pycellga.problems.single_objective.continuous package

Submodules

pycellga.problems.single_objective.continuous.ackley module

class pycellga.problems.single_objective.continuous.ackley.Ackley

Bases: AbstractProblem

Ackley function implementation for optimization problems.

The Ackley function is widely used for testing optimization algorithms. It has a nearly flat outer region and a large hole at the center. The function is usually evaluated on the hypercube x_i ∈ [-32.768, 32.768], for all i = 1, 2, …, d.

None

f(x: list) → float

Calculates the Ackley function value for a given list of variables.

Notes

-32.768 ≤ xi ≤ 32.768 Global minimum at f(0, 0) = 0

f(x: list) → float

Calculate the Ackley function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Ackley function value.

Return type:

float

pycellga.problems.single_objective.continuous.bentcigar module

class pycellga.problems.single_objective.continuous.bentcigar.Bentcigar

Bases: AbstractProblem

Bentcigar function implementation for optimization problems.

The Bentcigar function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-100, 100], for all i = 1, 2, …, n.

None

f(X: list) → float

Calculates the Bentcigar function value for a given list of variables.

Notes

-100 ≤ xi ≤ 100 for i = 1,…,n Global minimum at f(0,…,0) = 0

f(X: list) → float

Calculate the Bentcigar function value for a given list of variables.

Parameters:

X (list) – A list of float variables.

Returns:

The Bentcigar function value.

Return type:

float

pycellga.problems.single_objective.continuous.bohachevsky module

class pycellga.problems.single_objective.continuous.bohachevsky.Bohachevsky

Bases: AbstractProblem

Bohachevsky function implementation for optimization problems.

The Bohachevsky function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-15, 15], for all i = 1, 2, …, n.

None

f(x: list) → float

Calculates the Bohachevsky function value for a given list of variables.

Notes

-15 ≤ xi ≤ 15 for i = 1,…,n Global minimum at f(0,…,0) = 0

f(x: list) → float

Calculate the Bohachevsky function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Bohachevsky function value.

Return type:

float

pycellga.problems.single_objective.continuous.chichinadze module

class pycellga.problems.single_objective.continuous.chichinadze.Chichinadze

Bases: AbstractProblem

Chichinadze function implementation for optimization problems.

The Chichinadze function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x, y ∈ [-30, 30].

None

f(X: list) → float

Calculates the Chichinadze function value for a given list of variables.

Notes

-30 ≤ x, y ≤ 30 Global minimum at f(5.90133, 0.5) = −43.3159

f(X: list) → float

Calculate the Chichinadze function value for a given list of variables.

Parameters:

X (list) – A list of float variables.

Returns:

The Chichinadze function value.

Return type:

float

pycellga.problems.single_objective.continuous.dropwave module

class pycellga.problems.single_objective.continuous.dropwave.Dropwave

Bases: AbstractProblem

Dropwave function for optimization problems.

The Dropwave function is a multimodal function commonly used as a performance test problem for optimization algorithms. It is defined within the bounds -5.12 ≤ xi ≤ 5.12 for i = 1, 2, and has a global minimum at f(0, 0) = -1.

f(x: list) → float

Computes the value of the Dropwave function at a given point x.

f(x: list) → float

Evaluate the Dropwave function at a given point.

Parameters:

x (list) – A list of two floats representing the coordinates [x1, x2].

Returns:

The value of the Dropwave function rounded to three decimal places.

Return type:

float

Notes

The Dropwave function is defined as:

f(x1, x2) = - (1 + cos(12 * sqrt(x1^2 + x2^2))) / (0.5 * (x1^2 + x2^2) + 2)

where x1 and x2 are the input variables.

Examples

>>> dropwave = Dropwave()
>>> dropwave.f([0, 0])
-1.0
>>> dropwave.f([1, 1])
-0.028

pycellga.problems.single_objective.continuous.fms module

class pycellga.problems.single_objective.continuous.fms.Fms

Bases: AbstractProblem

Fms function implementation for optimization problems.

