N-D Test Functions U¶

class go_benchmark.Ursem01(dimensions=2)¶

Ursem 1 test objective function.

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

$f_{\text{Ursem01}}(\mathbf{x}) = - \sin(2x_1 - 0.5 \pi) - 3 \cos(x_2) - 0.5x_1$

Here, $n$ represents the number of dimensions and $x_1 \in [-2.5, 3]$ , $x_2 \in [-2, 2]$ .

Two-dimensional Ursem 1 function

Global optimum: $f(x_i) = -4.8168$ for $\mathbf{x} = [1.69714, 0.0]$

class go_benchmark.Ursem03(dimensions=2)¶

Ursem 3 test objective function.

This class defines the Ursem 3 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{Ursem03}}(\mathbf{x}) = - \sin(2.2 \pi x_1 + 0.5 \pi) \frac{2 - \lvert x_1 \rvert}{2} \frac{3 - \lvert x_1 \rvert}{2} - \sin(2.2 \pi x_2 + 0.5 \pi) \frac{2 - \lvert x_2 \rvert}{2} \frac{3 - \lvert x_2 \rvert}{2}$

Here, $n$ represents the number of dimensions and $x_1 \in [-2, 2]$ , $x_2 \in [-1.5, 1.5]$ .

Two-dimensional Ursem 3 function

Global optimum: $f(x_i) = -3$ for $x_i = 0$ for $i=1,2$

class go_benchmark.Ursem04(dimensions=2)¶

Ursem 4 test objective function.

This class defines the Ursem 4 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{Ursem04}}(\mathbf{x}) = -3 \sin(0.5 \pi x_1 + 0.5 \pi) \frac{2 - \sqrt{x_1^2 + x_2 ^ 2}}{4}$

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

Two-dimensional Ursem 4 function

Global optimum: $f(x_i) = -1.5$ for $x_i = 0$ for $i=1,2$

class go_benchmark.UrsemWaves(dimensions=2)¶

Ursem Waves test objective function.

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

$f_{\text{UrsemWaves}}(\mathbf{x}) = -0.9x_1^2 + (x_2^2 - 4.5x_2^2)x_1x_2 + 4.7 \cos \left[ 2x_1 - x_2^2(2 + x_1) \right ] \sin(2.5 \pi x_1)$

Here, $n$ represents the number of dimensions and $x_1 \in [-0.9, 1.2]$ , $x_2 \in [-1.2, 1.2]$ .

Two-dimensional Ursem Waves function

Global optimum: $f(x_i) = -8.5536$ for $x_i = 1.2$ for $i=1,2$

N-D Test Functions U¶

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