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| 1 | +# Configuration for circle packing constructor evolution (n=26) |
| 2 | +max_iterations: 100 # Increased iterations |
| 3 | +checkpoint_interval: 10 |
| 4 | +log_level: "INFO" |
| 5 | + |
| 6 | +# LLM configuration |
| 7 | +llm: |
| 8 | + primary_model: "google/gemini-2.0-flash-001" |
| 9 | + # primary_model: "llama3.1-8b" |
| 10 | + primary_model_weight: 0.8 |
| 11 | + secondary_model: "anthropic/claude-3.7-sonnet" |
| 12 | + # secondary_model: "llama-4-scout-17b-16e-instruct" |
| 13 | + secondary_model_weight: 0.2 |
| 14 | + api_base: "https://openrouter.ai/api/v1" |
| 15 | + # api_base: "https://api.cerebras.ai/v1" |
| 16 | + temperature: 0.7 |
| 17 | + top_p: 0.95 |
| 18 | + max_tokens: 8192 |
| 19 | + timeout: 600 |
| 20 | + |
| 21 | +# Prompt configuration |
| 22 | +prompt: |
| 23 | + system_message: | |
| 24 | + You are an expert mathematician specializing in circle packing problems and computational geometry. Your task is to improve a constructor function that directly produces a specific arrangement of 26 circles in a unit square, maximizing the sum of their radii. The AlphaEvolve paper achieved a sum of 2.635 for n=26. |
| 25 | +
|
| 26 | + Key geometric insights: |
| 27 | + - Circle packings often follow hexagonal patterns in the densest regions |
| 28 | + - Maximum density for infinite circle packing is pi/(2*sqrt(3)) ≈ 0.9069 |
| 29 | + - Edge effects make square container packing harder than infinite packing |
| 30 | + - Circles can be placed in layers or shells when confined to a square |
| 31 | + - Similar radius circles often form regular patterns, while varied radii allow better space utilization |
| 32 | + - Perfect symmetry may not yield the optimal packing due to edge effects |
| 33 | +
|
| 34 | + Focus on designing an explicit constructor that places each circle in a specific position, rather than an iterative search algorithm. |
| 35 | + num_top_programs: 3 |
| 36 | + use_template_stochasticity: true |
| 37 | + |
| 38 | +# Database configuration |
| 39 | +database: |
| 40 | + population_size: 60 # Increased population for more diversity |
| 41 | + archive_size: 25 |
| 42 | + num_islands: 4 |
| 43 | + elite_selection_ratio: 0.3 |
| 44 | + exploitation_ratio: 0.7 |
| 45 | + |
| 46 | +# Evaluator configuration |
| 47 | +evaluator: |
| 48 | + timeout: 60 |
| 49 | + cascade_evaluation: true |
| 50 | + cascade_thresholds: [0.5, 0.75] |
| 51 | + parallel_evaluations: 4 |
| 52 | + use_llm_feedback: true |
| 53 | + system_message: | |
| 54 | + You are an expert mathematician specializing in circle packing problems and computational geometry. Your task is to be an expert evaluator of a solution to the circle packing problem. |
| 55 | + You will be given a solution to the circle packing problem and you will need to evaluate it based on the following criteria: |
| 56 | + - The solution is a valid circle packing of 26 circles in a unit square. |
| 57 | + |
| 58 | +
|
| 59 | +# Evolution settings |
| 60 | +diff_based_evolution: false # Use full rewrites instead of diffs |
| 61 | +allow_full_rewrites: true # Allow full rewrites for constructor functions |
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