LLM-Guided Program Evolution for Circle Packing: Breaking 10 Packomania Records for $28
Wes Sander at Practical Systems runs an LLM-guided evolutionary loop over optimization algorithms and improves 10 published Packomania circle-packing records for a total LLM spend of $27.72.
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The loop. 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 checked by an independent verifier, improvements kept and failures discarded.
The results. Best known solutions improved for 10 values of N in the range 101 to 114 on the csqv variable-radius benchmark, with gains of 2.4% to 5.4% over prior records.
Independently accepted. The improvements were accepted by Packomania, which is external validation rather than self-reported evaluation.
Cost and iteration count. All within 15 iterations and $27.72 total, with an adaptive plateau-detection mechanism managing when to stop pushing a line of attack.
Why it matters. AlphaEvolve-style program evolution has mostly been demonstrated at frontier-lab scale. This is the same shape of result from a single author on a hobbyist budget.
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.