mfpml.problems

mfpml.problems.functions

class FunctionWrapper(function, args=())

Bases: object

Object to wrap user’s function, allowing pick lability

function wrapper

Parameters:

• function (any) – function

• args (tuple, optional) – additional parameters , by default ()

__init__(function, args=())

function wrapper

Parameters:

• function (any) – function

• args (tuple, optional) – additional parameters , by default ()

class Functions

Bases: ABC

_abc_impl = <_abc._abc_data object>

property _get_dimension: int

Get dimension of the function

Returns:

dimension – dimension of the problem

Return type:

int

property _get_low_fidelity: list

Get names of low fidelity functions :returns: name – name list of low fidelity functions :rtype: list

property _input_domain: ndarray

property _optimum: float

returns: optimum – name of the class :rtype: float

property _optimum_variable: list

returns: optimum_variable – Best design scheme :rtype: list

static f(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y – responses from single fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

static f_cons(x)

constrained functions of high-fidelity function

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

f_cons – constrained responses from the single fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

static f_der(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

f_der – responses from the single fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented. Subclasses should implement this method.

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

static hf_cons(x)

constrained functions of high-fidelity function

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

hf_cons – constrained responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

static hf_der(x)

derivative of high fidelity function

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

hf_der – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = None

static lf(x, factor=None)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

static lf_cons(x)

constrained functions of low-fidelity function

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

lf_cons – constrained responses from the low-fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

static lf_der(x)

derivative of high fidelity function

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

lf_der – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: list = None

num_cons: int = None

num_dim: int = None

optimum: float = None

optimum_scheme: list = None

mfpml.problems.multifidelity_functions

class ContinuousNonlinearCorrelation1D(num_dim=1)

Bases: MultiFidelityFunctions

Continuous Nonlinear Correlation 1D

Parameters:

MultiFidelityFunctions (class) – base class

_abc_impl = <_abc._abc_data object>

design_space: dict = {'x': [0.0, 1.0]}

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[0., 1.]])

static lf(x)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: list = None

num_cons: int = 0

num_dim: int = 1

num_obj: int = 1

optimum: float = None

optimum_scheme: list = None

class Forrester_1a(num_dim=1, cost=[1.0, 0.2])

Bases: MultiFidelityFunctions

_abc_impl = <_abc._abc_data object>

cost_ratio: list = None

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[0., 1.]])

static lf(x, factor=None)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: bool = True

num_cons: int = 0

num_dim: int = 1

num_obj: int = 1

optimum: float = -6.02074

optimum_scheme: list = [0.757248757841856]

class Forrester_1b(num_dim=1, cost=[1.0, 0.2])

Bases: MultiFidelityFunctions

Forrester function from Jicheng

_abc_impl = <_abc._abc_data object>

cost_ratio: list = None

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[0., 1.]])

static lf(x, factor=None)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: bool = True

num_cons: int = 0

num_dim: int = 1

num_obj: int = 1

optimum: float = -6.02074

optimum_scheme: list = [0.757248757841856]

class Forrester_1c(num_dim=1, cost=[1.0, 0.2])

Bases: MultiFidelityFunctions

Forrester function

_abc_impl = <_abc._abc_data object>

cost_ratio: list = None

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[0., 1.]])

static lf(x, factor=None)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: bool = True

num_cons: int = 0

num_dim: int = 1

num_obj: int = 1

optimum: float = -6.02074

optimum_scheme: list = [0.757248757841856]

class MultiFidelityFunctions

Bases: Functions

_abc_impl = <_abc._abc_data object>

classmethod is_dim_compatible(num_dim)

class PhaseShiftedOscillations(num_dim=1)

Bases: MultiFidelityFunctions

Phase shifted oscillations

Parameters:

MultiFidelityFunctions (class) – based class

_abc_impl = <_abc._abc_data object>

design_space: dict = {'x': [0.0, 1.0]}

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[0., 1.]])

static lf(x)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: list = None

num_cons: int = 0

num_dim: int = 1

num_obj: int = 1

optimum: float = None

optimum_scheme: list = None

class mf_Bohachevsky(num_dim=2)

