N-D Test Functions A¶

class go_benchmark.Ackley(dimensions=2)¶

Ackley test objective function.

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

$f_{\text{Ackley}}(\mathbf{x}) = -20e^{-0.2 \sqrt{\frac{1}{n} \sum_{i=1}^n x_i^2}} - e^{ \frac{1}{n} \sum_{i=1}^n \cos(2 \pi x_i)} + 20 + e$

Here, $n$ represents the number of dimensions and $x_i \in [-32, 32]$ for $i=1,...,n$ .

Two-dimensional Ackley function

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

class go_benchmark.Adjiman(dimensions=2)¶

Adjiman test objective function.

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

$f_{\text{Adjiman}}(\mathbf{x}) = \cos(x_1)\sin(x_2) - \frac{x_1}{(x_2^2 + 1)}$

Here, $n$ represents the number of dimensions and $x_1 \in [-1, 2]$ and $x_2 \in [-1, 1]$ .

Two-dimensional Adjiman function

Global optimum: $f(x_i) = -2.02181$ for $\mathbf{x} = [2, 0.10578]$

class go_benchmark.Alpine01(dimensions=2)¶

Alpine 1 test objective function.

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

$f_{\text{Alpine01}}(\mathbf{x}) = \sum_{i=1}^{n} \lvert {x_i \sin \left( x_i \right) + 0.1 x_i} \rvert$

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

Two-dimensional Alpine 1 function

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

class go_benchmark.Alpine02(dimensions=2)¶

Alpine 2 test objective function.

This class defines the Alpine 2 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{Alpine02}}(\mathbf{x}) = \prod_{i=1}^{n} \sqrt{x_i} \sin(x_i)$

Here, $n$ represents the number of dimensions and $x_i \in [0, 10]$ for $i=1,...,n$ .

Two-dimensional Alpine 2 function

Global optimum: $f(x_i) = -6.1295$ for $x_i = 7.917$ for $i=1,...,n$

class go_benchmark.AMGM(dimensions=2)¶

AMGM test objective function.

This class defines the Arithmetic Mean - Geometric Mean Equality global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{AMGM}}(\mathbf{x}) = \left ( \frac{1}{n} \sum_{i=1}^{n} x_i - \sqrt[n]{ \prod_{i=1}^{n} x_i} \right )^2$

Here, $n$ represents the number of dimensions and $x_i \in [0, 10]$ for $i=1,...,n$ .

Two-dimensional Arithmetic Mean - Geometric Mean Equality function

Global optimum: $f(x_i) = 0$ for $x_1 = x_2 = ... = x_n$ for $i=1,...,n$

N-D Test Functions A¶

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