LLM-Guided Program Evolution for Circle Packing: Breaking 10 Packomania Records for $28
Discovery Loop, a lightweight system using a large language model to iteratively evolve optimization algorithms, improved best known solutions for 10 values of N in the range 101-114 on the Packomania circle-packing benchmark, with gains of 2.4%-5.4% over prior records, within 15 iterations and at a total LLM cost of $27.72. Results were independently accepted by Packomania.
Researchers present Discovery Loop, a system that uses a large language model 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. The paper describes the method, analyzes cost-efficiency dynamics including an adaptive plateau-detection mechanism, and discusses implications for democratizing automated scientific discovery.
The system uses an LLM to propose algorithmic improvements based on a scoreboard and history of prior ideas, with an independent verifier to accept or reject candidates. An adaptive plateau-detection mechanism is used to manage cost-efficiency dynamics. The approach achieved record improvements on a combinatorial optimization benchmark with minimal LLM cost.
The low cost ($27.72) and rapid iteration (15 iterations) demonstrate that LLM-guided program evolution can be a practical tool for automated scientific discovery, potentially lowering barriers for researchers without extensive computational resources.
The method offers a cost-effective way to automate algorithm improvement, which could reduce R&D costs in fields requiring optimization, such as logistics, engineering design, and scientific computing.
Observable next signals include adoption of similar LLM-guided evolution systems in other optimization domains, further record improvements on Packomania, and publication of follow-up studies on cost-efficiency and plateau-detection mechanisms.