pyOptiGTest

A Python library of 282+ classical optimization test functions for benchmarking optimization and metaheuristic algorithms. Includes unconstrained, constrained, and multi-objective problems. All functions support vectorized NumPy evaluation and analytical gradient computation.

Features

• 282 test functions — Ackley, Beale, Branin, Rosenbrock, Rastrigin, Griewank, Schwefel, Sphere, and many more
• Analytical gradients — every function provides exact gradient computation via the grad parameter
• Vectorized evaluation — efficient batch evaluation using NumPy arrays
• Known global optima — each problem includes reference global minimum values and locations
• Variable dimensionality — many functions support arbitrary dimensions; fixed-dimension functions are also included
• Problem types — unconstrained, constrained, and multi-objective problems
• Lightweight — only depends on NumPy

Installation

pip install pyOptiGTest

Or install from source:

git clone https://github.com/luclaurent/optigtest.git
cd optigtest
pip install .

For testing:

pip install -e ".[test]"

and run

pytest 

or

pytest --pyargs pyOptiGTest

Quick Start

Using the optigtest class

import pyOptiGTest as PO
import numpy as np

# Load a test problem
obj = PO.optigtest('Ackley1', dim=2)

# Get design space bounds
xmin = obj.getXmin()
xmax = obj.getXmax()

# Create evaluation points
X = np.random.uniform(xmin, xmax, size=(100, 2))

# Evaluate the objective function
Z = obj.evalObj(X)

# Access known global minimum
print("Global minimum value:", obj.getGlobZmin())
print("Global minimum location:", obj.getGlobXmin())

Calling functions directly

Each function can also be called directly from the functions submodule:

from pyOptiGTest.functions.funRosenbrock import funRosenbrock
import numpy as np

X = np.array([[1.0, 1.0], [0.0, 0.0], [2.0, 3.0]])

# Function values only
Z = funRosenbrock(X)

# Function values and gradients
Z, dZ = funRosenbrock(X, grad=True)
# Z shape:  (3,)
# dZ shape: (3, 2)

Visualizing a test function

import pyOptiGTest as PO
import numpy as np
import matplotlib.pyplot as plt

obj = PO.optigtest('Ackley1', dim=2)

# Build evaluation grid
x = np.linspace(obj.getXmin()[0], obj.getXmax()[0], 200)
y = np.linspace(obj.getXmin()[1], obj.getXmax()[1], 200)
Xm, Ym = np.meshgrid(x, y)
XX = np.column_stack([Xm.ravel(), Ym.ravel()])

Z = obj.evalObj(XX)
Zm = Z.reshape(Xm.shape)

# Contour plot
plt.contourf(Xm, Ym, Zm, levels=50, cmap='viridis')
plt.colorbar()
plt.title('Ackley1')
plt.xlabel('$x_1$')
plt.ylabel('$x_2$')
plt.show()

Function Interface

All test functions follow a consistent interface:

def funName(X, grad=False):
    """
    Parameters
    ----------
    X : numpy.ndarray
        Input array of shape (n_samples, n_dimensions).
    grad : bool, optional
        If True, also compute and return analytical gradients.

    Returns
    -------
    p : numpy.ndarray
        Function values, shape (n_samples,).
    dp : numpy.ndarray (only if grad=True)
        Gradient array, shape (n_samples, n_dimensions).
    """

optigtest Class API

Method	Description
optigtest(namePb, dim=None, X=None)	Create a problem instance
evalObj(X, grad=False, num=None)	Evaluate objective function(s) at points X
evalCons(X, grad=False, num=None)	Evaluate constraint function(s) at points X
checkCons(X)	Check constraint feasibility (returns boolean array)
getDesignSpace()	Get bounds array of shape (dim, 2)
getXmin() / getXmax()	Get lower / upper bounds
getGlobZmin() / getGlobXmin()	Get global minimum value / location
getNbObj() / getNbCons()	Get number of objectives / constraints
getTypePb()	Get problem type (Unconstrained, Constrained, MultiObjective)
setDim(dim)	Change problem dimensionality
listPb(pbType=None)	List all available problems (optionally filtered by type)
showDetails()	Print problem details

Constrained Problems

5 constrained test problems with analytical constraints:

