cbx.objectives.Rastrigin

class cbx.objectives.Rastrigin(b=0.0, c=0.0, A=10.0)

Bases: cbx_objective

Rastrigin’s function

Rastrigin’s function is a multimodal function with a global minima at \((0,0)\). The function is originally defined on \(\mathbb{R}^2\) as

\[f(x,y) = (x^2 + y - 11)^2 + (x + y^2 - 7)^2.\]

See Rastrigin’s function. For our case we employ a shifted version on \(\mathbb{R}^d\), where the global minimum is at \((b)\) and we additonally employ a offset \(c\),

\[\tilde{f}(x,y) = \frac{1}{n} \sum_{i=1}^n \left[ (x_i - b)^2 - 10 \cos(2 \pi (x_i - b)) + 10 \right] + c.\]

Parameters:

• b (float, optional) – The first parameter of the function. The default is 0.0.

• c (float, optional) – The second parameter of the function. The default is 0.0.

Examples

>>> import numpy as np
>>> from cbx.objectives import Rastrigin
>>> x = np.array([[1,2], [3,4], [5,6]])
>>> f = Rastrigin()
>>> f(x)
array([  68.,  148., 1556.])

Visualization

(Source code, png, hires.png, pdf)