data/examples/alphaevolve_math_problems/hexagon_packing/12/config.yaml

# Evolution settings
max_iterations: 200
checkpoint_interval: 10
parallel_evaluations: 1

# LLM configuration
llm:
  api_base: "https://api.openai.com/v1"  # Or your LLM provider
  models:
    - name: "gpt-4"
      weight: 1.0
  temperature: 0.7
  max_tokens: 4000
  timeout: 120

# Database configuration (MAP-Elites algorithm)
database:
  population_size: 40
  num_islands: 5
  migration_interval: 40
  feature_dimensions:  # MUST be a list, not an integer
    - "score"
    - "complexity"

# Evaluation settings
evaluator:
  timeout: 360
  max_retries: 3

# Prompt configuration
prompt:
  system_message: |
    SETTING:
    You are an expert computational geometer and optimization specialist focusing on hexagon packing problems.
    Your task is to evolve a constructor function that generates an optimal arrangement of exactly 12 unit regular hexagons within a larger regular hexagon, maximizing 1/outer_hex_side_length (equivalently minimizing the outer hexagon's side length).
    
    PROBLEM CONTEXT:
    - Target: Establish new state-of-the-art for 12-hexagon packing of 1/outer_hex_side_length = 1/3.9419123 ≈ 0.2537
    - Constraint: All 12 inner hexagons must be unit regular hexagons (side length = 1) that are fully contained within the outer hexagon with no overlaps
    - Mathematical formulation: For hexagon i at position (xi, yi) with rotation θi:
      * Non-overlap: All pairs of inner hexagons must be disjoint
      * Containment: All vertices of inner hexagons must lie within the outer hexagon
      * Objective: maximize 1/R where R is the outer hexagon side length

    PERFORMANCE METRICS:
    1. **inv_outer_hex_side_length**: 1/outer_hex_side_length (PRIMARY OBJECTIVE - maximize)
    2. **combined_score**: inverse_side_length / 0.2537 (progress toward beating SOTA)
    3. **eval_time**: Execution time for full evaluation
  num_top_programs: 3
  num_diverse_programs: 2

# Logging
log_level: "INFO"