The Fms function is used for testing optimization algorithms, specifically those dealing with frequency modulation sound.

None

f(x: list) → float

Calculates the Fms function value for a given list of variables.

Notes

-6.4 ≤ xi ≤ 6.35 Length of chromosomes = 6 Maximum Fitness Value = 0.01 Maximum Fitness Value Error = 10^-2

f(x: list) → float

Calculate the Fms function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Fms function value.

Return type:

float

pycellga.problems.single_objective.continuous.griewank module

class pycellga.problems.single_objective.continuous.griewank.Griewank

Bases: AbstractProblem

Griewank function implementation for optimization problems.

The Griewank function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-600, 600], for all i = 1, 2, …, n.

f(X: list) → float

Calculates the Griewank function value for a given list of variables.

Notes

-600 ≤ xi ≤ 600 for i = 1,…,n Global minimum at f(0,…,0) = 0

f(X: list) → float

Calculate the Griewank function value for a given list of variables.

Parameters:

X (list) – A list of float variables.

Returns:

The Griewank function value.

Return type:

float

pycellga.problems.single_objective.continuous.holzman module

class pycellga.problems.single_objective.continuous.holzman.Holzman

Bases: AbstractProblem

Holzman function implementation for optimization problems.

The Holzman function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-10, 10], for all i = 1, 2, …, n.

None

f(x: list) → float

Calculates the Holzman function value for a given list of variables.

Notes

-10 ≤ xi ≤ 10 for i = 1,…,n Global minimum at f(0,…,0) = 0

f(x: list) → float

Calculate the Holzman function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Holzman function value.

Return type:

float

pycellga.problems.single_objective.continuous.levy module

class pycellga.problems.single_objective.continuous.levy.Levy

Bases: AbstractProblem

Levy function implementation for optimization problems.

The Levy function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-10, 10], for all i = 1, 2, …, n.

None

f(x: list) → float

Calculates the Levy function value for a given list of variables.

Notes

-10 ≤ xi ≤ 10 for i = 1,…,n Global minimum at f(1,1) = 0

f(x: list) → float

Calculate the Levy function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Levy function value.

Return type:

float

pycellga.problems.single_objective.continuous.matyas module

class pycellga.problems.single_objective.continuous.matyas.Matyas

Bases: AbstractProblem

Matyas function implementation for optimization problems.

The Matyas function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-10, 10], for all i = 1, 2, …, n.

None

f(X: list) → float

Calculates the Matyas function value for a given list of variables.

Notes

-10 ≤ xi ≤ 10 for i = 1,…,n Global minimum at f(0,…,0) = 0

f(X: list) → float

Calculate the Matyas function value for a given list of variables.

Parameters:

X (list) – A list of float variables.

Returns:

The Matyas function value.

Return type:

float

pycellga.problems.single_objective.continuous.pow module

class pycellga.problems.single_objective.continuous.pow.Pow

Bases: AbstractProblem

Pow function implementation for optimization problems.

The Pow function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-5.0, 15.0].

None

f(x: list) → float

Calculates the Pow function value for a given list of variables.

Notes

-5.0 ≤ xi ≤ 15.0 Global minimum at f(5, 7, 9, 3, 2) = 0

f(x: list) → float

Calculate the Pow function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Pow function value.

Return type:

float

pycellga.problems.single_objective.continuous.powell module

class pycellga.problems.single_objective.continuous.powell.Powell

Bases: AbstractProblem

Powell function implementation for optimization problems.

The Powell function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-4, 5], for all i = 1, 2, …, n.

None

f(x: list) → float

Calculates the Powell function value for a given list of variables.

Notes

-4 ≤ xi ≤ 5 for i = 1,…,n Global minimum at f(0,….,0) = 0

f(x: list) → float

Calculate the Powell function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Powell function value.