Bases: MultiFidelityFunctions

multi-fidelity Bohachevsky function

Parameters:

MultiFidelityFunctions (class) – base class

_abc_impl = <_abc._abc_data object>

design_space: dict = {'x1': [-5.0, 5.0], 'x2': [-5.0, 5.0]}

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[-5.,  5.],        [-5.,  5.]])

static lf(x)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: bool = True

num_cons: int = 0

num_dim: int = 2

num_obj: int = 1

optimum: float = 0.0

optimum_scheme: list = [0.0, 0.0]

class mf_Booth(num_dim=2)

Bases: MultiFidelityFunctions

multi-fidelity Booth function,

Parameters:

MultiFidelityFunctions (class) – base class

_abc_impl = <_abc._abc_data object>

design_space: dict = {'x1': [-10.0, 10.0], 'x2': [-10.0, 10.0]}

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[-10.,  10.],        [-10.,  10.]])

static lf(x)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: bool = True

num_cons: int = 0

num_dim: int = 2

num_obj: int = 1

optimum: float = 0.0

optimum_scheme: list = [1.0, 3.0]

class mf_Borehole(num_dim=8)

Bases: MultiFidelityFunctions

multi-fidelity Borehole function,

Parameters:

MultiFidelityFunctions (class) – base class

_abc_impl = <_abc._abc_data object>

static base(x, a, b)

Return type:

ndarray

design_space: dict = {'Hl': [700, 820], 'Hu': [990, 1110], 'Kw': [9855, 12045], 'L': [1120, 1680], 'Tl': [63.1, 116], 'Tu': [63070, 115600], 'r': [100, 50000], 'rw': [0.05, 0.15]}

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[5.0000e-02, 1.5000e-01],        [1.0000e+02, 5.0000e+04],        [6.3070e+04, 1.1560e+05],        [9.9000e+02, 1.1100e+03],        [6.3100e+01, 1.1600e+02],        [7.0000e+02, 8.2000e+02],        [1.1200e+03, 1.6800e+03],        [9.8550e+03, 1.2045e+04]])

static lf(x)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: bool = True

num_cons: int = 0

num_dim: int = 8

num_obj: int = 1

optimum: float = None

optimum_scheme: list = None

class mf_CurrinExp(num_dim=2)

Bases: MultiFidelityFunctions

multi-fidelity CurrinExp function,

Parameters:

MultiFidelityFunctions (class) – base class

_abc_impl = <_abc._abc_data object>

design_space: dict = {'x1': [0, 1], 'x2': [0, 1]}

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[0, 1],        [0, 1]])

static lf(x)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: bool = True

num_cons: int = 0

num_dim: int = 2

num_obj: int = 1

optimum: float = None

optimum_scheme: list = None

class mf_Discontinuous(num_dim=1)

Bases: MultiFidelityFunctions

multi-fidelity discontinuous function,

Parameters:

MultiFidelityFunctions (class) – multifidelity function class

_abc_impl = <_abc._abc_data object>

design_space: dict = {'x': [0.0, 1.0]}

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[0., 1.]])

static lf(x)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: list = None

num_cons: int = 0

num_dim: int = 1

num_obj: int = 1

optimum: float = None

optimum_scheme: list = None

class mf_Hartman3(num_dim=3, cost=[1.0, 0.2])

Bases: MultiFidelityFunctions

multi fidelity Hartman3 function

Parameters:

MultiFidelityFunctions (parent class) – multi-fidelity function

Returns:

_description_

Return type:

_type_

_abc_impl = <_abc._abc_data object>

design_space: dict = {'x1': [0.0, 1.0], 'x2': [0.0, 1.0], 'x3': [0.0, 1.0]}

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[0., 1.],        [0., 1.],        [0., 1.]])

static lf(x, factor=None)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: list = ['low']

num_cons: int = 0

num_dim: int = 3

num_obj: int = 1

optimum: float = -3.86278214782076

optimum_scheme: list = [0.1, 0.55592003, 0.85218259]

class mf_Hartman6(num_dim=6, cost=[1.0, 0.1])

