N-D Test Functions C¶

class go_benchmark.CarromTable(dimensions=2)¶

CarromTable test objective function.

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

$f_{\text{CarromTable}}(\mathbf{x}) = - \frac{1}{30} e^{2 \left|{1 - \frac{\sqrt{x_{1}^{2} + x_{2}^{2}}}{\pi}}\right|} \cos^{2}\left(x_{1}\right) \cos^{2}\left(x_{2}\right)$

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

Two-dimensional CarromTable function

Global optimum: $f(x_i) = -24.15681551650653$ for $x_i = \pm 9.646157266348881$ for $i=1,...,n$

class go_benchmark.Chichinadze(dimensions=2)¶

Chichinadze test objective function.

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

$f_{\text{Chichinadze}}(\mathbf{x}) = x_{1}^{2} - 12 x_{1} + 8 \sin\left(\frac{5}{2} \pi x_{1}\right) + 10 \cos\left(\frac{1}{2} \pi x_{1}\right) + 11 - 0.2 \frac{\sqrt{5}}{e^{\frac{1}{2} \left(x_{2} -0.5\right)^{2}}}$

Here, $n$ represents the number of dimensions and $x_i \in [-30, 30]$ for $i=1,2$ .

Two-dimensional Chichinadze function

Global optimum: $f(x_i) = -42.94438701899098$ for $\mathbf{x} = [6.189866586965680, 0.5]$

class go_benchmark.Cigar(dimensions=2)¶

Cigar test objective function.

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

$f_{\text{Cigar}}(\mathbf{x}) = x_1^2 + 10^6\sum_{i=2}^{n} x_i^2$

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

Two-dimensional Cigar function

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

class go_benchmark.Cola(dimensions=17)¶

Cola test objective function.

This class defines the Cola global optimization problem. The 17-dimensional function computes indirectly the formula $f(n, u)$ by setting $x_0 = y_0, x_1 = u_0, x_i = u_{2(i−2)}, y_i = u_{2(i−2)+1}$ :

$f_{\text{Cola}}(\mathbf{x}) = \sum_{i<j}^{n} \left (r_{i,j} - d_{i,j} \right )^2$

Where $r_{i,j}$ is given by:

$r_{i,j} = \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2}$

And $d$ is a symmetric matrix given by:

$\mathbf{d} = \left [ d_{ij} \right ] = \begin{pmatrix} 1.27 & & & & & & & & \\ 1.69 & 1.43 & & & & & & & \\ 2.04 & 2.35 & 2.43 & & & & & & \\ 3.09 & 3.18 & 3.26 & 2.85 & & & & & \\ 3.20 & 3.22 & 3.27 & 2.88 & 1.55 & & & & \\ 2.86 & 2.56 & 2.58 & 2.59 & 3.12 & 3.06 & & & \\ 3.17 & 3.18 & 3.18 & 3.12 & 1.31 & 1.64 & 3.00 & \\ 3.21 & 3.18 & 3.18 & 3.17 & 1.70 & 1.36 & 2.95 & 1.32 & \\ 2.38 & 2.31 & 2.42 & 1.94 & 2.85 & 2.81 & 2.56 & 2.91 & 2.97 \end{pmatrix}$

This function has bounds $0 \leq x_0 \leq 4$ and $-4 \leq x_i \leq 4$ for $i = 1,...,n-1$ . It has a global minimum of 11.7464.

class go_benchmark.Colville(dimensions=4)¶

Colville test objective function.

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

$f_{\text{Colville}}(\mathbf{x}) = \left(x_{1} -1\right)^{2} + 100 \left(x_{1}^{2} - x_{2}\right)^{2} + 10.1 \left(x_{2} -1\right)^{2} + \left(x_{3} -1\right)^{2} + 90 \left(x_{3}^{2} - x_{4}\right)^{2} + 10.1 \left(x_{4} -1\right)^{2} + 19.8 \frac{x_{4} -1}{x_{2}}$

Here, $n$ represents the number of dimensions and $x_i \in [-10, 10]$ for $i=1,...,4$ .

Global optimum: $f(x_i) = 0$ for $x_i = 1$ for $i=1,...,4$

class go_benchmark.Corana(dimensions=4)¶

Corana test objective function.

