N-D Test Functions Q¶

class Qing(dimensions=2)¶

Qing objective function.

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

$f_{\text{Qing}}(x) = \sum_{i=1}^{n} (x_i^2 - i)^2$

Here, $n$ represents the number of dimensions and $x_i \in [-500, 500]$ for $i = 1, ..., n$ .

Two-dimensional Qing function

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

Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions For Global Optimization Problems Int. Journal of Mathematical Modelling and Numerical Optimisation, 2013, 4, 150-194.

class Quadratic(dimensions=2)¶

Quadratic objective function.

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

$f_{\text{Quadratic}}(x) = -3803.84 - 138.08x_1 - 232.92x_2 + 128.08x_1^2 + 203.64x_2^2 + 182.25x_1x_2$

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

Two-dimensional Quadratic function

Global optimum: $f(x) = -3873.72418$ for $x = [0.19388, 0.48513]$

Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions For Global Optimization Problems Int. Journal of Mathematical Modelling and Numerical Optimisation, 2013, 4, 150-194.

class Quintic(dimensions=2)¶

Quintic objective function.

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

$f_{\text{Quintic}}(x) = \sum_{i=1}^{n} \left|{x_{i}^{5} - 3 x_{i}^{4} + 4 x_{i}^{3} + 2 x_{i}^{2} - 10 x_{i} -4}\right|$

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

Two-dimensional Quintic function

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

Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions For Global Optimization Problems Int. Journal of Mathematical Modelling and Numerical Optimisation, 2013, 4, 150-194.

N-D Test Functions Q¶

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