Bases: MultiFidelityFunctions

Initialization

__init__(num_dim=6, cost=[1.0, 0.1])

Initialization

_abc_impl = <_abc._abc_data object>

design_space: dict = {'x1': [0.0, 1.0], 'x2': [0.0, 1.0], 'x3': [0.0, 1.0], 'x4': [0.0, 1.0], 'x5': [0.0, 1.0], 'x6': [0.0, 1.0]}

static hf(x)

Return type:

ndarray

input_domain: ndarray = array([[0., 1.],        [0., 1.],        [0., 1.],        [0., 1.],        [0., 1.],        [0., 1.]])

static lf(x)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: list = None

num_cons: int = 0

num_dim: int = 6

num_obj: int = 1

optimum: float = -1.200677785132358

optimum_scheme: list = [0.20168952, 0.15001069, 0.47687398, 0.27533243, 0.31165162, 0.65730054]

class mf_Himmelblau(num_dim=2)

Bases: MultiFidelityFunctions

multi-fidelity Himmelblau function,

Parameters:

MultiFidelityFunctions (class) – base class

_abc_impl = <_abc._abc_data object>

design_space: dict = {'x1': [-4.0, 4.0], 'x2': [-4.0, 4.0]}

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[-4.,  4.],        [-4.,  4.]])

static lf(x)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: bool = True

num_cons: int = 0

num_dim: int = 2

num_obj: int = 1

optimum: float = None

optimum_scheme: list = None

class mf_Park91A(num_dim=4)

Bases: MultiFidelityFunctions

multi-fidelity Park91A function,

Parameters:

MultiFidelityFunctions (class) – base class

_abc_impl = <_abc._abc_data object>

design_space: dict = {'x1': [0.0, 1.0], 'x2': [0.0, 1.0], 'x3': [0.0, 1.0], 'x4': [0.0, 1.0]}

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[0., 1.],        [0., 1.],        [0., 1.],        [0., 1.]])

static lf(x)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: bool = True

num_cons: int = 0

num_dim: int = 4

num_obj: int = 1

optimum: float = None

optimum_scheme: list = None

class mf_Park91B(num_dim=4)

Bases: MultiFidelityFunctions

multi-fidelity Park91B function,

Parameters:

MultiFidelityFunctions (class) – base class

_abc_impl = <_abc._abc_data object>

design_space: dict = {'x1': [0.0, 1.0], 'x2': [0.0, 1.0], 'x3': [0.0, 1.0], 'x4': [0.0, 1.0]}

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[0., 1.],        [0., 1.],        [0., 1.],        [0., 1.]])

static lf(x)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: bool = True

num_cons: int = 0

num_dim: int = 4

num_obj: int = 1

optimum: float = None

optimum_scheme: list = None

class mf_Sixhump(num_dim=2, cost=[1.0, 0.2])

Bases: MultiFidelityFunctions

Initialization

__init__(num_dim=2, cost=[1.0, 0.2])

Initialization

_abc_impl = <_abc._abc_data object>

design_space: dict = {'x1': [-2.0, 2.0], 'x2': [-2.0, 2.0]}

static hf(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y_hf – responses from the high fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[-2.,  2.],        [-2.,  2.]])

static lf(x)

low fidelity function

Parameters:

• x (np.ndarray) – design scheme that needs to be evaluated

• factor (floatS) – a factor to control generating low fidelity functions

Returns:

y_lf – responses from the low functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

low_fidelity: list = None

num_cons: int = 0

num_dim: int = 2

num_obj: int = 1

optimum: float = -1.0316

optimum_scheme: list = [[0.0898, -0.7126], [-0.0898, 0.7126]]

mfpml.problems.singlefidelity_functions

class Ackley(num_dim, a=20, b=0.2, c=6.283185307179586)

Bases: Functions

Parameters:

• num_dim (int) – number of dimension

• a (float) – Parameters

• b (float) – Parameters

• c (float) – Parameters

__init__(num_dim, a=20, b=0.2, c=6.283185307179586)

Parameters:

• num_dim (int) – number of dimension

• a (float) – Parameters

• b (float) – Parameters

• c (float) – Parameters

__update_parameters()

update the class variable information

Return type:

