opytimark.markers.cec.year_2010

Please refer to the technical report for more information: http://titan.csit.rmit.edu.au/~e46507/publications/lsgo-cec10.pdf

class opytimark.markers.cec.year_2010.F1(name: Optional[str] = 'F1', year: Optional[str] = '2010', 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 Elliptic’s benchmarking function.

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

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F2(name: Optional[str] = 'F2', year: Optional[str] = '2010', 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

F2 class implements the Shifted Rastrigin’s benchmarking function.

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

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F3(name: Optional[str] = 'F3', year: Optional[str] = '2010', 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

F3 class implements the Shifted Ackley’s benchmarking function.

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

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F4(name: Optional[str] = 'F4', year: Optional[str] = '2010', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M'), dims: Optional[int] = 1000, group_size: Optional[int] = 50, 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 Single-group Shifted and m-rotated Elliptic’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = f_{rot\_elliptic}[z(P_1:P_m)] * 10^6 + f_{elliptic}[z(P_{m+1}:P_n)] \mid z_i = x_i - o_i, z_i = (x_i - o_i) \ast M_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F5(name: Optional[str] = 'F5', year: Optional[str] = '2010', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M'), dims: Optional[int] = 1000, group_size: Optional[int] = 50, 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 Single-group Shifted and m-rotated Rastrigin’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = f_{rot\_rastrigin}[z(P_1:P_m)] * 10^6 + f_{rastrigin}[z(P_{m+1}:P_n)] \mid z_i = x_i - o_i, z_i = (x_i - o_i) \ast M_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F6(name: Optional[str] = 'F6', year: Optional[str] = '2010', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M'), dims: Optional[int] = 1000, group_size: Optional[int] = 50, 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 Single-group Shifted and m-rotated Ackley’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = f_{rot\_ackley}[z(P_1:P_m)] * 10^6 + f_{ackley}[z(P_{m+1}:P_n)] \mid z_i = x_i - o_i, z_i = (x_i - o_i) \ast M_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F7(name: Optional[str] = 'F7', year: Optional[str] = '2010', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 1000, group_size: Optional[int] = 50, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = False, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F7 class implements the Single-group Shifted and m-rotated Schwefel’s Problem 1.2 benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = f_{schwefel}[z(P_1:P_m)] * 10^6 + f_{sphere}[z(P_{m+1}:P_n)] \mid z_i = x_i - o_i, z_i = (x_i - o_i) \ast M_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F8(name: Optional[str] = 'F8', year: Optional[str] = '2010', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 1000, group_size: Optional[int] = 50, 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 Single-group Shifted and m-rotated Rosenbrock’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = f_{rosenbrock}[z(P_1:P_m)] * 10^6 + f_{sphere}[z(P_{m+1}:P_n)] \mid z_i = x_i - o_i, z_i = (x_i - o_i) \ast M_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F9(name: Optional[str] = 'F9', year: Optional[str] = '2010', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M'), dims: Optional[int] = 1000, group_size: Optional[int] = 50, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = False, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F9 class implements the D/2m-group Shifted and m-rotated Elliptic’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{k=1}^{\frac{n}{2m}} f_{rot\_elliptic}[z(P_{(k-1)*m+1}:P_{k*m})] * 10^6 + f_{elliptic}[z(P_{\frac{n}{2}+1}:P_n)] \mid z_i = x_i - o_i, z_i = (x_i - o_i) \ast M_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F10(name: Optional[str] = 'F10', year: Optional[str] = '2010', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M'), dims: Optional[int] = 1000, group_size: Optional[int] = 50, 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 D/2m-group Shifted and m-rotated Rastrigin’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{k=1}^{\frac{n}{2m}} f_{rot\_rastrigin}[z(P_{(k-1)*m+1}:P_{k*m})] * 10^6 + f_{rastrigin}[z(P_{\frac{n}{2}+1}:P_n)] \mid z_i = x_i - o_i, z_i = (x_i - o_i) \ast M_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F11(name: Optional[str] = 'F11', year: Optional[str] = '2010', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M'), dims: Optional[int] = 1000, group_size: Optional[int] = 50, 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 