landscapes 0.0.7

A Python library of standardized optimization test functions

Installation

There are a couple ways in which you can use this library. The first and probably the easiest is by using pip and PyPi:

pip install landscapes

You can also install directly from this git repo:

pip install git+https://github.com/nathanrooy/landscapes

Lastly, you can always clone/download this repo and use as is.

wget https://github.com/nathanrooy/landscapes/archive/master.zip
unzip master.zip
cd landscapes-master

Usage

As a simple example, let's use the Nelder-Mead method via SciPy to minimize the sphere function. We'll start off by importing the sphere function from Landscapes and the minimize method from SciPy.

>>> from landscapes.single_objective import sphere
>>> from scipy.optimize import minimize

Next, we'll call the minimize method using a starting location of [5,5].

>>> minimize(sphere, x0=[5,5], method='Nelder-Mead')

The output of which should look close to this:

 final_simplex: (array([[-3.33051318e-05, -1.93825710e-05],
       [ 4.24925225e-05,  1.37129516e-05],
       [ 3.09383247e-05, -4.04797876e-05]]), array([1.48491586e-09, 1.99365951e-09, 2.59579314e-09]))
           fun: 1.4849158640215086e-09
       message: 'Optimization terminated successfully.'
          nfev: 80
           nit: 44
        status: 0
       success: True
             x: array([-3.33051318e-05, -1.93825710e-05])

Function Reference - Single Objective

Ackley function

from landscapes.single_objective import ackley

global minimum	bounds	usage
f(x=0,y=0)=0	-5.12 <= x, y <= 5.12	ackley([x,y])

Beale function

from landscapes.single_objective import beale

global minimum	bounds	usage
f(x=3, y=0.5) = 0	-4.5 <= x, y <= 4.5	beale([x,y])

Booth function

from landscapes.single_objective import booth

global minimum	bounds	usage
f(x=1, y=3) = 0	-10 <= x, y <= 10	booth([x,y])

Bukin N.6 function

from landscapes.single_objective import bukin_n6

global minimum	bounds	usage
f(x=-10, y=1) = 0	-15 <= x <= -5 -3 <= y <= 3	bukin_n6([x,y])

Cross-in-tray function

from landscapes.single_objective import cross_in_tray

global minimum(s)	bounds	usage
f(x=1.34941, y=-1.34941) = -2.06261 f(x=1.34941, y=1.34941) = -2.06261 f(x=-1.34941, y=1.34941) = -2.06261 f(x=-1.34941, y=-1.34941) = -2.06261	-10 <= x, y <= 10	cross_in_tray([x,y])

Easom function

from landscapes.single_objective import easom

global minimum	bounds	usage
f(x=pi, y=pi) = -1	-100 <= x, y <= 100	easom([x,y])

Eggholder function

from landscapes.single_objective import eggholder

global minimum	bounds	usage
f(x=512, y=404.2319) = -959.6407	-512 <= x, y <= 512	eggholder([x,y])

Goldstein–Price function

from landscapes.single_objective import goldstein_price

global minimum	bounds	usage
f(x=0, y=-1) = 3	-2 <= x, y <= 2	goldstein_price([x,y])

Himmelblau's function

from landscapes.single_objective import himmelblau

global minimum(s)	bounds	usage
f(x=3.0, y=2.0) = 0.0 f(x=-2.805118, y=3.131312) = 0.0 f(x=-3.779310, y=-3.283186) = 0.0 f(x=3.584428, y=-1.848126) = 0.0	-5 <= x, y <= 5	himmelblau([x,y])

Hölder table function

from landscapes.single_objective import holder_table

global minimum(s)	bounds	usage
f(x=8.05502, y=9.66459) = -19.2085 f(x=-8.05502, y=9.66459) = -19.2085 f(x=8.05502, y=-9.66459) = -19.2085 f(x=-8.05502, y=-9.66459) = -19.2085	-10 <= x, y <= 10	holder_table([x,y])

Lévi function N.13

from landscapes.single_objective import levi_n13

global minimum	bounds	usage
f(x=1, y=1) = 0	-10 <= x, y <= 10	levi_n13([x,y])

Matyas function

from landscapes.single_objective import mccormick

global minimum	bounds	usage
f(x=0, y=0) = 0	-10 <= x, y <= 10	matyas([x,y])

McCormick function

from landscapes.single_objective import mccormick

global minimum	bounds	usage
f(x=-0.54719, y=-1.54719) = -1.9133	-1.5 <= x <= 4 -3 <= y <= 4	mccormick([x,y])

Rastrigin function

from landscapes.single_objective import rastrigin

global minimum	bounds	usage
f([0,...,0]) = 0	-5.12 <= x_i <= 5.12	rastrigin([x_1,...,x_n])

Rosenbrock function

from landscapes.single_objective import rosenbrock

global minimum	bounds	usage
f([1,...,1]) = 0	-inf <= x_i <= inf	rosenbrock([x_1,...,x_n])

Schaffer function N.2

from landscapes.single_objective import schaffer_n2

global minimum	bounds	usage
f(x=0, y=0) = 0	-100 <= x, y <= 100	schaffer_n2([x,y])

Schaffer function N.4

from landscapes.single_objective import schaffer_n4

global minimum	bounds	usage
f(x=0, y=1.25313) = 0.292579 f(x=0, y=-1.25313) = 0.292579	-100 <= x, y <= 100	schaffer_n4([x,y])

Sphere function

from landscapes.single_objective import sphere

global minimum	bounds	usage
f([0,...,0]) = 0	-inf <= x_i <= inf	sphere([x_1,...x_n])

Styblinski–Tang function

from landscapes.single_objective import styblinski_tang

global minimum	bounds	usage
-39.16617n < f([-2.903534,...,-2.903534]) < -39.16616n	-5 <= x_i <= 5	styblinski_tang([x_1,...x_n])

Three-hump camel function

from landscapes.single_objective import three_hump_camel

global minimum	bounds	usage
-f(x=0, y=0) = 0	-5 <= x_i <= 5	three_hump_camel([x,y])