PyBenchFCN 1.0.1

A library for optimization benchmark functions in python

# PyBenchFCN #

Introduction

This library is a python implementation for the MatLab package BenchmarkFcns Toolbox.

You can simply install with command pip install PyBenchFCN.

• Pre-request: numpy

How to Use

To use the package, one may see the sample code in Factory.py in the repository, or follow the script below.

import numpy as np

# import single objective problems from PyBenchFCN
from PyBenchFCN import SingleObjectiveProblem as SOP

n_var = 10                                      # dimension of problem
n_pop = 3                                       # size of population

problem = SOP.ackleyfcn(n_var)                  # Ackley problem

'''same function as the code above
from PyBenchFCN import Factory
problem = Factory.set_sop("f1", n_var)
'''

print( np.round(problem.optimalF, 5) )          # show rounded optimal value

xl, xu = problem.boundaries                     # bound of problem

x = np.random.uniform(xl, xu, n_var)            # initialize a solution
print( problem.f(x) )                           # show fitness value

X = np.random.uniform( xl, xu, (n_pop, n_var) ) # initialize a population
print( problem.F(X) )                           # show fitness values

List of Functions

Totally, 61 functions are implemented. The plot of 2D versions of 59 problems are provided. Please check the homepage of BenchmarkFcns Toolbox for the further documentation.

• Ackley Function >>

n-dim differentiable non-convex multimodal separable

• Ackley N.2 Function >>

2-dim differentiable convex unimodal non-separable

• Ackley N.3 Function >>

2-dim differentiable non-convex multimodal non-separable

• Adjiman Function >>

2-dim differentiable non-convex multimodal non-separable

• Alpine N.1 Function >>

n-dim differentiable non-convex multimodal non-separable

• Alpine N.2 Function >>

n-dim differentiable non-convex multimodal non-separable

• Bartelsconn Function >>

2-dim non-differentiable non-convex multimodal non-separable

• Beale Function >>

2-dim differentiable non-convex multimodal non-separable

• Bird Function >>

2-dim differentiable non-convex multimodal non-separable

• Bohachevsky N.1 Function >>

2-dim differentiable non-convex multimodal non-separable

• Bohachevsky N.2 Function >>

2-dim differentiable non-convex multimodal non-separable

• Booth Function >>

2-dim differentiable convex unimodal non-separable

• Brent Function >>

2-dim differentiable convex unimodal non-separable

• BrownFunction >>

n-dim differentiable convex unimodal non-separable

• Bukin N.6 Function >>

2-dim non-differentiable convex multimodal non-separable

• Cross-in-Tray Function >>

2-dim non-differentiable non-convex multimodal non-separable

• Deckkers-Aarts Function >>

2-dim differentiable non-convex multimodal non-separable

• Dropwave Function >>

2-dim differentiable non-convex multimodal non-separable

• Easom Function >>

2-dim differentiable non-convex multimodal separable

• Egg Crate Function >>

2-dim differentiable non-convex multimodal separable

• Eggholder Function >>

2-dim differentiable non-convex multimodal non-separable

• Exponential Function >>

n-dim differentiable convex unimodal non-separable

• Goldstein-Price Function >>

2-dim differentiable non-convex multimodal non-separable

• Gramacy & Lee Function >>

1-dim differentiable non-convex multimodal separable

• Griewank Function >>

n-dim differentiable non-convex multimodal non-separable

• Happy Cat Function >>

n-dim differentiable non-convex multimodal non-separable

• Himmelblau Function >>

2-dim differentiable non-convex multimodal non-separable

• Holder-Table Function >>

2-dim non-differentiable non-convex multimodal non-separable

• Keane Function >>

2-dim differentiable non-convex multimodal non-separable

• Leon Function >>

2-dim differentiable non-convex multimodal non-separable

• Levi N.13 Function >>

2-dim differentiable non-convex multimodal non-separable

• Matyas Function >>

2-dim differentiable convex unimodal non-separable

• McCormick Function >>

2-dim differentiable convex multimodal non-separable

• Periodic Function >>

n-dim differentiable non-convex multimodal non-separable

• Picheny Function >>

2-dim differentiable non-convex multimodal non-separable

• Powell Sum Function >>

n-dim differentiable convex unimodal separable

• Qing Function >>

n-dim differentiable non-convex multimodal non-separable

• Quatric Function >>

n-dim differentiable non-convex multimodal separable random

• RastriginFunction >>

n-dim differentiable non-convex multimodal separable

• Ridge Function >>

n-dim differentiable non-convex multimodal non-separable

• Rosenbrock Function >>

n-dim differentiable convex unimodal non-separable

• Salomon Function >>

n-dim differentiable non-convex multimodal non-separable

• Schaffer N.1 Function >>

2-dim differentiable non-convex multimodal non-separable

• Schaffer N.2 Function >>

2-dim differentiable non-convex multimodal non-separable

• Schaffer N.3 Function >>

2-dim differentiable non-convex multimodal non-separable

• Schaffer N.4 Function >>

2-dim differentiable non-convex multimodal non-separable

• Schwefel 2.20 Function >>

n-dim non-differentiable convex unimodal separable

• Schwefel 2.21 Function >>

n-dim non-differentiable convex unimodal separable

• Schwefel 2.22 Function >>

n-dim non-differentiable convex unimodal non-separable

• Schwefel 2.23 Function >>

n-dim differentiable convex unimodal separable

• Schwefel Function >>

n-dim differentiable non-convex multimodal separable

• Sphere Function >>

n-dim differentiable convex unimodal separable

• Styblinski-Tang Function >>

n-dim differentiable non-convex multimodal separable

• Sum Squares Function >>

n-dim differentiable convex unimodal separable

• Three-Hump Camel Function >>

2-dim differentiable non-convex multimodal non-separable

• Wolfe Function >>

3-dim non-differentiable non-convex multimodal separable

• Xin-She Yang N.1 Function >>

n-dim non-differentiable non-convex multimodal separable random

• Xin-She Yang N.2 Function >>

n-dim non-differentiable non-convex multimodal non-separable

• Xin-She Yang N.3 Function >>

n-dim differentiable non-convex multimodal non-separable

• Xin-She Yang N.4 Function >>

n-dim non-differentiable non-convex multimodal non-separable

• Zakharov Function >>

n-dim differentiable convex unimodal non-separable

Acknowledgement

PyBenchFCN is maintained by Y1fanHE. The author of this repostory is very grateful to Mr. Mazhar Ansari Ardeh, who implemented the MatLab package BenchFCNs Toolbox.

• If you find any mistakes, please report at a new issue.
• If you want to help me implement more benchmarks (discrete optimization, multi-objective optimization), please contact at [e-mail].