optimization-benchmarks 0.1.0

A comprehensive collection of mathematical benchmark functions for testing optimization algorithms

optimization-benchmarks

A comprehensive Python package providing 50+ classical mathematical benchmark functions for testing and evaluating optimization algorithms.

🎯 Features

• 50+ Standard Benchmark Functions: Including Ackley, Rastrigin, Rosenbrock, Griewank, and many more
• Vectorized NumPy Implementation: Fast and efficient computation
• Well-Documented: Each function includes domain constraints and global minima
• Type Hints: Full type annotation support
• Command-Line Interface: Evaluate functions directly from the terminal
• Zero Dependencies: Only requires NumPy
• Academic Citations: Properly cited mathematical formulations

📦 Installation

From PyPI

pip install optimization-benchmarks

From Source

git clone https://github.com/ak-rahul/optimization-benchmarks.git
cd optimization-benchmarks
pip install -e .

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🚀 Quick Start

import numpy as np
from optimization_benchmarks import ackley, rastrigin, rosenbrock

x = np.zeros(5)
result = ackley(x)
print(f"Ackley(0) = {result}") # Should be close to 0

x = np.ones(10)
result = rosenbrock(x)
print(f"Rosenbrock(1) = {result}") # Should be 0

x = np.random.randn(5)
result = rastrigin(x)
print(f"Rastrigin(x) = {result}")

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📊 Usage Examples

Benchmarking an Optimization Algorithm

import numpy as np
from optimization_benchmarks import ackley, rastrigin, sphere

def my_optimizer(func, bounds, max_iter=1000):
"""Your optimization algorithm here."""
# ... implementation ...
pass

test_functions = {
'Sphere': (sphere, [(-5.12, 5.12)] * 10),
'Ackley': (ackley, [(-32, 32)] * 10),
'Rastrigin': (rastrigin, [(-5.12, 5.12)] * 10),
}

for name, (func, bounds) in test_functions.items():
best_x, best_f = my_optimizer(func, bounds)
print(f"{name}: f(x*) = {best_f}")

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🎮 Command-Line Interface

The package includes a CLI for quick function evaluation:

List all available functions

optbench --list

Get function information

optbench --info ackley

Evaluate a function

optbench --function rastrigin --values 0 0 0 0 0

Batch evaluation from CSV

optbench --function sphere --input points.csv --output results.json

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📚 Available Functions

Multimodal Functions

• ackley - Multiple local minima with deep global minimum
• rastrigin - Highly multimodal with regular structure
• griewank - Multimodal with product term
• schwefel2_26 - Deceptive with distant global minimum
• levy - Multimodal with sharp global minimum
• michalewicz - Steep ridges and valleys

Unimodal Functions

• sphere - Simple convex quadratic
• rosenbrock - Narrow curved valley
• sum_squares - Weighted sphere function
• hyperellipsoid - Axis-parallel ellipsoid

2D Test Functions

• beale - Narrow valley
• booth - Simple quadratic
• matyas - Plate-like surface
• himmelblau - Four identical local minima
• goldstein_price - Multiple local minima
• easom - Flat surface with narrow peak

Special Functions

• branin - Three global minima
• camel3 - Three-hump camel function
• camel6 - Six-hump camel function
• kowalik - Parameter estimation problem
• langerman - Multimodal test function

And 30+ more functions!

🔬 Function Properties

Each function includes:

• Domain: Valid input ranges
• Dimension: Number of variables (n for arbitrary dimensions)
• Global Minimum: Known optimal value and location
• Mathematical Formula: Documented in docstrings

🎓 Academic Use

This package is perfect for:

• Algorithm Development: Test new optimization algorithms
• Comparative Studies: Benchmark against existing methods
• Academic Research: Reproduce published results
• Teaching: Demonstrate optimization concepts
• Thesis Projects: Comprehensive evaluation suite

Citing This Package

If you use this package in academic work, please cite:

@software{optimization_benchmarks,
author = {AK Rahul},
title = {optimization-benchmarks: Benchmark Functions for Optimization Algorithms},
year = {2025},
publisher = {PyPI},
url = {https://github.com/ak-rahul/optimization-benchmarks}
}

Mathematical Formulations Based On

[1] Adorio, E. P. (2005). MVF - Multivariate Test Functions Library in C.
[2] Surjanovic, S. & Bingham, D. (2013). Virtual Library of Simulation Experiments.
[3] Jamil, M., & Yang, X. S. (2013). A literature survey of benchmark functions for global optimization problems.

🤝 Contributing

Contributions are welcome! Please see CONTRIBUTING.md for guidelines.

Quick Contribution Guide

1. Fork the repository
2. Create your feature branch (`git checkout -b feature/new-function`)
3. Add your function to `functions.py`
4. Add tests to `tests/test_functions.py`
5. Run tests: `pytest`
6. Submit a pull request

📄 License

This project is licensed under the MIT License - see the LICENSE file for details.

🙏 Acknowledgments

• Mathematical formulations based on the MVF C library by E.P. Adorio
• Function definitions from Virtual Library of Simulation Experiments
• Inspired by the optimization research community

📞 Support

• Issues: GitHub Issues
• Discussions: GitHub Discussions

🔗 Related Projects

• SciPy Optimize - Optimization algorithms
• PyGMO - Massively parallel optimization
• DEAP - Evolutionary algorithms

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Made with ❤️ for the optimization community