Problem	Constraints	Known Minimum
RosenbrockCubicLine	2 (<=)	0.0
RosenbrockDisk	1 (<=)	0.0
BirdDisk	1 (<)	-106.76
Townsend	1 (<)	-2.024
Simionescu	1 (<=)	-0.072

from pyOptiGTest.pyOptiGTest import optigtest
import numpy as np

pb = optigtest("Simionescu")
X = np.array([[0.5, 0.5]])
obj = pb.evalObj(X)
cons = pb.evalCons(X)
feasible = pb.checkCons(X)

Multi-Objective Problems

17 multi-objective test problems (BinhKorn, ChakongHaimes, FonsecaFleming, Kursawe, ZDT1–6, Viennet, etc.):

from pyOptiGTest.pyOptiGTest import optigtest
import numpy as np

pb = optigtest("BinhKorn")
X = np.array([[1.0, 1.0]])
results = pb.evalObj(X)  # returns [f1, f2]
feasible = pb.checkCons(X)

See examples.md for detailed usage examples.

Available Functions (selection)

Below is a non-exhaustive list of included test functions (almost complete list can be found here):

Function	Dimensions	Global Minimum
Ackley (1–4)	any	0
Alpine (1–2)	any	0
Beale	2	0
Booth	2	0
Branin (1–2)	2	0
Bukin (01–20)	2	varies
Camelback (3-hump, 6-hump)	2	0
Colville	4	0
Cross-in-Tray	2	−2.0626
Dixon-Price	any	0
Drop-Wave	2	−1
Easom	2	−1
Egg Holder	2	−959.6407
Goldstein-Price	2	3
Griewank	any	0
Hartmann (3, 6)	3, 6	varies
Levy	any	0
Michalewicz	any	varies
Rastrigin	any	0
Rosenbrock	any	0
Schwefel	any	0
Sphere	any	0
Styblinski-Tang	any	varies
... and 250+ more

Running Tests

# Run all tests
pytest tests/

# Run with coverage
pytest --cov=pyOptiGTest --cov-report=term-missing tests/

Project Structure

pyOptiGTest/
├── pyOptiGTest/
│   ├── __init__.py
│   ├── pyOptiGTest.py        # Main optigtest class
│   ├── dbProblems.py          # Problem database
│   ├── dbFunctions.py         # Function registry
│   ├── dbConstrained.py       # Constrained problem definitions
│   ├── dbUnconstrained.py     # Unconstrained problem definitions
│   ├── dbMultiObj.py          # Multi-objective problem definitions
│   └── functions/             # 282 individual test functions
│       ├── funAckley2.py
│       ├── funBeale.py
│       ├── funRosenbrock.py
│       └── ...
├── tests/                     # Test suite
├── pyproject.toml
├── LICENSE
└── README.md

MATLAB/Octave version

A similar MATLAB/Octave toolbox can be found here.

References

This toolbox is inspired by many existing codes and papers

• AMPGO (and github repository)
• E. P. Adorio and U. P. Diliman. MVF - Multivariate Test Functions Library in C for Unconstrained Global Optimization.
• P. N. Suganthan, N. Hansen, J. J. Liang, K. Deb, Y. P. Chen, A. Auger and S. Tiwari. Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. KanGAL report, 2005.Link
• V. Bicik, Continuous optimization algorithms, Master thesis, Czech Technical University in Prague, 2010 Link
• M. Jamil and Xin-She Yang, A literature survey of benchmark functions for global optimization problems, Int. Journal of Mathematical Modelling and Numerical Optimisation, Vol. 4, No. 2, pp. 150--194 (2013) doi: 10.1504/IJMMNO.2013.055204 arXiv: 1308.4008 PDF
• M. Molga, C. Smutnick. Test functions for optimization needs, Comput. Inform. Sci., 1-43, 2005. Link
• M. M. Ali, C. Khompatraporn and Z. B. Zabinsky, Journal of Global Optimisation (2005) 31:635. doi: 10.1007/s10898-004-9972-2 PDF
• Virtual Library of Simulation Experiments
• Wikipedia. Test functions for optimization, 2018. [Online; accessed 13-May-2018]

License

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

Author

Luc Laurent — luc.laurent@lecnam.net

Links

• Repository: https://github.com/luclaurent/pyoptigtest
• Issues: https://github.com/luclaurent/pyoptigtest/issues