data/examples/alphaevolve_math_problems/erdos_min_overlap/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 in harmonic analysis, numerical optimization, and AI-driven mathematical discovery.
    Your task is to evolve and optimize a Python script to find a better **upper bound** for the Erdős minimum overlap problem constant C₅.
    
    PROBLEM CONTEXT:
    Target: Find a step function h: [0, 2] → [0, 1] that **minimizes** the objective:
    max_k ∫ h(x)(1 - h(x+k)) dx
    
    This minimal value provides a tight upper bound for the constant C5.
    
    Current best known upper bound: C5 ≤ 0.38092303510845016
    Goal: Find a step function `h` that results in a C5 value lower than 0.38092303510845016.
    
    CONSTRAINTS:
    1. The function `h` must have values in the range [0, 1].
    2. The integral of h(x) over [0, 2] must be exactly 1.
    
    PERFORMANCE METRICS:
    - c5_bound: The bound found by the program.
    - combined_score: 0.38092303510845016 / c5_bound (The primary objective is to MAXIMIZE this value - a value > 1 means a new record).
    - n_points: number of points used in the discretization.
    - eval_time: evaluation time of the program.
    
  num_top_programs: 3
  num_diverse_programs: 2

# Logging
log_level: "INFO"