N-D Test Functions G¶

class go_benchmark.Gear(dimensions=4)¶

Gear test objective function.

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

$f_{\text{Gear}}(\mathbf{x}) = \left \{ \frac{1.0}{6.931} - \frac{\lfloor x_1\rfloor \lfloor x_2 \rfloor } {\lfloor x_3 \rfloor \lfloor x_4 \rfloor } \right\}^2$

Here, $n$ represents the number of dimensions and $x_i \in [12, 60]$ for $i=1,...,4$ .

Global optimum: $f(x_i) = 2.7 \cdot 10^{-12}$ for $\mathbf{x} = [16, 19, 43, 49]$ , where the various $x_i$ may be permuted.

class go_benchmark.Giunta(dimensions=2)¶

Giunta test objective function.

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

$f_{\text{Giunta}}(\mathbf{x}) = 0.6 + \sum_{i=1}^{n} \left[\sin^{2}\left(1 - \frac{16}{15} x_i\right) - \frac{1}{50} \sin\left(4 - \frac{64}{15} x_i\right) - \sin\left(1 - \frac{16}{15} x_i\right)\right]$

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

Two-dimensional Giunta function

Global optimum: $f(x_i) = 0.06447042053690566$ for $\mathbf{x} = [0.4673200277395354, 0.4673200169591304]$

class go_benchmark.GoldsteinPrice(dimensions=2)¶

Goldstein-Price test objective function.

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

$f_{\text{GoldsteinPrice}}(\mathbf{x}) = \left[ 1+(x_1+x_2+1)^2(19-14x_1+3x_1^2-14x_2+6x_1x_2+3x_2^2) \right] \left[ 30+(2x_1-3x_2)^2(18-32x_1+12x_1^2+48x_2-36x_1x_2+27x_2^2) \right]$