LLM Breaks 10 Records for Circle Packing Problem

Instead of solving the problem directly, the LLM applied a method of iteratively evolving the optimization algorithm itself, breaking existing records for the circle packing problem (Packomania csqv). Starting from a simple seed solver, the LLM proposed algorithm modifications, and an independent validator scored the results, adopting only improvements.

Key Results and Costs

• Record Breaking: Improved 10 existing best sum-of-radii records by 2.4% to 5.4% in the range of N=101 to 114.
• Efficiency: Achieved in a total of 15 iterations, with total LLM invocation costs amounting to $27.72.
• Validation: Packomania independently approved the results.

This approach demonstrates the potential to surpass the limitations of existing heuristics in complex combinatorial optimization problems by utilizing the LLM as an algorithm exploration agent rather than a code generation tool.