config_phase_1_anthropic.yaml

# Configuration for circle packing constructor evolution (n=26)
max_iterations: 100 # Increased iterations
checkpoint_interval: 10
log_level: "INFO"

# LLM configuration
llm:
  primary_model: "claude-sonnet-4-5-20250929"
  primary_model_weight: 0.8
  secondary_model: "claude-opus-4-5-20251101"
  secondary_model_weight: 0.2
  api_base: "https://api.anthropic.com/v1"
  api_key: "${ANTHROPIC_API_KEY}"
  temperature: 0.7
  max_tokens: 8192
  timeout: 600

# Prompt configuration
prompt:
  system_message: |
    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.

    Key geometric insights:
    - Circle packings often follow hexagonal patterns in the densest regions
    - Maximum density for infinite circle packing is pi/(2*sqrt(3)) ≈ 0.9069
    - Edge effects make square container packing harder than infinite packing
    - Circles can be placed in layers or shells when confined to a square
    - Similar radius circles often form regular patterns, while varied radii allow better space utilization
    - Perfect symmetry may not yield the optimal packing due to edge effects

    Focus on designing an explicit constructor that places each circle in a specific position, rather than an iterative search algorithm.
  num_top_programs: 3
  use_template_stochasticity: true

# Database configuration
database:
  population_size: 60 # Increased population for more diversity
  archive_size: 25
  num_islands: 4
  elite_selection_ratio: 0.3
  exploitation_ratio: 0.7

# Evaluator configuration
evaluator:
  timeout: 60
  cascade_evaluation: true
  cascade_thresholds: [0.5, 0.75]
  parallel_evaluations: 4
  use_llm_feedback: false

# Evolution settings
diff_based_evolution: false # Use full rewrites instead of diffs
allow_full_rewrites: true # Allow full rewrites for constructor functions