opytimark.markers.cec.year_2005

Please refer to the technical report for more information: http://www.cmap.polytechnique.fr/~nikolaus.hansen/Tech-Report-May-30-05.pdf

class opytimark.markers.cec.year_2005.F1(name: Optional[str] = 'F1', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 100, 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 \(x_i \in [-100, 100] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

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

class opytimark.markers.cec.year_2005.F2(name: Optional[str] = 'F2', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 100, 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 1.2 benchmarking function.

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

Domain:

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

Global Minima:

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

class opytimark.markers.cec.year_2005.F3(name: Optional[str] = 'F3', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), dims: Optional[int] = -1, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = False, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F3 class implements the Shifted Rotated High Conditioned Elliptic’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n} (10^6)^\frac{i-1}{n-1} z_i^2 - 450 \mid z_i = (x_i - o_i) * M_i\]

Domain:

The function is commonly evaluated using \(x_i \in [-100, 100] \mid i = \{1, 2, \ldots, n\}, n \in \{2, 10, 30, 50\}\).

Global Minima:

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

class opytimark.markers.cec.year_2005.F4(name: Optional[str] = 'F4', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = False, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F4 class implements the Shifted Schwefel’s 1.2 with Noise in Fitness benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n} (\sum_{j=1}^i z_j)^2 * (1 + 0.4|N(0,1)|) - 450 \mid z_i = x_i - o_i\]

Domain:

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

Global Minima:

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

class opytimark.markers.cec.year_2005.F5(name: Optional[str] = 'F5', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'A'), dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = False, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F5 class implements the Schwefel’s Problem 2.6 with Global Optimum on Bounds benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \max{|A_i x - B_i|} - 310 \mid B_i = A_i - o_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = -310 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2005.F6(name: Optional[str] = 'F6', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 100, 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 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 \(x_i \in [-100, 100] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

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

class opytimark.markers.cec.year_2005.F7(name: Optional[str] = 'F7', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), dims: Optional[int] = -1, 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 Shifted Rotated Griewank’s without Bounds benchmarking function.

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

Domain:

The function is commonly evaluated using \(x_i \in [0, 600] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

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

class opytimark.markers.cec.year_2005.F8(name: Optional[str] = 'F8', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), dims: Optional[int] = -1, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F8 class implements the Shifted Rotated Ackley’s with Global Optimum on Bounds benchmarking function.

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

Domain:

The function is commonly evaluated using \(x_i \in [-32, 32] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

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

class opytimark.markers.cec.year_2005.F9(name: Optional[str] = 'F9', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = True)

Bases: opytimark.core.CECBenchmark

F9 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 \(x_i \in [-5, 5] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

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

class opytimark.markers.cec.year_2005.F10(name: Optional[str] = 'F10', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F10 class implements the Shifted Rotated Rastrigin’s benchmarking function.

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

Domain:

The function is commonly evaluated using \(x_i \in [-5, 5] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

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

class opytimark.markers.cec.year_2005.F11(name: Optional[str] = 'F11', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F11 class implements the Shifted Rotated Weierstrass’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n} (\sum_{k=0}^{20} [0.5^k cos(2\pi 3^k(z_i+0.5))]) - n \sum_{k=0}^{20}[0.5^k cos(2\pi 3^k 0.5)] \mid z_i = (x_i - o_i) * M_i\]

Domain:

The function is commonly evaluated using \(x_i \in [-0.5, 0.5] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

\(f(\mathbf{x^*}) = 90 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2005.F12(name: Optional[str] = 'F12', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('alpha', 'a', 'b'), dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F12 class implements the Schwefel’s Problem 2.13 benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n} (A_i - B_i)^2 - 460 \mid A_i = \sum_{j=1}^{n} a_{ij} sin(\alpha_j) + b_{ij} cos(\alpha_j), A_i = \sum_{j=1}^{n} a_{ij} sin(x_j) + b_{ij} cos(x_j)\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = -460 \mid \mathbf{x^*} = \mathbf{lpha}\).

