cbx.objectives.Holder_table#

class cbx.objectives.Holder_table(factor=1.0, shift=0)[source]#

Bases: cbx_objective

Holder table

The Holder table function is a function with many local minima and four global minima [1]. It is defined as

\[f(x,y) = -\left| \sin(x) \cos(y) \exp \left( \left| 1 - \frac{\sqrt{x^2 + y^2}}{\pi} \right| \right) \right|,\]

and its domain is \([-10,10]^2\). Note, that this function can decrease further if the domain is enlarged.

Parameters:

None

Global minima#

  • \(f(x,y) = -19.2085\) at \((x,y) = (8.05502, 9.66459)\)

  • \(f(x,y) = -19.2085\) at \((x,y) = (-8.05502, 9.66459)\)

  • \(f(x,y) = -19.2085\) at \((x,y) = (8.05502, -9.66459)\)

  • \(f(x,y) = -19.2085\) at \((x,y) = (-8.05502, -9.66459)\)

Examples

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

Visualization#

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

../../_images/cbx-objectives-Holder_table-1.png

References