# {py:mod}`evox.problems.numerical`

```{py:module} evox.problems.numerical
```

```{autodoc2-docstring} evox.problems.numerical
:allowtitles:
```

## Submodules

```{toctree}
:titlesonly:
:maxdepth: 1

evox.problems.numerical.basic
evox.problems.numerical.cec2022
evox.problems.numerical.dtlz
```

## Package Contents

### Classes

````{list-table}
:class: autosummary longtable
:align: left

* - {py:obj}`Ackley <evox.problems.numerical.basic.Ackley>`
  - ```{autodoc2-docstring} evox.problems.numerical.basic.Ackley
    :summary:
    ```
* - {py:obj}`Griewank <evox.problems.numerical.basic.Griewank>`
  - ```{autodoc2-docstring} evox.problems.numerical.basic.Griewank
    :summary:
    ```
* - {py:obj}`Rastrigin <evox.problems.numerical.basic.Rastrigin>`
  - ```{autodoc2-docstring} evox.problems.numerical.basic.Rastrigin
    :summary:
    ```
* - {py:obj}`Rosenbrock <evox.problems.numerical.basic.Rosenbrock>`
  - ```{autodoc2-docstring} evox.problems.numerical.basic.Rosenbrock
    :summary:
    ```
* - {py:obj}`Schwefel <evox.problems.numerical.basic.Schwefel>`
  - ```{autodoc2-docstring} evox.problems.numerical.basic.Schwefel
    :summary:
    ```
* - {py:obj}`Sphere <evox.problems.numerical.basic.Sphere>`
  - ```{autodoc2-docstring} evox.problems.numerical.basic.Sphere
    :summary:
    ```
* - {py:obj}`Ellipsoid <evox.problems.numerical.basic.Ellipsoid>`
  - ```{autodoc2-docstring} evox.problems.numerical.basic.Ellipsoid
    :summary:
    ```
* - {py:obj}`CEC2022 <evox.problems.numerical.cec2022.CEC2022>`
  - ```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022
    :summary:
    ```
* - {py:obj}`DTLZ1 <evox.problems.numerical.dtlz.DTLZ1>`
  -
* - {py:obj}`DTLZ2 <evox.problems.numerical.dtlz.DTLZ2>`
  -
* - {py:obj}`DTLZ3 <evox.problems.numerical.dtlz.DTLZ3>`
  -
* - {py:obj}`DTLZ4 <evox.problems.numerical.dtlz.DTLZ4>`
  -
* - {py:obj}`DTLZ5 <evox.problems.numerical.dtlz.DTLZ5>`
  -
* - {py:obj}`DTLZ6 <evox.problems.numerical.dtlz.DTLZ6>`
  -
* - {py:obj}`DTLZ7 <evox.problems.numerical.dtlz.DTLZ7>`
  -
````

### Functions

````{list-table}
:class: autosummary longtable
:align: left

* - {py:obj}`ackley_func <evox.problems.numerical.basic.ackley_func>`
  - ```{autodoc2-docstring} evox.problems.numerical.basic.ackley_func
    :summary:
    ```
* - {py:obj}`griewank_func <evox.problems.numerical.basic.griewank_func>`
  - ```{autodoc2-docstring} evox.problems.numerical.basic.griewank_func
    :summary:
    ```
* - {py:obj}`rastrigin_func <evox.problems.numerical.basic.rastrigin_func>`
  - ```{autodoc2-docstring} evox.problems.numerical.basic.rastrigin_func
    :summary:
    ```
* - {py:obj}`rosenbrock_func <evox.problems.numerical.basic.rosenbrock_func>`
  - ```{autodoc2-docstring} evox.problems.numerical.basic.rosenbrock_func
    :summary:
    ```
* - {py:obj}`schwefel_func <evox.problems.numerical.basic.schwefel_func>`
  - ```{autodoc2-docstring} evox.problems.numerical.basic.schwefel_func
    :summary:
    ```
* - {py:obj}`sphere_func <evox.problems.numerical.basic.sphere_func>`
  - ```{autodoc2-docstring} evox.problems.numerical.basic.sphere_func
    :summary:
    ```
* - {py:obj}`ellipsoid_func <evox.problems.numerical.basic.ellipsoid_func>`
  - ```{autodoc2-docstring} evox.problems.numerical.basic.ellipsoid_func
    :summary:
    ```
````

### API

