englund/openmdao-benchmarks

OpenMDAO Optimization Benchmarks

This dataset contains comprehensive benchmarking results from OpenMDAO optimization runs on standard test problems from the optimization literature.

Key Results

• Best Performer: SLSQP (63% success rate)
• Problem Difficulty: Rosenbrock (70% success) → Booth (67%) → Beale (36%) → Ackley/Rastrigin (0%)
• Comprehensive Metrics: Accuracy, efficiency, robustness scores included

Problems Included

1. Rosenbrock Function - Classic banana function (moderate difficulty)

   • Global optimum: [1.0, 1.0], minimum value: 0.0
   • Reference: Rosenbrock, H.H. (1960)

2. Beale Function - Multimodal valley function (moderate difficulty)

   • Global optimum: [3.0, 0.5], minimum value: 0.0
   • Reference: Beale, E.M.L. (1958)

3. Booth Function - Simple quadratic bowl (easy)

   • Global optimum: [1.0, 3.0], minimum value: 0.0
   • Reference: Standard test function

4. Rastrigin Function - Highly multimodal (hard)

   • Global optimum: [0.0, 0.0], minimum value: 0.0
   • Reference: Rastrigin, L.A. (1974)

5. Ackley Function - Multimodal with many local minima (hard)

   • Global optimum: [0.0, 0.0], minimum value: 0.0
   • Reference: Ackley, D.H. (1987)

Optimizers Benchmarked

• SLSQP: Sequential Least Squares Programming (gradient-based)

  • Success rate: 63%
  • Best for: Smooth, well-behaved functions

• COBYLA: Constrained Optimization BY Linear Approximations (derivative-free)

  • Success rate: 0% (on these test problems)
  • Better for: Constraint-heavy problems

• L-BFGS-B: Limited-memory BFGS with bounds (gradient-based)

  • Success rate: 41%
  • Good for: Large-scale optimization

Dataset Structure

Each record contains:

Basic Information

• run_id: Unique identifier
• optimizer: Algorithm used
• problem: Test function name
• dimension: Problem dimensionality

Results

• optimal_value: Final objective value
• optimal_point: Final design variables
• error_from_known: Distance from known global optimum
• success: Boolean convergence flag

Performance Metrics

• iterations: Number of optimization iterations
• function_evaluations: Objective function calls
• time_elapsed: Wall clock time (seconds)
• convergence_rate: Rate of convergence

Evaluation Scores

• accuracy_score: 1/(1 + error_from_known)
• efficiency_score: 1/(1 + iterations/50)
• robustness_score: Convergence stability
• overall_score: Weighted combination

Metadata

• convergence_history: Last 10 objective values
• problem_reference: Literature citation
• timestamp: When run was executed

Usage Examples

import json
import pandas as pd

# Load the dataset
with open('data.json', 'r') as f:
    data = json.load(f)

df = pd.DataFrame(data)

# Analyze success rates by optimizer
success_by_optimizer = df.groupby('optimizer')['success'].mean()
print("Success rates:", success_by_optimizer)

# Find best performing runs
best_runs = df.nlargest(10, 'overall_score')
print("Top 10 runs:")
print(best_runs[['optimizer', 'problem', 'overall_score']])

# Problem difficulty analysis
difficulty = df.groupby('problem')['success'].mean().sort_values(ascending=False)
print("Problem difficulty ranking:", difficulty)

Research Applications

This dataset enables several research directions:

1. Algorithm Selection: Predict best optimizer for given problem characteristics
2. Performance Modeling: Build models to predict optimization outcomes
3. Hyperparameter Tuning: Optimize algorithm parameters
4. Problem Classification: Categorize problems by difficulty
5. Convergence Analysis: Study optimization trajectories

Quality Assurance

• ✅ Literature-validated test problems
• ✅ Multiple runs for statistical significance
• ✅ Comprehensive evaluation metrics
• ✅ Real convergence data (not synthetic)
• ✅ Proper error analysis and success criteria

Citation

If you use this dataset, please cite:

@dataset{openmdao_benchmarks_2025,
  author = {OpenMDAO Development Team},
  title = {OpenMDAO Optimization Benchmarks},
  year = {2025},
  url = {https://huggingface.co/datasets/englund/openmdao-benchmarks},
  note = {Comprehensive benchmarking of optimization algorithms on standard test functions}
}

License

Apache 2.0 - Free for research and commercial use.

Contact

For questions or contributions, please open an issue on the dataset repository.

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This dataset was created using the OpenMDAO optimization framework and represents real benchmark results from optimization algorithm comparisons.