class opytimark.markers.cec.year_2005.F13(name: Optional[str] = 'F13', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F13 class implements the Shifted Expanded Griewank’s plus Rosenbrock’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = f(x_1, x_2) + f(x_2, x_3) + \ldots + f(x_n, x_1) - 130 \mid z_i = x_i - o_i + 1\]

Domain:

The function is commonly evaluated using \(x_i \in [-3, 1] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

\(f(\mathbf{x^*}) = -130 \mid \mathbf{x^*} = \mathbf{lpha}\).

class opytimark.markers.cec.year_2005.F14(name: Optional[str] = 'F14', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F14 class implements the Shifted Rotated Expanded Scaffer’s F6 benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = f(x_1, x_2) + f(x_2, x_3) + \ldots + f(x_n, x_1) - 300 \mid z_i = x_i - o_i + 1\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = -300 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2005.F15(name: Optional[str] = 'F15', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), bias: Optional[int] = 120, dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = True)

Bases: opytimark.core.CECCompositeBenchmark

F15 class implements the Hybrid Composition 1 benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n}{w_i \ast [f_i'((\mathbf{x}-\mathbf{o_i})/ \lambda_i \ast \mathbf{M_i}) + bias_i]} + f_{bias}\]

Domain:

The function is commonly evaluated using \(x_i \in [-5, 5] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

\(f(\mathbf{x^*}) = 120 \mid \mathbf{x^*} = \mathbf{o_1}\).

class opytimark.markers.cec.year_2005.F16(name: Optional[str] = 'F16', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), bias: Optional[int] = 120, dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECCompositeBenchmark

F16 class implements the Rotated Hybrid Composition 1 benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n}{w_i \ast [f_i'((\mathbf{x}-\mathbf{o_i})/ \lambda_i \ast \mathbf{M_i}) + bias_i]} + f_{bias}\]

Domain:

The function is commonly evaluated using \(x_i \in [-5, 5] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

\(f(\mathbf{x^*}) = 120 \mid \mathbf{x^*} = \mathbf{o_1}\).

class opytimark.markers.cec.year_2005.F17(name: Optional[str] = 'F17', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), bias: Optional[int] = 120, dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECCompositeBenchmark

F17 class implements the Rotated Hybrid Composition 1 with Noise benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n}{w_i \ast [f_i'((\mathbf{x}-\mathbf{o_i})/ \lambda_i \ast \mathbf{M_i}) + bias_i]} + f_{bias}\]

Domain:

The function is commonly evaluated using \(x_i \in [-5, 5] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

\(f(\mathbf{x^*}) = 120 \mid \mathbf{x^*} = \mathbf{o_1}\).

class opytimark.markers.cec.year_2005.F18(name: Optional[str] = 'F18', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), bias: Optional[int] = 10, dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECCompositeBenchmark

F18 class implements the Rotated Hybrid Composition 2 benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n}{w_i \ast [f_i'((\mathbf{x}-\mathbf{o_i})/ \lambda_i \ast \mathbf{M_i}) + bias_i]} + f_{bias}\]

Domain:

The function is commonly evaluated using \(x_i \in [-5, 5] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

\(f(\mathbf{x^*}) = 10 \mid \mathbf{x^*} = \mathbf{o_1}\).

class opytimark.markers.cec.year_2005.F19(name: Optional[str] = 'F19', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), bias: Optional[int] = 10, dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECCompositeBenchmark

F19 class implements the Rotated Hybrid Composition 2 with Narrow Basin Global Optimum benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n}{w_i \ast [f_i'((\mathbf{x}-\mathbf{o_i})/ \lambda_i \ast \mathbf{M_i}) + bias_i]} + f_{bias}\]

Domain:

The function is commonly evaluated using \(x_i \in [-5, 5] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

\(f(\mathbf{x^*}) = 10 \mid \mathbf{x^*} = \mathbf{o_1}\).