`````{py:class} Ackley(a: float = 20.0, b: float = 0.2, c: float = 2 * torch.pi, **kwargs)
:canonical: evox.problems.numerical.basic.Ackley

Bases: {py:obj}`evox.problems.numerical.basic.ShiftAffineNumericalProblem`

```{autodoc2-docstring} evox.problems.numerical.basic.Ackley
```

```{rubric} Initialization
```

```{autodoc2-docstring} evox.problems.numerical.basic.Ackley.__init__
```

````{py:method} _true_evaluate(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.basic.Ackley._true_evaluate

```{autodoc2-docstring} evox.problems.numerical.basic.Ackley._true_evaluate
```

````

`````

`````{py:class} Griewank(**kwargs)
:canonical: evox.problems.numerical.basic.Griewank

Bases: {py:obj}`evox.problems.numerical.basic.ShiftAffineNumericalProblem`

```{autodoc2-docstring} evox.problems.numerical.basic.Griewank
```

```{rubric} Initialization
```

```{autodoc2-docstring} evox.problems.numerical.basic.Griewank.__init__
```

````{py:method} _true_evaluate(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.basic.Griewank._true_evaluate

```{autodoc2-docstring} evox.problems.numerical.basic.Griewank._true_evaluate
```

````

`````

`````{py:class} Rastrigin(**kwargs)
:canonical: evox.problems.numerical.basic.Rastrigin

Bases: {py:obj}`evox.problems.numerical.basic.ShiftAffineNumericalProblem`

```{autodoc2-docstring} evox.problems.numerical.basic.Rastrigin
```

```{rubric} Initialization
```

```{autodoc2-docstring} evox.problems.numerical.basic.Rastrigin.__init__
```

````{py:method} _true_evaluate(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.basic.Rastrigin._true_evaluate

```{autodoc2-docstring} evox.problems.numerical.basic.Rastrigin._true_evaluate
```

````

`````

`````{py:class} Rosenbrock(**kwargs)
:canonical: evox.problems.numerical.basic.Rosenbrock

Bases: {py:obj}`evox.problems.numerical.basic.ShiftAffineNumericalProblem`

```{autodoc2-docstring} evox.problems.numerical.basic.Rosenbrock
```

```{rubric} Initialization
```

```{autodoc2-docstring} evox.problems.numerical.basic.Rosenbrock.__init__
```

````{py:method} _true_evaluate(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.basic.Rosenbrock._true_evaluate

```{autodoc2-docstring} evox.problems.numerical.basic.Rosenbrock._true_evaluate
```

````

`````

`````{py:class} Schwefel(**kwargs)
:canonical: evox.problems.numerical.basic.Schwefel

Bases: {py:obj}`evox.problems.numerical.basic.ShiftAffineNumericalProblem`

```{autodoc2-docstring} evox.problems.numerical.basic.Schwefel
```

```{rubric} Initialization
```

```{autodoc2-docstring} evox.problems.numerical.basic.Schwefel.__init__
```

````{py:method} _true_evaluate(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.basic.Schwefel._true_evaluate

```{autodoc2-docstring} evox.problems.numerical.basic.Schwefel._true_evaluate
```

````

`````

`````{py:class} Sphere(**kwargs)
:canonical: evox.problems.numerical.basic.Sphere

Bases: {py:obj}`evox.problems.numerical.basic.ShiftAffineNumericalProblem`

```{autodoc2-docstring} evox.problems.numerical.basic.Sphere
```

```{rubric} Initialization
```

```{autodoc2-docstring} evox.problems.numerical.basic.Sphere.__init__
```

````{py:method} _true_evaluate(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.basic.Sphere._true_evaluate

```{autodoc2-docstring} evox.problems.numerical.basic.Sphere._true_evaluate
```

````

`````

`````{py:class} Ellipsoid(**kwargs)
:canonical: evox.problems.numerical.basic.Ellipsoid

