N-D Test Functions E¶

class go_benchmark.Easom(dimensions=2)¶

Easom test objective function.

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

$f_{\text{Easom}}(\mathbf{x}) = a - \frac{a}{e^{b \sqrt{\frac{\sum_{i=1}^{n} x_i^{2}}{n}}}} + e - e^{\frac{\sum_{i=1}^{n} \cos\left(c x_i\right)}{n}}$

Where, in this exercise, $a = 20, b = 0.2$ and $c = 2\pi$ .

Here, $n$ represents the number of dimensions and $x_i \in [-100, 100]$ for $i=1,2$ .

Two-dimensional Easom function

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

class go_benchmark.EggCrate(dimensions=2)¶

Egg Crate test objective function.

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

$f_{\text{EggCrate}}(\mathbf{x}) = x_1^2 + x_2^2 + 25 \left[ \sin^2(x_1) + \sin^2(x_2) \right]$

Here, $n$ represents the number of dimensions and $x_i \in [-5, 5]$ for $i=1,2$ .

Two-dimensional Egg Crate function

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

class go_benchmark.EggHolder(dimensions=2)¶

Egg Holder test objective function.

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

$f_{\text{EggHolder}}(\mathbf{x}) = - x_{1} \sin\left(\sqrt{\lvert{x_{1} - x_{2} -47}\rvert}\right) - \left(x_{2} + 47\right) \sin\left(\sqrt{\left|{\frac{1}{2} x_{1} + x_{2} + 47}\right|}\right)$

Here, $n$ represents the number of dimensions and $x_i \in [-512, 512]$ for $i=1,2$ .

Two-dimensional Egg Holder function

Global optimum: $f(x_i) = -959.640662711$ for $\mathbf{x} = [512, 404.2319]$

class go_benchmark.ElAttarVidyasagarDutta(dimensions=2)¶

El-Attar-Vidyasagar-Dutta test objective function.

This class defines the El-Attar-Vidyasagar-Dutta function global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{ElAttarVidyasagarDutta}}(\mathbf{x}) = (x_1^2 + x_2 - 10)^2 + (x_1 + x_2^2 - 7)^2 + (x_1^2 + x_2^3 - 1)^2$

Here, $n$ represents the number of dimensions and $x_i \in [-100, 100]$ for $i=1,2$ .

Two-dimensional El-Attar-Vidyasagar-Dutta function

Global optimum: $f(x_i) = 1.712780354$ for $\mathbf{x} = [3.40918683, -2.17143304]$

class go_benchmark.Exp2(dimensions=2)¶

Exp2 test objective function.

This class defines the Exp2 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{Exp2}}(\mathbf{x}) = \sum_{i=0}^9 \left ( e^{-ix_1/10} - 5e^{-ix_2/10} -e^{-i/10} + 5e^{-i} \right )^2$

Here, $n$ represents the number of dimensions and $x_i \in [0, 20]$ for $i=1,2$ .

Two-dimensional Exp2 function

Global optimum: $f(x_i) = 0$ for $x_i = [1, 0.1]$

class go_benchmark.Exponential(dimensions=2)¶

Exponential test objective function.

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

$f_{\text{Exponential}}(\mathbf{x}) = -e^{-0.5 \sum_{i=1}^n x_i^2}$

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

Two-dimensional Exponential function

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

N-D Test Functions E¶

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