N-D Test Functions M¶

class go_benchmark.Matyas(dimensions=2)¶

Matyas test objective function.

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

$f_{\text{Matyas}}(\mathbf{x}) = 0.26(x_1^2 + x_2^2) - 0.48x_1x_2$

Here, $n$ represents the number of dimensions and $x_i \in [-10, 10]$ for $i=1,2$ .

Two-dimensional Matyas function

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

class go_benchmark.McCormick(dimensions=2)¶

McCormick test objective function.

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

$f_{\text{McCormick}}(\mathbf{x}) = - x_{1} + 2 x_{2} + \left(x_{1} - x_{2}\right)^{2} + \sin\left(x_{1} + x_{2}\right) + 1$

Here, $n$ represents the number of dimensions and $x_1 \in [-1.5, 4]$ , $x_2 \in [-3, 4]$ .

Two-dimensional McCormick function

Global optimum: $f(x_i) = -1.913222954981037$ for $\mathbf{x} = [-0.5471975602214493, -1.547197559268372]$

class go_benchmark.Michalewicz(dimensions=2)¶

Michalewicz test objective function.

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

$f_{\text{Michalewicz}}(\mathbf{x}) = - \sum_{i=1}^{2} \sin\left(x_i\right) \sin^{2 m}\left(\frac{i x_i^{2}}{\pi}\right)$

Where, in this exercise, $m = 10$ .

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

Two-dimensional Michalewicz function

Global optimum: $f(x_i) = -1.8013$ for $x_i = 0$ for $i=1,2$

class go_benchmark.MieleCantrell(dimensions=4)¶

Miele-Cantrell test objective function.

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

$f_{\text{MieleCantrell}}(\mathbf{x}) = (e^{-x_1} - x_2)^4 + 100(x_2 - x_3)^6 + \tan^4(x_3 - x_4) + x_1^8$

Here, $n$ represents the number of dimensions and $x_i \in [-1, 1]$ for $i=1,...,4$ .

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

class go_benchmark.Mishra01(dimensions=2)¶

Mishra 1 test objective function.

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

$f_{\text{Mishra01}}(\mathbf{x}) = (1 + x_n)^{x_n} \hspace{10pt} ; \hspace{10pt} x_n = n - \sum_{i=1}^{n-1} x_i$

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

Two-dimensional Mishra 1 function

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

class go_benchmark.Mishra02(dimensions=2)¶

Mishra 2 test objective function.

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

$f_{\text{Mishra02}}(\mathbf{x}) = (1 + x_n)^{x_n} \hspace{10pt} ; \hspace{10pt} x_n = n - \sum_{i=1}^{n-1} \frac{(x_i + x_{i+1})}{2}$

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

Two-dimensional Mishra 2 function

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

class go_benchmark.Mishra03(dimensions=2)¶

Mishra 3 test objective function.

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

$f_{\text{Mishra03}}(\mathbf{x}) = \sqrt{\lvert \cos{\sqrt{\lvert x_1^2 + x_2^2 \rvert}} \rvert} + 0.01(x_1 + x_2)$

Here, $n$ represents the number of dimensions and $x_i \in [-10, 10]$ for $i=1,2$ .

Two-dimensional Mishra 3 function

Global optimum: $f(x_i) = -0.18467$ for $x_i = -10$ for $i=1,2$

class go_benchmark.Mishra04(dimensions=2)¶

Mishra 4 test objective function.

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

$f_{\text{Mishra04}}(\mathbf{x}) = \sqrt{\lvert \sin{\sqrt{\lvert x_1^2 + x_2^2 \rvert}} \rvert} + 0.01(x_1 + x_2)$

Here, $n$ represents the number of dimensions and $x_i \in [-10, 10]$ for $i=1,2$ .

Two-dimensional Mishra 4 function

Global optimum: $f(x_i) = -0.199409$ for $x_i = -10$ for $i=1,2$

class go_benchmark.Mishra05(dimensions=2)¶

Mishra 5 test objective function.

This class defines the Mishra 5 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{Mishra05}}(\mathbf{x}) = \left [ \sin^2 ((\cos(x_1) + \cos(x_2))^2) + \cos^2 ((\sin(x_1) + \sin(x_2))^2) + x_1 \right ]^2 + 0.01(x_1 + x_2)$

Here, $n$ represents the number of dimensions and $x_i \in [-10, 10]$ for $i=1,2$ .