Bases: {py:obj}`evox.problems.numerical.basic.ShiftAffineNumericalProblem`

```{autodoc2-docstring} evox.problems.numerical.basic.Ellipsoid
```

```{rubric} Initialization
```

```{autodoc2-docstring} evox.problems.numerical.basic.Ellipsoid.__init__
```

````{py:method} _true_evaluate(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.basic.Ellipsoid._true_evaluate

```{autodoc2-docstring} evox.problems.numerical.basic.Ellipsoid._true_evaluate
```

````

`````

`````{py:class} CEC2022(problem_number: int, dimension: int, device: torch.device | None = None)
:canonical: evox.problems.numerical.cec2022.CEC2022

Bases: {py:obj}`evox.core.Problem`

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022
```

```{rubric} Initialization
```

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.__init__
```

````{py:method} shift(x: torch.Tensor, offset: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.shift

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.shift
```

````

````{py:method} rotate(x: torch.Tensor, M: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.rotate

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.rotate
```

````

````{py:method} cut(x: torch.Tensor, Gp: typing.List[float], sh_flag: bool, rot_flag: bool, offset: torch.Tensor, M: torch.Tensor) -> typing.List[torch.Tensor]
:canonical: evox.problems.numerical.cec2022.CEC2022.cut

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.cut
```

````

````{py:method} sr_func_rate(x: torch.Tensor, sh_rate: float, sh_flag: bool, rot_flag: bool, offset: torch.Tensor, M: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.sr_func_rate

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.sr_func_rate
```

````

````{py:method} cf_cal(x: torch.Tensor, fit: typing.List[torch.Tensor], delta: typing.List[int], bias: typing.List[int]) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.cf_cal

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.cf_cal
```

````

````{py:method} cec2022_f1(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.cec2022_f1

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.cec2022_f1
```

````

````{py:method} cec2022_f2(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.cec2022_f2

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.cec2022_f2
```

````

````{py:method} cec2022_f3(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.cec2022_f3

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.cec2022_f3
```

````

````{py:method} cec2022_f4(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.cec2022_f4

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.cec2022_f4
```

````

````{py:method} cec2022_f5(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.cec2022_f5

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.cec2022_f5
```

````

````{py:method} cec2022_f6(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.cec2022_f6

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.cec2022_f6
```

````

````{py:method} cec2022_f7(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.cec2022_f7

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.cec2022_f7
```

````

````{py:method} cec2022_f8(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.cec2022_f8

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.cec2022_f8
```

````

````{py:method} cec2022_f9(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.cec2022_f9

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.cec2022_f9
```

````

````{py:method} cec2022_f10(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.cec2022_f10

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.cec2022_f10
```

````

````{py:method} cec2022_f11(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.cec2022_f11

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.cec2022_f11
```

````

````{py:method} cec2022_f12(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.cec2022_f12

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.cec2022_f12
```

````

````{py:method} levy_func(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.levy_func

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.levy_func
```

````

````{py:method} bent_cigar_func(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.bent_cigar_func

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.bent_cigar_func
```

````

````{py:method} hgbat_func(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.hgbat_func

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.hgbat_func
```

````

````{py:method} katsuura_func(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.katsuura_func

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.katsuura_func
```

````

````{py:method} modified_schwefel_func(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.modified_schwefel_func

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.modified_schwefel_func
```

````

````{py:method} schaffer_F7_func(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.schaffer_F7_func

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.schaffer_F7_func
```

````

````{py:method} escaffer6_func(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.escaffer6_func

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.escaffer6_func
```

````

````{py:method} happycat_func(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.happycat_func

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.happycat_func
```

````

````{py:method} grie_rosen_func(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.grie_rosen_func

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.grie_rosen_func
```

````

````{py:method} discus_func(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.discus_func

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.discus_func
```

````

````{py:method} ellips_func(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.ellips_func

```{autodoc2-docstring} evox.problems.numerical.cec2022.CEC2022.ellips_func
```

````

````{py:method} evaluate(pop: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.cec2022.CEC2022.evaluate

````

