Problems Revisited in the Era of LLMs\n\n[View PDF](https://arxiv.org/pdf/2601.05943)\n\n[HTML (experimental)](https://arxiv.org/html/2601.05943v2)\n\nAbstract: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)?\n\nWe 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.\n\n## Submission history\n\nFrom: Timo Berthold [\n[view email](https://arxiv.org/show-email/2bc85032/2601.05943)]\n\n**Fri, 9 Jan 2026 16:59:52 UTC (927 KB)**\n\n[\\[v1\\]](https://arxiv.org/abs/2601.05943v1)\n**[v2]** Thu, 15 Jan 2026 07:41:55 UTC (927 KB)\n\n### References & Citations\n\nLoading...\n\n# Bibliographic and Citation Tools\n\nBibliographic Explorer \n\n*(*[What is the Explorer?](https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer))\nConnected Papers \n\n*(*[What is Connected Papers?](https://www.connectedpapers.com/about))\nLitmaps \n\n*(*[What is Litmaps?](https://www.litmaps.co/))\nscite Smart Citations \n\n*(*[What are Smart Citations?](https://www.scite.ai/))\n# Code, Data and Media Associated with this Article\n\nalphaXiv \n\n*(*[What is alphaXiv?](https://alphaxiv.org/))\nCatalyzeX Code Finder for Papers \n\n*(*[What is CatalyzeX?](https://www.catalyzex.com))\nDagsHub \n\n*(*[What is DagsHub?](https://dagshub.com/))\nGotit.pub \n\n*(*[What is GotitPub?](http://gotit.pub/faq))\nHugging Face \n\n*(*[What is Huggingface?](https://huggingface.co/huggingface))\nScienceCast \n\n*(*[What is ScienceCast?](https://sciencecast.org/welcome))\n# Demos\n\n# Recommenders and Search Tools\n\nInfluence Flower \n\n*(*[What are Influence Flowers?](https://influencemap.cmlab.dev/))\nCORE Recommender \n\n*(*[What is CORE?](https://core.ac.uk/services/recommender))\n# arXivLabs: experimental projects with community collaborators\n\narXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.\n\nBoth 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.\n\nHave an idea for a project that will add value for arXiv's community? [**Learn more about arXivLabs**](https://info.arxiv.org/labs/index.html).", "url": "https://wpnews.pro/news/global-optimization-for-combinatorial-geometry-problems-revisited-in-era-of-llms", "canonical_source": "https://arxiv.org/abs/2601.05943", "published_at": "2026-11-14 11:53:06+00:00", "updated_at": "2026-11-14 12:20:01.024625+00:00", "lang": "en", "topics": ["artificial-intelligence", "ai-research", "large-language-models", "machine-learning"], "entities": ["Timo Berthold", "DeepMind", "AlphaEvolve", "FICO Xpress", "SCIP", "arXiv"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/global-optimization-for-combinatorial-geometry-problems-revisited-in-era-of-llms", "markdown": "https://wpnews.pro/news/global-optimization-for-combinatorial-geometry-problems-revisited-in-era-of-llms.md", "text": "https://wpnews.pro/news/global-optimization-for-combinatorial-geometry-problems-revisited-in-era-of-llms.txt", "jsonld": "https://wpnews.pro/news/global-optimization-for-combinatorial-geometry-problems-revisited-in-era-of-llms.jsonld"}}