LLM-guided program evolution improves 10 best-known circle-packing solutions (Packomania csqv, N=101-114) [R]

An LLM was used to iteratively evolve an optimization algorithm, improving 10 best-known circle-packing solutions on the Packomania csqv benchmark for N values from 101 to 114. The LLM proposed algorithmic changes based on a scoreboard and history, with an independent verifier scoring candidates. This process led to improvements in the sum-of-radii by 2.4% to 5.4% over 15 iterations, costing $27.72. Packomania independently accepted these results.