class opytimark.markers.cec.year_2005.F20(name: Optional[str] = 'F20', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), bias: Optional[int] = 10, dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECCompositeBenchmark

F20 class implements the Rotated Hybrid Composition 2 with Global Optimum on the Bounds benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n}{w_i \ast [f_i'((\mathbf{x}-\mathbf{o_i})/ \lambda_i \ast \mathbf{M_i}) + bias_i]} + f_{bias}\]

Domain:

The function is commonly evaluated using \(x_i \in [-5, 5] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

\(f(\mathbf{x^*}) = 10 \mid \mathbf{x^*} = \mathbf{o_1}\).

class opytimark.markers.cec.year_2005.F21(name: Optional[str] = 'F21', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), bias: Optional[int] = 360, dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECCompositeBenchmark

F21 class implements the Rotated Hybrid Composition 3 benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n}{w_i \ast [f_i'((\mathbf{x}-\mathbf{o_i})/ \lambda_i \ast \mathbf{M_i}) + bias_i]} + f_{bias}\]

Domain:

The function is commonly evaluated using \(x_i \in [-5, 5] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

\(f(\mathbf{x^*}) = 360 \mid \mathbf{x^*} = \mathbf{o_1}\).

class opytimark.markers.cec.year_2005.F22(name: Optional[str] = 'F22', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), bias: Optional[int] = 360, dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECCompositeBenchmark

F22 class implements the Rotated Hybrid Composition 3 with High Condition Number Matrix benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n}{w_i \ast [f_i'((\mathbf{x}-\mathbf{o_i})/ \lambda_i \ast \mathbf{M_i}) + bias_i]} + f_{bias}\]

Domain:

The function is commonly evaluated using \(x_i \in [-5, 5] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

\(f(\mathbf{x^*}) = 360 \mid \mathbf{x^*} = \mathbf{o_1}\).

class opytimark.markers.cec.year_2005.F23(name: Optional[str] = 'F23', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), bias: Optional[int] = 360, dims: Optional[int] = 100, continuous: Optional[bool] = False, convex: Optional[bool] = True, differentiable: Optional[bool] = False, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECCompositeBenchmark

F23 class implements the Non-Continuous Rotated Hybrid Composition 3 benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n}{w_i \ast [f_i'((\mathbf{x}-\mathbf{o_i})/ \lambda_i \ast \mathbf{M_i}) + bias_i]} + f_{bias}\]

Domain:

The function is commonly evaluated using \(x_i \in [-5, 5] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

\(f(\mathbf{x^*}) \approx 360 \mid \mathbf{x^*} = \mathbf{o_1}\).

class opytimark.markers.cec.year_2005.F24(name: Optional[str] = 'F24', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), bias: Optional[int] = 260, dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECCompositeBenchmark

F24 class implements the Rotated Hybrid Composition 4 benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n}{w_i \ast [f_i'((\mathbf{x}-\mathbf{o_i})/ \lambda_i \ast \mathbf{M_i}) + bias_i]} + f_{bias}\]

Domain:

The function is commonly evaluated using \(x_i \in [-5, 5] \mid i = \{1, 2, \ldots, n\}, n \leq 100\).

Global Minima:

\(f(\mathbf{x^*}) = 260 \mid \mathbf{x^*} = \mathbf{o_1}\).

class opytimark.markers.cec.year_2005.F25(name: Optional[str] = 'F25', year: Optional[str] = '2005', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M2', 'M10', 'M30', 'M50'), bias: Optional[int] = 260, dims: Optional[int] = 100, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECCompositeBenchmark

F25 class implements the Rotated Hybrid Composition 4 without Bounds benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^{n}{w_i \ast [f_i'((\mathbf{x}-\mathbf{o_i})/ \lambda_i \ast \mathbf{M_i}) + bias_i]} + f_{bias}\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 260 \mid \mathbf{x^*} = \mathbf{o_1}\).