LLM-Guided Program Evolution for Circle Packing: Breaking 10 Packomania Records for $28

Abstract:We present Discovery Loop, a lightweight system that uses a large language model (LLM) to iteratively evolve optimization algorithms. Starting from a simple seed solver, the LLM proposes algorithmic improvements guided by a scoreboard of results and a history of prior ideas. Each candidate is evaluated against an independent verifier; improvements are kept and failures discarded. Applied to the Packomania circle-packing benchmark (csqv: maximize the sum of radii of N variable-radius circles in the unit square), the system improved the best known solutions for 10 values of N in the range 101-114, with gains of 2.4%-5.4% over prior records, all within 15 iterations and at a total LLM cost of $27.72. These results have been independently accepted by Packomania. We describe the method, analyze cost-efficiency dynamics including an adaptive plateau-detection mechanism, and discuss implications for democratizing automated scientific discovery.

8 pages. Code and solutions: this https URL

Artificial Intelligence (cs.AI)

arXiv:2609.05093 [cs.AI]

(or arXiv:2609.05093v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2609.05093 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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