test_functions 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.

Giunta function

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]

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

Goldstein-Price function

Two-dimensional Goldstein-Price function

Global optimum: f(x_i) = 3 for \mathbf{x} = [0, -1]


class go_benchmark.Griewank(dimensions=2)

Griewank test objective function.

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

f_{\text{Griewank}}(\mathbf{x}) = \frac{1}{4000}\sum_{i=1}^n x_i^2 - \prod_{i=1}^n\cos\left(\frac{x_i}{\sqrt{i}}\right) + 1

Here, n represents the number of dimensions and x_i \in [-600, 600] for i=1,...,n.

Griewank function

Two-dimensional Griewank function

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


class go_benchmark.Gulf(dimensions=3)

Gulf test objective function.

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

f_{\text{Gulf}}(\mathbf{x}) = \sum_{i=1}^m \left( e^{-\frac{\lvert y_i - x_2 \rvert^{x_3}}{x_1}    }  - t_i \right)

Where, in this exercise:

t_i = i/100 \\
y_i = 25 + [-50 \log(t_i)]^{2/3}

Here, n represents the number of dimensions and x_i \in [0, 60] for i=1,2,3.

Global optimum: f(x_i) = 0 for \mathbf{x} = [50, 25, 1.5]

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