`````

`````{py:class} DTLZ1(d: int = 7, m: int = 3, ref_num: int = 1000)
:canonical: evox.problems.numerical.dtlz.DTLZ1

Bases: {py:obj}`evox.problems.numerical.dtlz.DTLZ`

````{py:method} evaluate(X: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.dtlz.DTLZ1.evaluate

````

`````

`````{py:class} DTLZ2(d: int = 12, m: int = 3, ref_num: int = 1000)
:canonical: evox.problems.numerical.dtlz.DTLZ2

Bases: {py:obj}`evox.problems.numerical.dtlz.DTLZ`

````{py:method} evaluate(X: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.dtlz.DTLZ2.evaluate

````

````{py:method} pf()
:canonical: evox.problems.numerical.dtlz.DTLZ2.pf

````

`````

`````{py:class} DTLZ3(d: int = 12, m: int = 3, ref_num: int = 1000)
:canonical: evox.problems.numerical.dtlz.DTLZ3

Bases: {py:obj}`evox.problems.numerical.dtlz.DTLZ2`

````{py:method} evaluate(X: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.dtlz.DTLZ3.evaluate

````

`````

`````{py:class} DTLZ4(d: int = 12, m: int = 3, ref_num: int = 1000)
:canonical: evox.problems.numerical.dtlz.DTLZ4

Bases: {py:obj}`evox.problems.numerical.dtlz.DTLZ2`

````{py:method} evaluate(X: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.dtlz.DTLZ4.evaluate

````

`````

`````{py:class} DTLZ5(d: int = 12, m: int = 3, ref_num: int = 1000)
:canonical: evox.problems.numerical.dtlz.DTLZ5

Bases: {py:obj}`evox.problems.numerical.dtlz.DTLZ`

````{py:method} evaluate(X: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.dtlz.DTLZ5.evaluate

````

````{py:method} pf()
:canonical: evox.problems.numerical.dtlz.DTLZ5.pf

````

`````

`````{py:class} DTLZ6(d: int = 12, m: int = 3, ref_num: int = 1000)
:canonical: evox.problems.numerical.dtlz.DTLZ6

Bases: {py:obj}`evox.problems.numerical.dtlz.DTLZ`

````{py:method} evaluate(X: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.dtlz.DTLZ6.evaluate

````

````{py:method} pf()
:canonical: evox.problems.numerical.dtlz.DTLZ6.pf

````

`````

`````{py:class} DTLZ7(d: int = 21, m: int = 3, ref_num: int = 1000)
:canonical: evox.problems.numerical.dtlz.DTLZ7

Bases: {py:obj}`evox.problems.numerical.dtlz.DTLZ`

````{py:method} evaluate(X: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.dtlz.DTLZ7.evaluate

````

````{py:method} pf()
:canonical: evox.problems.numerical.dtlz.DTLZ7.pf

````

`````

````{py:function} ackley_func(a: float, b: float, c: float, x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.basic.ackley_func

```{autodoc2-docstring} evox.problems.numerical.basic.ackley_func
```
````

````{py:function} griewank_func(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.basic.griewank_func

```{autodoc2-docstring} evox.problems.numerical.basic.griewank_func
```
````

````{py:function} rastrigin_func(x: torch.Tensor) -> torch.Tensor
:canonical: evox.problems.numerical.basic.rastrigin_func

```{autodoc2-docstring} evox.problems.numerical.basic.rastrigin_func
```
````

````{py:function} rosenbrock_func(x)
:canonical: evox.problems.numerical.basic.rosenbrock_func

```{autodoc2-docstring} evox.problems.numerical.basic.rosenbrock_func
```
````

````{py:function} schwefel_func(x)
:canonical: evox.problems.numerical.basic.schwefel_func

```{autodoc2-docstring} evox.problems.numerical.basic.schwefel_func
```
````

````{py:function} sphere_func(x)
:canonical: evox.problems.numerical.basic.sphere_func

```{autodoc2-docstring} evox.problems.numerical.basic.sphere_func
```
````

````{py:function} ellipsoid_func(x: torch.Tensor)
:canonical: evox.problems.numerical.basic.ellipsoid_func

```{autodoc2-docstring} evox.problems.numerical.basic.ellipsoid_func
```
````