data/examples/alphaevolve_math_problems/kissing_number/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 high-dimensional geometry, lattice theory, and combinatorial optimization, specializing in sphere packing and coding theory problems.
    Your task is to devise a computational strategy and generate a set of points that provides a new state-of-the-art lower bound for a specific variant of the kissing number problem in 11 dimensions.

    PROBLEM CONTEXT:
    Your goal is to find the largest possible set of points $S \subset \mathbb{Z}^{11}$ (points with 11 integer coordinates) that satisfies the following geometric constraint: the maximum L2 norm of any point from the origin must be less than or equal to the minimum pairwise L2 distance between any two distinct points in the set.

    - **Target**: Beat the AlphaEvolve benchmark of **num_points = 593**.
    - **Constraint**: For the set of points $S = \{p_1, p_2, ..., p_k\}$ where $p_i \in \mathbb{Z}^{11}$:
      $$\max_{i} \|p_i\|_2 \le \min_{i \neq j} \|p_i - p_j\|_2$$
    - **Objective**: Maximize the cardinality of the set, $k = |S|$.

    PERFORMANCE METRICS:
    1.  **num_points**: The number of points in the final set $S$. **This is the primary objective to maximize.**
    2.  **combined_score**: Your `num_points` / 593. The goal is to achieve a ratio > 1.0.
    3.  **eval_time**: The total wall-clock time in seconds to generate the solution.

    TECHNICAL REQUIREMENTS:
    - **Determinism & Reproducibility**: Your solution must be fully reproducible. If you use any stochastic algorithms (like simulated annealing or genetic algorithms), you **must use a fixed random seed** (e.g., `numpy.random.seed(42)`).
    - **Efficiency**: While secondary to correctness and the number of points, your algorithm should be reasonably efficient. Avoid brute-force searches over the entire $\mathbb{Z}^{11}$ lattice, which is computationally infeasible.

  num_top_programs: 3
  num_diverse_programs: 2

# Logging
log_level: "INFO"