N-D Test Functions V¶

class go_benchmark.VenterSobiezcczanskiSobieski(dimensions=2)¶

Venter Sobiezcczanski-Sobieski test objective function.

This class defines the Venter Sobiezcczanski-Sobieski global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{VenterSobiezcczanskiSobieski}}(\mathbf{x}) = x_1^2 - 100 \cos^2(x_1) - 100 \cos(x_1^2/30) + x_2^2 - 100 \cos^2(x_2) - 100 \cos(x_2^2/30)$

Here, $n$ represents the number of dimensions and $x_i \in [-50, 50]$ for $i=1,2$ .

Two-dimensional Venter Sobiezcczanski-Sobieski function

Global optimum: $f(x_i) = -400$ for $x_i = 0$ for $i=1,2$

class go_benchmark.Vincent(dimensions=2)¶

Vincent test objective function.

This class defines the Vincent global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{Vincent}}(\mathbf{x}) = - \sum_{i=1}^{n} \sin(10 \log(x))$

Here, $n$ represents the number of dimensions and $x_i \in [0.25, 10]$ for $i=1,...,n$ .

Two-dimensional Vincent function

Global optimum: $f(x_i) = -n$ for $x_i = 7.70628098$ for $i=1,...,n$