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

$f_{\text{Corana}}(\mathbf{x}) = \begin{cases} \sum_{i=1}^n 0.15 d_i [z_i - 0.05\textrm{sgn}(z_i)]^2 & \textrm{if}|x_i-z_i| < 0.05 \\ d_ix_i^2 & \textrm{otherwise}\end{cases}$

Where, in this exercise:

$z_i = 0.2 \lfloor |x_i/s_i|+0.49999\rfloor\textrm{sgn}(x_i), d_i=(1,1000,10,100, ...)$

Here, $n$ represents the number of dimensions and $x_i \in [-5, 5]$ for $i=1,...,4$ .

Global optimum: $f(x_i) = 0$ for $x_i = 0$ for $i=1,...,4$

class go_benchmark.CosineMixture(dimensions=2)¶

Cosine Mixture test objective function.

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

$f_{\text{CosineMixture}}(\mathbf{x}) = -0.1 \sum_{i=1}^n \cos(5 \pi x_i) - \sum_{i=1}^n x_i^2$

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

Two-dimensional Cosine Mixture function

Global optimum: $f(x_i) = -0.1N$ for $x_i = 0$ for $i=1,...,N$

class go_benchmark.CrossInTray(dimensions=2)¶

Cross-in-Tray test objective function.

This class defines the Cross-in-Tray global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{CrossInTray}}(\mathbf{x}) = - 0.0001 \left(\left|{e^{\left|{100 - \frac{\sqrt{x_{1}^{2} + x_{2}^{2}}}{\pi}}\right|} \sin\left(x_{1}\right) \sin\left(x_{2}\right)}\right| + 1\right)^{0.1}$

Here, $n$ represents the number of dimensions and $x_i \in [-15, 15]$ for $i=1,2$ .

Two-dimensional Cross-in-Tray function

Global optimum: $f(x_i) = -2.062611870822739$ for $x_i = \pm 1.349406608602084$ for $i=1,2$

class go_benchmark.CrossLegTable(dimensions=2)¶

Cross-Leg-Table test objective function.

This class defines the Cross-Leg-Table global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{CrossLegTable}}(\mathbf{x}) = - \frac{1}{\left(\left|{e^{\left|{100 - \frac{\sqrt{x_{1}^{2} + x_{2}^{2}}}{\pi}}\right|} \sin\left(x_{1}\right) \sin\left(x_{2}\right)}\right| + 1\right)^{0.1}}$

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

Two-dimensional Cross-Leg-Table function

Global optimum: $f(x_i) = -1$ . The global minimum is found on the planes $x_1 = 0$ and $x_2 = 0$

class go_benchmark.CrownedCross(dimensions=2)¶

Crowned Cross test objective function.

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

$f_{\text{CrownedCross}}(\mathbf{x}) = 0.0001 \left(\left|{e^{\left|{100- \frac{\sqrt{x_{1}^{2} + x_{2}^{2}}}{\pi}}\right|} \sin\left(x_{1}\right) \sin\left(x_{2}\right)}\right| + 1\right)^{0.1}$

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

Two-dimensional Crowned Cross function

Global optimum: $f(x_i) = 0.0001$ . The global minimum is found on the planes $x_1 = 0$ and $x_2 = 0$

class go_benchmark.Csendes(dimensions=2)¶

Csendes test objective function.

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

$f_{\text{Csendes}}(\mathbf{x}) = \sum_{i=1}^n x_i^6 \left[ 2 + \sin \left( \frac{1}{x_i} \right ) \right]$

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

Two-dimensional Csendes function

Global optimum: $f(x_i) = 0.0$ for $x_i = 0$ for $i=1,...,N$

class go_benchmark.Cube(dimensions=2)¶

Cube test objective function.

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

$f_{\text{Cube}}(\mathbf{x}) = 100(x_2 - x_1^3)^2 + (1 - x1)^2$

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

Two-dimensional Cube function

Global optimum: $f(x_i) = 0.0$ for $\mathbf{x} = [1, 1]$

N-D Test Functions C¶

Previous topic

Next topic

This Page

Navigation

N-D Test Functions C¶

Previous topic

Next topic

This Page

Quick search

Navigation