N-D Test Functions N¶

class go_benchmark.NeedleEye(dimensions=2)¶

NeedleEye test objective function.

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

$f_{\text{NeedleEye}}(\mathbf{x}) = \begin{cases} 1 & \textrm{if} \hspace{5pt} \lvert x_i \rvert < eye \hspace{5pt} \forall i \\ \sum_{i=1}^n (100 + \lvert x_i \rvert) & \textrm{if} \hspace{5pt} \lvert x_i \rvert > eye \\ 0 & \textrm{otherwise} \end{cases}$

Where, in this exercise, $eye = 0.0001$ .

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

Two-dimensional NeedleEye function

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

class go_benchmark.NewFunction01(dimensions=2)¶

NewFunction01 test objective function.

This class defines the NewFunction01 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{NewFunction01}}(\mathbf{x}) = \left | {\cos\left(\sqrt{\left|{x_{1}^{2} + x_{2}}\right|}\right)} \right |^{0.5} + (x_{1} + x_{2})/100$

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

Two-dimensional NewFunction01 function

Global optimum: $f(x_i) = -0.17894509347721144$ for $\mathbf{x} = [-8.4666, -9.9988]$

class go_benchmark.NewFunction02(dimensions=2)¶

NewFunction02 test objective function.

This class defines the NewFunction02 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{NewFunction02}}(\mathbf{x}) = \left | {\sin\left(\sqrt{\lvert{x_{1}^{2} + x_{2}}\rvert}\right)} \right |^{0.5} + (x_{1} + x_{2})/100$

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

Two-dimensional NewFunction02 function

Global optimum: $f(x_i) = -0.1971881059905$ for $\mathbf{x} = [-9.94112, -9.99952]$

class go_benchmark.NewFunction03(dimensions=2)¶

NewFunction03 test objective function.

This class defines the NewFunction03 global optimization problem. This is a multimodal minimization problem defined as follows:

$f_{\text{NewFunction03}}(\mathbf{x}) = 0.01 x_{1} + 0.1 x_{2} + \left\{x_{1} + \sin^{2}\left[\left(\cos\left(x_{1}\right) + \cos\left(x_{2}\right)\right)^{2}\right] + \cos^{2}\left[\left(\sin\left(x_{1}\right) + \sin\left(x_{2}\right)\right)^{2}\right]\right\}^{2}$