N-D Test Functions Q¶

class go_benchmark.Qing(dimensions=2)¶

Qing test objective function.

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

$f_{\text{Qing}}(\mathbf{x}) = \sum_{i=1}^{n} (x_i^2 - i)^2$

Here, $n$ represents the number of dimensions and $x_i \in [-500, 500]$ for $i=1,...,n$ .

Two-dimensional Qing function

Global optimum: $f(x_i) = 0$ for $x_i = \pm \sqrt(i)$ for $i=1,...,n$

class go_benchmark.Quadratic(dimensions=2)¶

Quadratic test objective function.

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

$f_{\text{Quadratic}}(\mathbf{x}) = -3803.84 - 138.08x_1 - 232.92x_2 + 128.08x_1^2 + 203.64x_2^2 + 182.25x_1x_2$

Here, $n$ represents the number of dimensions and $x_i \in [-10, 10]$ for $i=1,2$ .

Two-dimensional Quadratic function

Global optimum: $f(x_i) = -3873.72418$ for $\mathbf{x} = [0.19388, 0.48513]$

class go_benchmark.Quintic(dimensions=2)¶

Quintic test objective function.

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

$f_{\text{Quintic}}(\mathbf{x}) = \sum_{i=1}^{n} \left|{x_{i}^{5} - 3 x_{i}^{4} + 4 x_{i}^{3} + 2 x_{i}^{2} - 10 x_{i} -4}\right|$

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

Two-dimensional Quintic function

Global optimum: $f(x_i) = 0$ for $x_i = -1$ for $i=1,...,n$