Two-dimensional Mishra 5 function

Global optimum: $f(x_i) = -0.119829$ for $\mathbf{x} = [-1.98682, -10]$

class go_benchmark.Mishra06(dimensions=2)¶

Mishra 6 test objective function.

This class defines the Mishra 6 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{Mishra06}}(\mathbf{x}) = -\log{\left [ \sin^2 ((\cos(x_1) + \cos(x_2))^2) - \cos^2 ((\sin(x_1) + \sin(x_2))^2) + x_1 \right ]^2} + 0.01 \left[(x_1 -1)^2 + (x_2 - 1)^2 \right]$

Here, $n$ represents the number of dimensions and $x_i \in [-10, 10]$ for $i=1,2$ .

Two-dimensional Mishra 6 function

Global optimum: $f(x_i) = -2.28395$ for $\mathbf{x} = [2.88631, 1.82326]$

class go_benchmark.Mishra07(dimensions=2)¶

Mishra 7 test objective function.

This class defines the Mishra 7 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{Mishra07}}(\mathbf{x}) = \left [\prod_{i=1}^{n} x_i - n! \right]^2$

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

Two-dimensional Mishra 7 function

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

class go_benchmark.Mishra08(dimensions=2)¶

Mishra 8 test objective function.

This class defines the Mishra 8 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{Mishra08}}(\mathbf{x}) = 0.001 \left[\lvert x_1^{10} - 20x_1^9 + 180x_1^8 - 960 x_1^7 + 3360x_1^6 - 8064x_1^5 + 13340x_1^4 - 15360x_1^3 + 11520x_1^2 - 5120x_1 + 2624 \rvert \lvert x_2^4 + 12x_2^3 + 54x_2^2 + 108x_2 + 81 \rvert \right]^2$

Here, $n$ represents the number of dimensions and $x_i \in [-10, 10]$ for $i=1,2$ .

Two-dimensional Mishra 8 function

Global optimum: $f(x_i) = 0$ for $\mathbf{x} = [2, -3]$

class go_benchmark.Mishra09(dimensions=3)¶

Mishra 9 test objective function.

This class defines the Mishra 9 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{Mishra09}}(\mathbf{x}) = \left[ ab^2c + abc^2 + b^2 + (x_1 + x_2 - x_3)^2 \right]^2$

Where, in this exercise:

$\begin{cases} a = 2x_1^3 + 5x_1x_2^2 + 4x_3 - 2x_1^2x_3 - 18 \\ b = x_1 + x_2^3 + x_1x_3^2 - 22 \\ c = 8x_1^2 + 2x_2x_3 + 2x_2^2 + 3x_2^3 - 52 \end{cases}$

Here, $n$ represents the number of dimensions and $x_i \in [-10, 10]$ for $i=1,2,3$ .

Global optimum: $f(x_i) = 0$ for $\mathbf{x} = [1, 2, 3]$

class go_benchmark.Mishra10(dimensions=2)¶

Mishra 10 test objective function.

This class defines the Mishra 10 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{Mishra10}}(\mathbf{x}) = \left[ \lfloor x_1 \perp x_2 \rfloor - \lfloor x_1 \rfloor - \lfloor x_2 \rfloor \right]^2$

Here, $n$ represents the number of dimensions and $x_i \in [-10, 10]$ for $i=1,2$ .

Two-dimensional Mishra 10 function

Global optimum: $f(x_i) = 0$ for $\mathbf{x} = [2, 2]$

class go_benchmark.Mishra11(dimensions=2)¶

Mishra 11 test objective function.

This class defines the Mishra 11 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{Mishra11}}(\mathbf{x}) = \left [ \frac{1}{n} \sum_{i=1}^{n} \lvert x_i \rvert - \left(\prod_{i=1}^{n} \lvert x_i \rvert \right )^{\frac{1}{n}} \right]^2$

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

Two-dimensional Mishra 11 function

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

class go_benchmark.MultiModal(dimensions=2)¶

MultiModal test objective function.

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

$f_{\text{MultiModal}}(\mathbf{x}) = \left( \sum_{i=1}^n \lvert x_i \rvert \right) \left( \prod_{i=1}^n \lvert x_i \rvert \right)$

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

Two-dimensional MultiModal function

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

N-D Test Functions M¶

Previous topic

Next topic

This Page

Navigation

N-D Test Functions M¶

Previous topic

Next topic

This Page

Quick search

Navigation