---
title: OpenMDAO Optimization Benchmarks
tags:
- optimization
- engineering
- openmdao
- benchmarking
- scipy
license: apache-2.0
task_categories:
- tabular-regression
- tabular-classification
size_categories:
- n<1K
---

# OpenMDAO Optimization Benchmarks

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

## Dataset Description

- **Total Samples**: 55
- **Problems**: 5 literature-validated test functions (Rosenbrock, Beale, Booth, Rastrigin, Ackley)
- **Optimizers**: 3 algorithms (SLSQP, COBYLA, L-BFGS-B)
- **Multiple Runs**: 3-5 runs per optimizer-problem combination
- **Created**: 2025-08-24

## 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

```python
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:

```bibtex
@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.*