用大模型自动优化圆打包算法，15轮内刷新10项世界纪录。
LLM-Guided Program Evolution for Circle Packing: Breaking 10 Packomania Records for $28
- 大模型根据历史结果和评分榜，迭代改进优化算法。
- 在101-114个圆的打包问题上提升2.4%-5.4%性能。
- 成本仅27.72美元，适合快速探索科学新解法。
我们提出Discovery Loop，一个轻量级系统，利用大语言模型（LLM）迭代演化优化算法。从简单初始求解器出发，LLM基于结果评分表和过往想法历史，提出算法改进；每个候选方案由独立验证器评估，成功保留，失败丢弃。应用于Packomania圆打包基准（csqv：在单位正方形中最大化N个可变半径圆的半径之和），该系统在N=101至114的10个数值上突破了先前最优解，性能提升2.4%-5.4%，所有改进均在15轮内完成，总LLM成本为27.72美元。这些成果已获Packomania官方确认。本文描述方法，分析成本效率动态，包括自适应平台检测机制，并讨论其对推动自动化科学发现民主化的意义。
原文摘要 · Abstract (English)
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.
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