test_functions.py

from math import sqrt, pi
from numpy import sin, cos, exp, asarray

class BOHACHEVSKY:
    minimum = 0.0
    minima = (0, 0)
    x1_bounds = (-10, 10)
    x2_bounds = (-10, 10)

    def z(x, y):
        return x**2.0 + 2*(y**2.0) - 0.3*cos(3*pi*x) -0.4*cos(4*pi*y) + 0.7

    def df(x, y):
        return asarray([
            2*x + 0.9*pi*sin(3*pi*x),
            4*y + 1.6*pi*sin(4*pi*y)
        ])

class EASOM:
    minimum = -1
    minima = (pi, pi)
    x1_bounds = (1.8, 4.5)
    x2_bounds = (1.8, 4.5)

    def z(x, y):
        t1 = cos(x)
        t2 = cos(y)
        t3 = exp(-1*((x-pi)**2 + (y-pi)**2))
        return -1*t1*t2*t3

    def df(x, y):
        t2 = exp(-1*((x-pi)**2 + (y-pi)**2))
        return asarray([
            cos(y)*(cos(x)*t2*2*(x-pi) + t2*sin(x)),
            cos(x)*(cos(y)*t2*2*(y-pi) + t2*sin(y)),
        ])

class MCCORMICK:
    minimum = -1.9133
    minima = (-0.54719, -1.54719)
    x1_bounds = (-1.5, 4)
    x2_bounds = (-3, 4)

    def z(x, y):
        return sin(x+y) + (x-y)**2 - 1.5*x + 2.5*y + 1

    def df(x, y):
        return asarray([
            cos(x+y) + 2*(x-y) - 1.5,
            cos(x+y) - 2*(x-y) + 2.5,
        ])

class THREEHUMP_CAMEL:
    minimum = 0
    minima = (0, 0)
    x1_bounds = (-2, 2)
    x2_bounds = (-2, 2)

    def z(x, y):
        return 2*(x**2) - 1.05*(x**4) + (1/6)*(x**6) + x*y + y**2

    def df(x, y):
        return asarray([
            4*x - 1.05*4*(x**3) + x**5 + y,
            x + 2*y,
        ])

class SPHERE:
    minimum = 0
    minima = (0, 0)
    x1_bounds = (-5.12, 5.12)
    x2_bounds = (-5.12, 5.12)

    def z(x, y):
        return x**2 + y**2

    def df(x, y):
        return asarray([
            2*x,
            2*y,
        ])