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

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reddit.com: I used an LLM to iteratively evolve an optimization algorithm rather than solve the packing directly. Starting from a simple seed solver, the LLM proposes algorithmic changes guided by a scoreboard of results and a history of prior attempts, and each candidate is scored by an independent verifier so improvements are kept and failures discarded. On the Packomania csqv benchmark it improved the best-known sum-of-radii for 10 values of N from 101 to 114, by 2.4 to 5.4%, in 15 iterations. Total LLM cost was $27.72. Packomania accepted the results independently. Paper: arxiv.org/abs/2609.05093 Code + solutions: github.com/ucsandman/discovery-loop Benchmark: packomania.com/csqv/csqv.html Happy to discuss the plateau-detection stopping rule, that s the piece I d most want critique on. submitted by /u/SIGH_I_CALL [link] [comments]

arxiv.org: arXiv:2609.05093v1 Announce Type: new 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.