LLM Guided Evolution for Circle Packing: Breaking 10 Packomania Records for $28 (arxiv.org)

A new system named Discovery Loop has emerged in the AI community, leveraging a large language model (LLM) to iteratively enhance optimization algorithms. This innovative approach starts with a basic solver and allows the LLM to propose algorithmic refinements based on a feedback loop of past results. By applying this method to the Packomania benchmark for circle packing, Discovery Loop successfully broke 10 existing records, achieving improvements of 2.4% to 5.4% over prior solutions, all accomplished in just 15 iterations at a minimal cost of $27.72. The results have been independently verified and accepted by Packomania, showcasing the system's efficacy and reliability. The significance of this development lies in its potential to democratize automated scientific discovery by making advanced algorithm optimization accessible and cost-effective. The paper also discusses the adaptive plateau-detection mechanism that improves cost-efficiency, emphasizing the practical implications of using LLMs for solving complex problems. This breakthrough exemplifies how AI technologies can transform traditional optimization processes, paving the way for more innovative and efficient applications across various fields.