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

arXiv: https://arxiv.org/abs/2609.05093 · HTML: https://mlsanity.com/paper/2609.05093/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
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- First posted on arXiv 4 Sep 2026.

## Abstract (arXiv)

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.