D/2m-group Shifted and m-rotated Ackley’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{k=1}^{\frac{n}{2m}} f_{rot\_ackley}[z(P_{(k-1)*m+1}:P_{k*m})] * 10^6 + f_{ackley}[z(P_{\frac{n}{2}+1}:P_n)] \mid z_i = x_i - o_i, z_i = (x_i - o_i) \ast M_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F12(name: Optional[str] = 'F12', year: Optional[str] = '2010', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 1000, group_size: Optional[int] = 50, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = False, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F12 class implements the D/2m-group Shifted and m-rotated Schwefel’s Problem 1.2 benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{k=1}^{\frac{n}{2m}} f_{schwefel}[z(P_{(k-1)*m+1}:P_{k*m})] * 10^6 + f_{sphere}[z(P_{\frac{n}{2}+1}:P_n)] \mid z_i = x_i - o_i, z_i = (x_i - o_i) \ast M_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F13(name: Optional[str] = 'F13', year: Optional[str] = '2010', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 1000, group_size: Optional[int] = 50, 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 D/2m-group Shifted and m-rotated Rosenbrock benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{k=1}^{\frac{n}{2m}} f_{rosenbrock}[z(P_{(k-1)*m+1}:P_{k*m})] * 10^6 + f_{sphere}[z(P_{\frac{n}{2}+1}:P_n)] \mid z_i = x_i - o_i, z_i = (x_i - o_i) \ast M_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F14(name: Optional[str] = 'F14', year: Optional[str] = '2010', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M'), dims: Optional[int] = 1000, group_size: Optional[int] = 50, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = False, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F14 class implements the D/m-group Shifted and m-rotated Elliptic’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{k=1}^{\frac{n}{m}} f_{rot\_elliptic}[z(P_{(k-1)*m+1}:P_{k*m})] \mid z_i = (x_i - o_i) \ast M_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F15(name: Optional[str] = 'F15', year: Optional[str] = '2010', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M'), dims: Optional[int] = 1000, group_size: Optional[int] = 50, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F15 class implements the D/m-group Shifted and m-rotated Rastrigin’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{k=1}^{\frac{n}{m}} f_{rot\_elliptic}[z(P_{(k-1)*m+1}:P_{k*m})] \mid z_i = (x_i - o_i) \ast M_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F16(name: Optional[str] = 'F16', year: Optional[str] = '2010', auxiliary_data: Optional[Tuple[str, Ellipsis]] = ('o', 'M'), dims: Optional[int] = 1000, group_size: Optional[int] = 50, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F16 class implements the D/m-group Shifted and m-rotated Ackley’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{k=1}^{\frac{n}{m}} f_{rot\_elliptic}[z(P_{(k-1)*m+1}:P_{k*m})] \mid z_i = (x_i - o_i) \ast M_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F17(name: Optional[str] = 'F17', year: Optional[str] = '2010', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 1000, group_size: Optional[int] = 50, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = False, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F17 class implements the D/m-group Shifted Schwefel’s Problem 1.2 benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{k=1}^{\frac{n}{m}} f_{rot\_elliptic}[z(P_{(k-1)*m+1}:P_{k*m})] \mid z_i = x_i - o_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F18(name: Optional[str] = 'F18', year: Optional[str] = '2010', auxiliary_data: Optional[Tuple[str, Ellipsis]] = 'o', dims: Optional[int] = 1000, group_size: Optional[int] = 50, continuous: Optional[bool] = True, convex: Optional[bool] = True, differentiable: Optional[bool] = True, multimodal: Optional[bool] = True, separable: Optional[bool] = False)

Bases: opytimark.core.CECBenchmark

F18 class implements the D/m-group Shifted Rosenbrock’s benchmarking function.

\[f(\mathbf{x}) = f(x_1, x_2, \ldots, x_n) = \sum_{k=1}^{\frac{n}{m}} f_{rot\_elliptic}[z(P_{(k-1)*m+1}:P_{k*m})] \mid z_i = x_i - o_i\]

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o} + 1\).

class opytimark.markers.cec.year_2010.F19(name: Optional[str] = 'F19', year: Optional[str] = '2010', 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

F19 class implements the Shifted Schwefel’s Problem 1.2 benchmarking function.

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

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o}\).

class opytimark.markers.cec.year_2010.F20(name: Optional[str] = 'F20', year: Optional[str] = '2010', 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

F20 class implements the Shifted Rosenbrock’s benchmarking function.

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

Domain:

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

Global Minima:

\(f(\mathbf{x^*}) = 0 \mid \mathbf{x^*} = \mathbf{o} + 1\).