# N-D Test Functions S¶

class go_benchmark.Salomon(dimensions=2)

Salomon test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional Salomon function

Global optimum: for for

class go_benchmark.Sargan(dimensions=2)

Sargan test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional Sargan function

Global optimum: for for

class go_benchmark.Schaffer01(dimensions=2)

Schaffer 1 test objective function.

This class defines the Schaffer 1 global optimization problem. This is a multimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Schaffer 1 function

Global optimum: for for

class go_benchmark.Schaffer02(dimensions=2)

Schaffer 2 test objective function.

This class defines the Schaffer 2 global optimization problem. This is a multimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Schaffer 2 function

Global optimum: for for

class go_benchmark.Schaffer03(dimensions=2)

Schaffer 3 test objective function.

This class defines the Schaffer 3 global optimization problem. This is a multimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Schaffer 3 function

Global optimum: for

class go_benchmark.Schaffer04(dimensions=2)

Schaffer 4 test objective function.

This class defines the Schaffer 4 global optimization problem. This is a multimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Schaffer 4 function

Global optimum: for

class go_benchmark.SchmidtVetters(dimensions=3)

Schmidt-Vetters test objective function.

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

Here, represents the number of dimensions and for .

Global optimum: for for

class go_benchmark.Schwefel01(dimensions=2)

Schwefel 1 test objective function.

This class defines the Schwefel 1 global optimization problem. This is a unimodal minimization problem defined as follows:

Where, in this exercise, .

Here, represents the number of dimensions and for .

Two-dimensional Schwefel 1 function

Global optimum: for for

class go_benchmark.Schwefel02(dimensions=2)

Schwefel 2 test objective function.

This class defines the Schwefel 2 global optimization problem. This is a unimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Schwefel 2 function

Global optimum: for for

class go_benchmark.Schwefel04(dimensions=2)

Schwefel 4 test objective function.

This class defines the Schwefel 4 global optimization problem. This is a multimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Schwefel 4 function

Global optimum: for for

class go_benchmark.Schwefel06(dimensions=2)

Schwefel 6 test objective function.

This class defines the Schwefel 6 global optimization problem. This is a unimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Schwefel 6 function

Global optimum: for

class go_benchmark.Schwefel20(dimensions=2)

Schwefel 20 test objective function.

This class defines the Schwefel 20 global optimization problem. This is a unimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Schwefel 20 function

Global optimum: for for

class go_benchmark.Schwefel21(dimensions=2)

Schwefel 21 test objective function.

This class defines the Schwefel 21 global optimization problem. This is a unimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Schwefel 21 function

Global optimum: for for

class go_benchmark.Schwefel22(dimensions=2)

Schwefel 22 test objective function.

This class defines the Schwefel 22 global optimization problem. This is a multimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Schwefel 22 function

Global optimum: for for

class go_benchmark.Schwefel26(dimensions=2)

Schwefel 26 test objective function.

This class defines the Schwefel 26 global optimization problem. This is a multimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Schwefel 26 function

Global optimum: for for

class go_benchmark.Schwefel36(dimensions=2)

Schwefel 36 test objective function.

This class defines the Schwefel 36 global optimization problem. This is a multimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Schwefel 36 function

Global optimum: for

class go_benchmark.Shekel05(dimensions=4)

Shekel 5 test objective function.

This class defines the Shekel 5 global optimization problem. This is a multimodal minimization problem defined as follows:

Where, in this exercise:

Here, represents the number of dimensions and for .

Global optimum: for for

class go_benchmark.Shekel07(dimensions=4)

Shekel 7 test objective function.

This class defines the Shekel 7 global optimization problem. This is a multimodal minimization problem defined as follows:

Where, in this exercise:

Here, represents the number of dimensions and for .

Global optimum: for for

class go_benchmark.Shekel10(dimensions=4)

Shekel 10 test objective function.

This class defines the Shekel 10 global optimization problem. This is a multimodal minimization problem defined as follows:

Where, in this exercise:

Here, represents the number of dimensions and for .

Global optimum: for for

class go_benchmark.Shubert01(dimensions=2)

Shubert 1 test objective function.

This class defines the Shubert 1 global optimization problem. This is a multimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Shubert 1 function

Global optimum: for (and many others).

class go_benchmark.Shubert03(dimensions=2)

Shubert 3 test objective function.

This class defines the Shubert 3 global optimization problem. This is a multimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Shubert 3 function

Global optimum: for (and many others).

class go_benchmark.Shubert04(dimensions=2)

Shubert 4 test objective function.

This class defines the Shubert 4 global optimization problem. This is a multimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Shubert 4 function

Global optimum: for (and many others).

class go_benchmark.SineEnvelope(dimensions=2)

SineEnvelope test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional SineEnvelope function

Global optimum: for for

class go_benchmark.SixHumpCamel(dimensions=2)

Six Hump Camel test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional Six Hump Camel function

Global optimum: for or

class go_benchmark.Sodp(dimensions=2)

Sodp test objective function.

This class defines the Sum Of Different Powers global optimization problem. This is a multimodal minimization problem defined as follows:

Here, represents the number of dimensions and for .

Two-dimensional Sum Of Different Powers function

Global optimum: for for

class go_benchmark.Sphere(dimensions=2)

Sphere test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional Sphere function

Global optimum: for for

class go_benchmark.Step(dimensions=2)

Step test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional Step function

Global optimum: for for

class go_benchmark.Stochastic(dimensions=2)

Stochastic test objective function.

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

The variable is a random variable uniformly distributed in .

Here, represents the number of dimensions and for .

Two-dimensional Stochastic function

Global optimum: for for

class go_benchmark.StretchedV(dimensions=2)

StretchedV test objective function.

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

Where, in this exercise:

Here, represents the number of dimensions and for .

Two-dimensional StretchedV function

Global optimum: for when .

class go_benchmark.StyblinskiTang(dimensions=2)

StyblinskiTang test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional Styblinski-Tang function

Global optimum: for for

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