# N-D Test Functions P¶

class go_benchmark.Parsopoulos(dimensions=2)

Parsopoulos test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional Parsopoulos function

Global optimum: This function has inﬁnite number of global minima in R2, at points , where and

In the given domain problem, function has 12 global minima all equal to zero.

class go_benchmark.Pathological(dimensions=2)

Pathological test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional Pathological function

Global optimum: for for

class go_benchmark.Paviani(dimensions=10)

Paviani test objective function.

This class defines the Paviani 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.Penalty01(dimensions=2)

Penalty 1 test objective function.

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

Where, in this exercise:

And:

Here, represents the number of dimensions and for .

Two-dimensional Penalty 1 function

Global optimum: for for

class go_benchmark.Penalty02(dimensions=2)

Penalty 2 test objective function.

This class defines the Penalty 2 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 Penalty 2 function

Global optimum: for for

class go_benchmark.PenHolder(dimensions=2)

PenHolder test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional PenHolder function

Global optimum: for for

class go_benchmark.PermFunction01(dimensions=2)

PermFunction 1 test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional PermFunction 1 function

Global optimum: for for

class go_benchmark.PermFunction02(dimensions=2)

PermFunction 2 test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional PermFunction 2 function

Global optimum: for for

class go_benchmark.Pinter(dimensions=2)

Pinter test objective function.

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

Where, in this exercise:

Where and .

Here, represents the number of dimensions and for .

Two-dimensional Pinter function

Global optimum: for for

class go_benchmark.Plateau(dimensions=2)

Plateau test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional Plateau function

Global optimum: for for

class go_benchmark.Powell(dimensions=4)

Powell test objective function.

This class defines the Powell 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.PowerSum(dimensions=4)

Power sum test objective function.

This class defines the Power Sum 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

class go_benchmark.Price01(dimensions=2)

Price 1 test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional Price 1 function

Global optimum: for or or or

class go_benchmark.Price02(dimensions=2)

Price 2 test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional Price 2 function

Global optimum: for for

class go_benchmark.Price03(dimensions=2)

Price 3 test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional Price 3 function

Global optimum: for , , ,

class go_benchmark.Price04(dimensions=2)

Price 4 test objective function.

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

Here, represents the number of dimensions and for .

Two-dimensional Price 4 function

Global optimum: for , and

#### Previous topic

N-D Test Functions O

#### Next topic

N-D Test Functions Q