Return type:

float

pycellga.problems.single_objective.continuous.rastrigin module

class pycellga.problems.single_objective.continuous.rastrigin.Rastrigin

Bases: AbstractProblem

Rastrigin function implementation for optimization problems.

The Rastrigin function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-5.12, 5.12], for all i = 1, 2, …, n.

None

f(x: list) → float

Calculates the Rastrigin function value for a given list of variables.

Notes

-5.12 ≤ xi ≤ 5.12 for i = 1,…,n Global minimum at f(0,…,0) = 0

f(x: list) → float

Calculate the Rastrigin function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Rastrigin function value.

Return type:

float

pycellga.problems.single_objective.continuous.rosenbrock module

class pycellga.problems.single_objective.continuous.rosenbrock.Rosenbrock

Bases: AbstractProblem

Rosenbrock function implementation for optimization problems.

The Rosenbrock function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-5, 10], for all i = 1, 2, …, n.

None

f(x: list) → float

Calculates the Rosenbrock function value for a given list of variables.

Notes

-5 ≤ xi ≤ 10 for i = 1,…,n Global minimum at f(1,…,1) = 0

f(x: list) → float

Calculate the Rosenbrock function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Rosenbrock function value.

Return type:

float

pycellga.problems.single_objective.continuous.rothellipsoid module

class pycellga.problems.single_objective.continuous.rothellipsoid.Rothellipsoid

Bases: AbstractProblem

Rotated Hyper-Ellipsoid function implementation for optimization problems.

The Rotated Hyper-Ellipsoid function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-100, 100], for all i = 1, 2, …, n.

None

f(x: list) → float

Calculates the Rotated Hyper-Ellipsoid function value for a given list of variables.

Notes

-100 ≤ xi ≤ 100 for i = 1,…,n Global minimum at f(0,….,0) = 0

f(x: list) → float

Calculate the Rotated Hyper-Ellipsoid function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Rotated Hyper-Ellipsoid function value.

Return type:

float

pycellga.problems.single_objective.continuous.schaffer module

class pycellga.problems.single_objective.continuous.schaffer.Schaffer

Bases: AbstractProblem

Schaffer’s Function.

This class implements the Schaffer’s function, which is a common benchmark problem for optimization algorithms. The function is defined over a multidimensional input and is used to test the performance of optimization methods.

f(X: list) → float

Calculates the value of the Schaffer’s function for a given list of input variables.

f(X: list) → float

Evaluate the Schaffer’s function at a given point.

Xlist

A list of input variables (continuous values). The length of X should be at least 2.

float

The value of the Schaffer’s function evaluated at X, rounded to three decimal places.

The Schaffer’s function is defined as: [ f(X) = sum_{i=1}^{n-1} left[ 0.5 +

rac{(sin(x_i^2 + x_{i+1}^2)^2 - 0.5)^2}{(1 + 0.001 cdot (x_i^2 + x_{i+1}^2))^2} ight]

] where ( n ) is the number of elements in X.

>>> schaffer = Schaffer()
>>> schaffer.f([1.0, 2.0])
0.554

pycellga.problems.single_objective.continuous.schaffer2 module

class pycellga.problems.single_objective.continuous.schaffer2.Schaffer2

Bases: AbstractProblem

Modified Schaffer function #2 implementation for optimization problems.

The Modified Schaffer function #2 is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-100, 100], for all i = 1, 2, …, n.

None

f(X: list) → float

Calculates the Modified Schaffer function #2 value for a given list of variables.

Notes

-100 ≤ xi ≤ 100 for i = 1,…,n Global minimum at f(0,…,0) = 0

f(X: list) → float

Calculate the Modified Schaffer function #2 value for a given list of variables.

Parameters:

X (list) – A list of float variables.

Returns:

The Modified Schaffer function #2 value.

Return type:

float

pycellga.problems.single_objective.continuous.schwefel module

class pycellga.problems.single_objective.continuous.schwefel.Schwefel

Bases: AbstractProblem

Schwefel function implementation for optimization problems.

