pyGKLS

pyGKLS is a Python wrapper for the GKLS generator of global optimization test functions (Giavano et al., 2003). It uses the original C implementation of the generator and provides a Python interface using Cython to generate the test functions. pyGKLS encompass a C++ class that wraps the original C implementation to provide a more user-friendly interface that can be used in C++ projects (see src/example.cc) or Python projects (see test.py).

Random number generator

The original GKLS generator uses a random number generator based introduced by Knuth in his book "The Art of Computer Programming". pyGKLS uses the Mersenne Twister random number generator from the C++ standard library to generate random numbers.

Installation

To install pyGKLS, one needs to have Python 3.12 or later.

Linux (x86_64) or macOS (arm64)

Run the following command:

pip install gkls

Other platforms

You need to build the package from source. CMake (3.30 or later) and a C++ compiler that supports C++23 are required. Run the following command:

pip install gkls

Usage

The Python interface is simple and easy to use. Here is an example of how to generate a GKLS function:

from gkls import GKLS

# Create an instance of the GKLS class
gkls = GKLS(2, 2, [-1, 1], -1)

x = [0.5, 0.5]

print(f"D_f = {gkls.get_d_f(x)}")
print(f"D2_f = {gkls.get_d2_f(x)}")
print(f"ND_f = {gkls.get_nd_f(x)}")

print(f"D_grad = {gkls.get_d_grad(x)}")
print(f"D2_grad = {gkls.get_d2_grad(x)}")

print(f"D2_hessian = {gkls.get_d2_hess(x)}")

One output of the above code (stochastic) could be:

D_f = 2.0314828290164897
D2_f = 2.0314828290164897
ND_f = 2.0314828290164897
D_grad = [1.7408628759925895, 2.2572832704507357]
D2_grad = [1.7408628759925895, 2.2572832704507357]
D2_hessian = [[2.0, 0.0], [0.0, 2.0]]

Arguments can be passed to the GKLS constructor function to control the properties of the generated function. The constructor has the following signature:

GKLS(
  dim : int, # dimension of the function
  num_minima : int, # number of local minima
  domain : List[float], # domain of the function (i.e. [domain_low, domain_high])
  global_min : float # global minimum value
  global_dist=None : float, # distance from the paraboloid minimizer to the global minimizer
  global_radius=None : float, # radius of the global minimizer attraction region
  deterministic=False : bool, # if True, the generation of the function is deterministic
)