LLM-guided Program Evolution Achieves Breakthroughs in Packomania’s Top 10 Circle-Packing Solutions

Summary:A Reddit user employed a Large Language Model (LLM) to iteratively evolve an optimization algorithm, achieving significant improvements in the Packomania csqv benchmark. The method involves the LLM proposing algorithmic changes, which are then evaluated by an independent verifier. Successful improvements are retained, while failures are discarded. Over 15 iterations, the LLM improved the best-known sum-of-radii for 10 values of N (101-114) by 2.4% to 5.4%. This showcases the potential of LLMs in

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Key Breakthroughs

• LLM-guided Algorithmic Evolution: The approach uses a Large Language Model (LLM) to iteratively evolve an optimization algorithm rather than solving the packing problem directly.
• Iterative Optimization Process: Starting from a simple seed solver, the LLM proposes algorithmic changes based on a scoreboard of results and a history of prior attempts. Each candidate is scored by an independent verifier, retaining successful improvements and discarding failures.
• Significant Results: Over 15 iterations, the LLM improved the best-known sum-of-radii for 10 values of N (101-114) by 2.4% to 5.4% in the Packomania csqv benchmark.

Technical Highlights

• Cost-Effective and Efficient: The total LLM cost was $27.72, demonstrating its potential to solve complex problems with limited resources.
• Automated Verification Mechanism: The use of an independent verifier ensures the validity and reliability of the improvements.
• Scalability: The method is not limited to the Packomania problem and could be applied to other optimization problems.

Industry Impact

• New Direction in Algorithmic Evolution: The LLM-guided approach offers a novel perspective on traditional optimization algorithms, potentially driving innovation in algorithm design.
• AI and Optimization Problems: This showcases the significant potential of AI in solving complex optimization problems, opening new avenues for AI applications.

Developer Recommendations

• Experiment with Similar Methods: Developers can explore applying LLMs to other optimization problems to uncover their potential in different domains.
• Emphasize Independent Verification: Ensure the use of independent verification mechanisms to guarantee the validity of results during algorithmic evolution.

Conclusion

This research demonstrates the powerful capabilities of LLMs in algorithmic evolution, providing a new perspective on the combination of AI and optimization problems. As LLM technology continues to advance, its application in solving complex problems will become even more promising.

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Source: Reddit r/MachineLearning (2026-09-07)

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Tags: #LLMs & Foundation Models #Algorithmic Optimization #Packomania #AI Research #Optimization Problems