[Submitted on 9 Jan 2026 (
[v1](https://arxiv.org/abs/2601.05943v1)), last revised 15 Jan 2026 (this version, v2)]
[View PDF](https://arxiv.org/pdf/2601.05943)
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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)
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