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Add Azure GPT and Gemini configs for alphaevolve_math_problems
- Add config_azure_gpt.yaml for all 16 problems (Azure OpenAI gpt-5) - Add config_gemini.yaml for all 16 problems (Gemini + Azure paradigm) - All configs use ${ENV_VAR} syntax for API keys (no hardcoded keys) - Add env var expansion support to config.py - Fix indentation in openai.py for Azure client - Add AutoEvolve features: paradigm breakthrough, error retry, adaptive search - Shell scripts with API keys excluded via .gitignore
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‎.gitignore‎

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# NFS temp files
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.nfs*
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# Shell scripts with API keys
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examples/alphaevolve_math_problems/run_*.sh

‎examples/alphaevolve_math_problems/circle_packing_rect/config_azure_gpt.yaml‎

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# Evolution settings
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max_iterations: 100
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checkpoint_interval: 10
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log_level: "INFO"
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# LLM configuration (Azure OpenAI)
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llm:
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primary_model: "gpt-5"
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api_base: "https://east-docetl.openai.azure.com/openai/deployments/gpt-4.1?api-version=2024-12-01-preview"
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api_key: "${OPENAI_API_KEY}"
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primary_model_weight: 1.0
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temperature: 0.7
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max_tokens: 32000
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timeout: 600
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# Database configuration (MAP-Elites algorithm)
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database:
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population_size: 40
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num_islands: 5
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migration_interval: 40
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feature_dimensions:
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- "score"
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- "complexity"
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# Adaptive exploration settings
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use_adaptive_search: true
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adaptive_window_size: 20
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adaptive_min_exploration: 0.1
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adaptive_max_exploration: 0.7
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# Softmax sampling for exploitation
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exploitation_temperature: 1.0
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# Stagnation detection and multi-child generation
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stagnation_threshold: 10
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stagnation_multi_child_count: 3
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sibling_context_limit: 5
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# ============================================
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# AutoEvolve Advanced Features (Sky Lab UC Berkeley)
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# ============================================
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# Paradigm Breakthrough
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enable_paradigm_breakthrough: true
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stagnation_window: 5
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stagnation_improvement_threshold: 0.01
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stagnation_paradigm_samples: 3
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paradigm_model: "gpt-5-mini"
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paradigm_api_base: "https://east-docetl.openai.azure.com/openai/deployments/gpt-4.1?api-version=2024-12-01-preview"
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paradigm_api_key: "${OPENAI_API_KEY}"
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# Error Retry
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enable_error_retry: true
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max_error_retries: 2
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evaluator:
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timeout: 360
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max_retries: 3
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# Prompt configuration
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prompt:
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system_message: |
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SETTING:
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You are an expert computational geometer and optimization specialist with deep expertise in circle packing problems, geometric optimization algorithms, and constraint satisfaction.
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Your mission is to evolve and optimize a constructor function that generates an optimal arrangement of exactly 21 non-overlapping circles within a rectangle, maximizing the sum of their radii.
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PROBLEM CONTEXT:
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- **Objective**: Create a function that returns optimal (x, y, radius) coordinates for 21 circles
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- **Benchmark**: Beat the AlphaEvolve state-of-the-art result of sum_radii = 2.3658321334167627
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- **Container**: Rectangle with perimeter = 4 (width + height = 2). You may choose optimal width/height ratio
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- **Constraints**:
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* All circles must be fully contained within rectangle boundaries
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* No circle overlaps (distance between centers ≥ sum of their radii)
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* Exactly 21 circles required
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* All radii must be positive
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PERFORMANCE METRICS:
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1. **sum_radii**: Total sum of all 21 circle radii (PRIMARY OBJECTIVE - maximize)
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2. **combined_score**: sum_radii / 2.3658321334167627 (progress toward beating benchmark)
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3. **eval_time**: Execution time in seconds (keep reasonable, prefer accuracy over speed)
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TECHNICAL REQUIREMENTS:
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- **Determinism**: Use fixed random seeds if employing stochastic methods for reproducibility
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- **Error handling**: Graceful handling of optimization failures or infeasible configurations
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- **Memory efficiency**: Avoid excessive memory allocation for distance matrix computations
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- **Scalability**: Design with potential extension to different circle counts in mind
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num_top_programs: 3
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num_diverse_programs: 2
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‎examples/alphaevolve_math_problems/circle_packing_rect/config_gemini.yaml‎

