opytimark.markers.cec.year_2008

Please refer to the technical report for more information: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.515.821&rep=rep1&type=pdf

class opytimark.markers.cec.year_2008.F1(name: Optional[str] = 'F1', year: Optional[str] = '2008', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 1000, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = False, separable: Optional[bool] = True)

Bases: opytimark.core.CECBenchmark

F1 class implements the Shifted Sphere’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n} z_i^2 - 450 \mid z_i = x_i - o_i\]

Domain:

The function is commonly evaluated using \(x_i \in [-100, 100] \mid i = \{1, 2, \ldots, n\}, n \leq 1000\).

Global Minima:

\(f(\mathbf{x^*}) = -450 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2008.F2(name: Optional[str] = 'F2', year: Optional[str] = '2008', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 1000, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = False, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F2 class implements the Shifted Schwefel’s 2.21 benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \max_{i=1, \ldots, n}|z_i| - 450 \mid z_i = x_i - o_i\]

Domain:

The function is commonly evaluated using \(x_i \in [-100, 100] \mid i = \{1, 2, \ldots, n\}, n \leq 1000\).

Global Minima:

\(f(\mathbf{x^*}) = -450 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2008.F3(name: Optional[str] = 'F3', year: Optional[str] = '2008', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 1000, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F3 class implements the Shifted Rosenbrock’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n-1} (100(z_i^2-z_{i+1})^2 + (z_i - 1)^2) + 390 \mid z_i = x_i - o_i\]

Domain:

The function is commonly evaluated using \(x_i \in [-100, 100] \mid i = \{1, 2, \ldots, n\}, n \leq 1000\).

Global Minima:

\(f(\mathbf{x^*}) = -390 \mid \mathbf{x^*} = \mathbf{o} + 1\).

class opytimark.markers.cec.year_2008.F4(name: Optional[str] = 'F4', year: Optional[str] = '2008', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 1000, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = True)

Bases: opytimark.core.CECBenchmark

F4 class implements the Shifted Rastrigin’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n} (z_i^2 - 10cos(2 \pi z_i) + 10) - 330 \mid z_i = x_i - o_i\]

Domain:

The function is commonly evaluated using \(x_i \in [-5, 5] \mid i = \{1, 2, \ldots, n\}, n \leq 1000\).

Global Minima:

\(f(\mathbf{x^*}) = -330 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2008.F5(name: Optional[str] = 'F5', year: Optional[str] = '2008', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 1000, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F5 class implements the Shifted Griewank’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = 1 + \sum_{i=1}^{n}\frac{x_i^2}{4000} - \prod cos(\frac{x_i}{\sqrt{i}}) - 180 \mid z_i = x_i - o_i\]

Domain:

The function is commonly evaluated using \(x_i \in [-600, 600] \mid i = \{1, 2, \ldots, n\}, n \leq 1000\).

Global Minima:

\(f(\mathbf{x^*}) = -180 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2008.F6(name: Optional[str] = 'F6', year: Optional[str] = '2008', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 1000, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F6 class implements the Shifted Ackley’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = -20e^{-0.2\sqrt{\frac{1}{n}\sum_{i=1}^{n}x_i^2}}-e^{\frac{1}{n}\sum_{i=1}^{n}cos(2 \pi x_i)}+ 20 + e - 140 \mid z_i = x_i - o_i\]

Domain:

The function is commonly evaluated using \(x_i \in [-32, 32] \mid i = \{1, 2, \ldots, n\}, n \leq 1000\).

Global Minima:

\(f(\mathbf{x^*}) = -140 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2008.F7(name: Optional[str] = 'F7', year: Optional[str] = '2008', auxiliary_data: Optional[Tuple[str, Ellipsis]] = (), dims: Optional[int] = 1000, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F7 class implements the Fast Fractal Double Dip’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n} fractal1D(x_i + twist(x_{(i mod n) + 1}))\]

Domain:

The function is commonly evaluated using \(x_i \in [-1, 1] \mid i = \{1, 2, \ldots, n\}, n \leq 1000\).

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = (1, 1, \ldots, 1)\).