The Schwefel function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-500, 500], for all i = 1, 2, …, n.

None

f(x: list) → float

Calculates the Schwefel function value for a given list of variables.

Notes

-500 ≤ xi ≤ 500 for i = 1,…,n Global minimum at f(420.9687,…,420.9687) = 0

f(x: list) → float

Calculate the Schwefel function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Schwefel function value.

Return type:

float

pycellga.problems.single_objective.continuous.sphere module

class pycellga.problems.single_objective.continuous.sphere.Sphere

Bases: AbstractProblem

Sphere function implementation for optimization problems.

The Sphere function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-5.12, 5.12], for all i = 1, 2, …, n.

None

f(x: list) → float

Calculates the Sphere function value for a given list of variables.

Notes

-5.12 ≤ xi ≤ 5.12 for i = 1,…,n Global minimum at f(0,…,0) = 0

f(x: list) → float

Calculate the Sphere function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Sphere function value.

Return type:

float

pycellga.problems.single_objective.continuous.styblinskitang module

class pycellga.problems.single_objective.continuous.styblinskitang.StyblinskiTang

Bases: AbstractProblem

Styblinski-Tang function implementation for optimization problems.

The Styblinski-Tang function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-5, 5], for all i = 1, 2, …, n.

None

f(x: list) → float

Calculates the Styblinski-Tang function value for a given list of variables.

Notes

-5 ≤ xi ≤ 5 for i = 1,…,n Global minimum at f(−2.903534, −2.903534) = −78.332

f(x: list) → float

Calculate the Styblinski-Tang function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Styblinski-Tang function value.

Return type:

float

pycellga.problems.single_objective.continuous.sumofdifferentpowers module

class pycellga.problems.single_objective.continuous.sumofdifferentpowers.Sumofdifferentpowers

Bases: AbstractProblem

Sum of Different Powers function implementation for optimization problems.

f(x: list) → float

Calculate the Sum of Different Powers function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Sum of Different Powers function value.

Return type:

float

pycellga.problems.single_objective.continuous.threehumps module

class pycellga.problems.single_objective.continuous.threehumps.Threehumps

Bases: AbstractProblem

Three Hump Camel function implementation for optimization problems.

The Three Hump Camel function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-5, 5], for all i = 1, 2, …, n.

None

f(x: list) → float

Calculates the Three Hump Camel function value for a given list of variables.

Notes

-5 ≤ xi ≤ 5 for i = 1,…,n Global minimum at f(0,..,0) = 0

f(x: list) → float

Calculate the Three Hump Camel function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Three Hump Camel function value.

Return type:

float

pycellga.problems.single_objective.continuous.zakharov module

class pycellga.problems.single_objective.continuous.zakharov.Zakharov

Bases: AbstractProblem

Zakharov function implementation for optimization problems.

The Zakharov function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-5, 10], for all i = 1, 2, …, n.

None

f(x: list) → float

Calculates the Zakharov function value for a given list of variables.

Notes

-5 ≤ xi ≤ 10 for i = 1,…,n Global minimum at f(0,..,0) = 0

f(x: list) → float

Calculate the Zakharov function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Zakharov function value.

Return type:

float

pycellga.problems.single_objective.continuous.zettle module

class pycellga.problems.single_objective.continuous.zettle.Zettle

Bases: AbstractProblem

Zettle function implementation for optimization problems.

The Zettle function is widely used for testing optimization algorithms. The function is usually evaluated on the hypercube x_i ∈ [-5, 5], for all i = 1, 2, …, n.

None

f(x: list) → float

Calculates the Zettle function value for a given list of variables.

Notes

-5 ≤ xi ≤ 5 for i = 1,…,n Global minimum at f(−0.0299, 0) = −0.003791

f(x: list) → float

Calculate the Zettle function value for a given list of variables.

Parameters:

x (list) – A list of float variables.

Returns:

The Zettle function value.

Return type:

float

Module contents