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# Evolution settings
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max_iterations: 100
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checkpoint_interval: 10
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log_level: "INFO"
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# LLM configuration (Gemini)
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llm:
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primary_model: "gemini-3-pro-preview"
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api_base: "https://generativelanguage.googleapis.com/v1beta/openai/"
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api_key: "${OPENAI_API_KEY}"
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primary_model_weight: 1.0
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temperature: 0.7
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max_tokens: 32000
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timeout: 600
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# Database configuration (MAP-Elites algorithm)
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database:
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population_size: 40
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num_islands: 5
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migration_interval: 40
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feature_dimensions:
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- "score"
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- "complexity"
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# Adaptive exploration settings
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use_adaptive_search: true
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adaptive_window_size: 20
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adaptive_min_exploration: 0.1
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adaptive_max_exploration: 0.7
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# Softmax sampling for exploitation
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exploitation_temperature: 1.0
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# Stagnation detection and multi-child generation
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stagnation_threshold: 10
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stagnation_multi_child_count: 3
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sibling_context_limit: 5
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# ============================================
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# AutoEvolve Advanced Features (Sky Lab UC Berkeley)
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# ============================================
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# Paradigm Breakthrough
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enable_paradigm_breakthrough: true
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stagnation_window: 5
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stagnation_improvement_threshold: 0.01
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stagnation_paradigm_samples: 3
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paradigm_model: "gpt-5-mini"
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paradigm_api_base: "https://east-docetl.openai.azure.com/openai/deployments/gpt-4.1?api-version=2024-12-01-preview"
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paradigm_api_key: "${PARADIGM_API_KEY}"
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# Error Retry
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enable_error_retry: true
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max_error_retries: 2
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evaluator:
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timeout: 360
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max_retries: 3
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# Prompt configuration
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prompt:
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system_message: |
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SETTING:
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You are an expert computational geometer and optimization specialist with deep expertise in circle packing problems, geometric optimization algorithms, and constraint satisfaction.
65+
Your mission is to evolve and optimize a constructor function that generates an optimal arrangement of exactly 21 non-overlapping circles within a rectangle, maximizing the sum of their radii.
66+
67+
PROBLEM CONTEXT:
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- **Objective**: Create a function that returns optimal (x, y, radius) coordinates for 21 circles
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- **Benchmark**: Beat the AlphaEvolve state-of-the-art result of sum_radii = 2.3658321334167627
70+
- **Container**: Rectangle with perimeter = 4 (width + height = 2). You may choose optimal width/height ratio
71+
- **Constraints**:
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* All circles must be fully contained within rectangle boundaries
73+
* No circle overlaps (distance between centers ≥ sum of their radii)
74+
* Exactly 21 circles required
75+
* All radii must be positive
76+
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PERFORMANCE METRICS:
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1. **sum_radii**: Total sum of all 21 circle radii (PRIMARY OBJECTIVE - maximize)
79+
2. **combined_score**: sum_radii / 2.3658321334167627 (progress toward beating benchmark)
80+
3. **eval_time**: Execution time in seconds (keep reasonable, prefer accuracy over speed)
81+
82+
TECHNICAL REQUIREMENTS:
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- **Determinism**: Use fixed random seeds if employing stochastic methods for reproducibility
84+
- **Error handling**: Graceful handling of optimization failures or infeasible configurations
85+
- **Memory efficiency**: Avoid excessive memory allocation for distance matrix computations
86+
- **Scalability**: Design with potential extension to different circle counts in mind
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num_top_programs: 3
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num_diverse_programs: 2
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‎examples/alphaevolve_math_problems/erdos_min_overlap/config_azure_gpt.yaml‎

