N-D Test Functions R¶

class go_benchmark.Rana(dimensions=2)¶

Rana test objective function.

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

$f_{\text{Rana}}(\mathbf{x}) = \sum_{i=1}^{n} \left[x_{i} \sin\left(\sqrt{\lvert{x_{1} - x_{i} + 1}\rvert}\right) \cos\left(\sqrt{\lvert{x_{1} + x_{i} + 1}\rvert}\right) + \left(x_{1} + 1\right) \sin\left(\sqrt{\lvert{x_{1} + x_{i} + 1}\rvert}\right) \cos\left(\sqrt{\lvert{x_{1} - x_{i} + 1}\rvert}\right)\right]$

Here, $n$ represents the number of dimensions and $x_i \in [-500.000001, 500.000001]$ for $i=1,...,n$ .

Two-dimensional Rana function

Global optimum: $f(x_i) = -928.5478$ for $x_i = -500$ for $i=1,...,n$

class go_benchmark.Rastrigin(dimensions=2)¶

Rastrigin test objective function.

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

$f_{\text{Rastrigin}}(\mathbf{x}) = 10n \sum_{i=1}^n \left[ x_i^2 - 10 \cos(2\pi x_i) \right]$

Here, $n$ represents the number of dimensions and $x_i \in [-5.12, 5.12]$ for $i=1,...,n$ .

Two-dimensional Rastrigin function

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

class go_benchmark.Ripple01(dimensions=2)¶

Ripple 1 test objective function.

This class defines the Ripple 1 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{Ripple01}}(\mathbf{x}) = \sum_{i=1}^2 -e^{-2 \log 2 (\frac{x_i-0.1}{0.8})^2} \left[\sin^6(5 \pi x_i) + 0.1\cos^2(500 \pi x_i) \right]$

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

Two-dimensional Ripple 1 function

Global optimum: $f(x_i) = -2.2$ for $x_i = 0.1$ for $i=1,2$

class go_benchmark.Ripple25(dimensions=2)¶

Ripple 25 test objective function.

This class defines the Ripple 25 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{Ripple25}}(\mathbf{x}) = \sum_{i=1}^2 -e^{-2 \log 2 (\frac{x_i-0.1}{0.8})^2} \left[\sin^6(5 \pi x_i) \right]$

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

Two-dimensional Ripple 25 function

Global optimum: $f(x_i) = -2$ for $x_i = 0.1$ for $i=1,2$

class go_benchmark.Rosenbrock(dimensions=2)¶

Rosenbrock test objective function.

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

$f_{\text{Rosenbrock}}(\mathbf{x}) = \sum_{i=1}^{n-1} [100(x_i^2 - x_{i+1})^2 + (x_i - 1)^2]$

Here, $n$ represents the number of dimensions and $x_i \in [-5, 10]$ for $i=1,...,n$ .

Two-dimensional Rosenbrock function

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

class go_benchmark.RosenbrockModified(dimensions=2)¶

Modified Rosenbrock test objective function.

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

$f_{\text{RosenbrockModified}}(\mathbf{x}) = 74 + 100(x_2 - x_1^2)^2 + (1 - x_1)^2 - 400 e^{-\frac{(x_1+1)^2 + (x_2 + 1)^2}{0.1}}$

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

Two-dimensional Modified Rosenbrock function

Global optimum: $f(x_i) = 34.37$ for $\mathbf{x} = [-0.9, -0.95]$

class go_benchmark.RotatedEllipse01(dimensions=2)¶

Rotated Ellipse 1 test objective function.

This class defines the Rotated Ellipse 1 global optimization problem. This is a unimodal minimization problem defined as follows:

$f_{\text{RotatedEllipse01}}(\mathbf{x}) = 7x_1^2 - 6 \sqrt{3} x_1x_2 + 13x_2^2$

Here, $n$ represents the number of dimensions and $x_i \in [-500, 500]$ for $i=1,2$ .

Two-dimensional Rotated Ellipse 1 function

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

class go_benchmark.RotatedEllipse02(dimensions=2)¶

Rotated Ellipse 2 test objective function.

This class defines the Rotated Ellipse 2 global optimization problem. This is a unimodal minimization problem defined as follows:

$f_{\text{RotatedEllipse02}}(\mathbf{x}) = x_1^2 - x_1x_2 + x_2^2$

Here, $n$ represents the number of dimensions and $x_i \in [-500, 500]$ for $i=1,2$ .

Two-dimensional Rotated Ellipse 2 function

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

N-D Test Functions R¶

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