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# Evolution settings
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max_iterations: 200
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checkpoint_interval: 10
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log_level: "INFO"
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# LLM configuration (Azure OpenAI)
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llm:
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primary_model: "gpt-5"
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api_base: "https://east-docetl.openai.azure.com/openai/deployments/gpt-4.1?api-version=2024-12-01-preview"
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api_key: "${OPENAI_API_KEY}"
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primary_model_weight: 1.0
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temperature: 0.7
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max_tokens: 32000
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timeout: 600
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# Database configuration (MAP-Elites algorithm)
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database:
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population_size: 40
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num_islands: 5
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migration_interval: 40
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feature_dimensions:
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- "score"
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- "complexity"
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# Adaptive exploration settings
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use_adaptive_search: true
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adaptive_window_size: 20
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adaptive_min_exploration: 0.1
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adaptive_max_exploration: 0.7
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# Softmax sampling for exploitation
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exploitation_temperature: 1.0
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# Stagnation detection and multi-child generation
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stagnation_threshold: 10
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stagnation_multi_child_count: 3
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sibling_context_limit: 5
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# ============================================
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# AutoEvolve Advanced Features (Sky Lab UC Berkeley)
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# ============================================
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# Paradigm Breakthrough
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enable_paradigm_breakthrough: true
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stagnation_window: 5
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stagnation_improvement_threshold: 0.01
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stagnation_paradigm_samples: 3
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paradigm_model: "gpt-5-mini"
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paradigm_api_base: "https://east-docetl.openai.azure.com/openai/deployments/gpt-4.1?api-version=2024-12-01-preview"
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paradigm_api_key: "${OPENAI_API_KEY}"
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# Error Retry
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enable_error_retry: true
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max_error_retries: 2
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evaluator:
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timeout: 360
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max_retries: 3
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# Prompt configuration
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prompt:
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system_message: |
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SETTING:
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You are an expert in harmonic analysis, numerical optimization, and AI-driven mathematical discovery.
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Your task is to evolve and optimize a Python script to find a better **upper bound** for the Erdős minimum overlap problem constant C₅.
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PROBLEM CONTEXT:
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Target: Find a step function h: [0, 2] → [0, 1] that **minimizes** the objective:
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max_k ∫ h(x)(1 - h(x+k)) dx
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This minimal value provides a tight upper bound for the constant C5.
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Current best known upper bound: C5 ≤ 0.38092303510845016
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Goal: Find a step function `h` that results in a C5 value lower than 0.38092303510845016.
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CONSTRAINTS:
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1. The function `h` must have values in the range [0, 1].
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2. The integral of h(x) over [0, 2] must be exactly 1.
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PERFORMANCE METRICS:
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- c5_bound: The bound found by the program.
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- combined_score: 0.38092303510845016 / c5_bound (The primary objective is to MAXIMIZE this value - a value > 1 means a new record).
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- n_points: number of points used in the discretization.
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- eval_time: evaluation time of the program.
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num_top_programs: 3
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num_diverse_programs: 2
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‎examples/alphaevolve_math_problems/erdos_min_overlap/config_gemini.yaml‎

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# Evolution settings
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max_iterations: 200
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checkpoint_interval: 10
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log_level: "INFO"
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# LLM configuration (Gemini)
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llm:
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primary_model: "gemini-3-pro-preview"
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api_base: "https://generativelanguage.googleapis.com/v1beta/openai/"
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api_key: "${OPENAI_API_KEY}"
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primary_model_weight: 1.0
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temperature: 0.7
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max_tokens: 32000
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timeout: 600
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# Database configuration (MAP-Elites algorithm)
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database:
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population_size: 40
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num_islands: 5
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migration_interval: 40
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feature_dimensions:
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- "score"
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- "complexity"
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# Adaptive exploration settings
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use_adaptive_search: true
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adaptive_window_size: 20
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adaptive_min_exploration: 0.1
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adaptive_max_exploration: 0.7
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# Softmax sampling for exploitation
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exploitation_temperature: 1.0
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# Stagnation detection and multi-child generation
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stagnation_threshold: 10
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stagnation_multi_child_count: 3
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sibling_context_limit: 5
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# ============================================
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# AutoEvolve Advanced Features (Sky Lab UC Berkeley)
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# ============================================
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# Paradigm Breakthrough
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enable_paradigm_breakthrough: true
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stagnation_window: 5
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stagnation_improvement_threshold: 0.01
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stagnation_paradigm_samples: 3
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paradigm_model: "gpt-5-mini"
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paradigm_api_base: "https://east-docetl.openai.azure.com/openai/deployments/gpt-4.1?api-version=2024-12-01-preview"
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paradigm_api_key: "${PARADIGM_API_KEY}"
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# Error Retry
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enable_error_retry: true
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max_error_retries: 2
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evaluator:
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timeout: 360
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max_retries: 3
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# Prompt configuration
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prompt:
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system_message: |
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SETTING:
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You are an expert in harmonic analysis, numerical optimization, and AI-driven mathematical discovery.
65+
Your task is to evolve and optimize a Python script to find a better **upper bound** for the Erdős minimum overlap problem constant C₅.
66+
67+
PROBLEM CONTEXT:
68+
Target: Find a step function h: [0, 2] → [0, 1] that **minimizes** the objective:
69+
max_k ∫ h(x)(1 - h(x+k)) dx
70+
71+
This minimal value provides a tight upper bound for the constant C5.
72+
73+
Current best known upper bound: C5 ≤ 0.38092303510845016
74+
Goal: Find a step function `h` that results in a C5 value lower than 0.38092303510845016.
75+
76+
CONSTRAINTS:
77+
1. The function `h` must have values in the range [0, 1].
78+
2. The integral of h(x) over [0, 2] must be exactly 1.
79+
80+
PERFORMANCE METRICS:
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- c5_bound: The bound found by the program.
82+
- combined_score: 0.38092303510845016 / c5_bound (The primary objective is to MAXIMIZE this value - a value > 1 means a new record).
83+
- n_points: number of points used in the discretization.
84+
- eval_time: evaluation time of the program.
85+
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num_top_programs: 3
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num_diverse_programs: 2
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