None

_abc_impl = <_abc._abc_data object>

f(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y – responses from single fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

get_param()

Return type:

dict[str, float]

input_domain: ndarray = None

classmethod is_dim_compatible(d)

low_fidelity: List = None

num_cons: int = 0

num_dim: int = None

num_obj: int = 1

optimum: float = None

optimum_scheme: List = None

class AckleyN2(num_dim=2)

Bases: Functions

_abc_impl = <_abc._abc_data object>

static f(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y – responses from single fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[-32.,  32.],        [-32.,  32.]])

classmethod is_dim_compatible(d)

low_fidelity: List = None

num_cons: int = 0

num_dim: int = 2

num_obj: int = 1

optimum: float = [0.0, 0.0]

optimum_scheme: List = -200.0

class Branin(num_dim=2)

Bases: Functions

Initialization

__init__(num_dim=2)

Initialization

_abc_impl = <_abc._abc_data object>

static f(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y – responses from single fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[-5., 10.],        [ 0., 15.]])

classmethod is_dim_compatible(num_dim)

Return type:

int

low_fidelity: List = None

num_cons: int = 0

num_dim: int = 2

num_obj: int = 1

optimum: float = 0.397887

optimum_scheme: List = [[-3.141592653589793, 12.275], [3.141592653589793, 2.275], [9.42478, 2.475]]

class Forrester(num_dim=1)

Bases: Functions

Forrester function

_abc_impl = <_abc._abc_data object>

cost_ratio: List = None

static f(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y – responses from single fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[0., 1.]])

classmethod is_dim_compatible(num_dim)

Return type:

Any

low_fidelity: bool = None

num_cons: int = 0

num_dim: int = 1

num_obj: int = 1

optimum: float = -6.02074

optimum_scheme: List = [0.757248757841856]

class GoldPrice(num_dim=2)

Bases: Functions

Initialization

__init__(num_dim=2)

Initialization

_abc_impl = <_abc._abc_data object>

static f(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y – responses from single fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[-2.,  2.],        [-2.,  2.]])

classmethod is_dim_compatible(num_dim)

low_fidelity: List = None

num_cons: int = 0

num_dim: int = 2

num_obj: int = 1

optimum: float = 3.0

optimum_scheme: List = [0.0, 1.0]

class Hartman3(num_dim=3)

Bases: Functions

Initialization

__init__(num_dim=3)

Initialization

_abc_impl = <_abc._abc_data object>

static f(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y – responses from single fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[0., 1.],        [0., 1.],        [0., 1.]])

classmethod is_dim_compatible(num_dim)

low_fidelity: List = None

num_cons: int = 0

num_dim: int = 3

num_obj: int = 1

optimum: float = -3.86278214782076

optimum_scheme: List = [0.1, 0.55592003, 0.85218259]

class Hartman6(num_dim=6)

Bases: Functions

Initialization

__init__(num_dim=6)

Initialization

_abc_impl = <_abc._abc_data object>

static f(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y – responses from single fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[0., 1.],        [0., 1.],        [0., 1.],        [0., 1.],        [0., 1.],        [0., 1.]])

classmethod is_dim_compatible(num_dim)

low_fidelity: list = None

num_cons: int = 0

num_dim: int = 6

num_obj: int = 1

optimum: float = -1.200677785132358

optimum_scheme: list = [0.20168952, 0.15001069, 0.47687398, 0.27533243, 0.31165162, 0.65730054]

class Sasena(num_dim=2)

Bases: Functions

Initialization

__init__(num_dim=2)

Initialization

_abc_impl = <_abc._abc_data object>

static f(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y – responses from single fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[0., 5.],        [0., 5.]])

classmethod is_dim_compatible(num_dim)

low_fidelity: List = None

num_cons: int = 0

num_dim: int = 2

num_obj: int = 1

optimum: float = -1.4565

optimum_scheme: List = [2.5044, 2.5778]

class Sixhump(num_dim=2)

Bases: Functions

Initialization

__init__(num_dim=2)

Initialization

_abc_impl = <_abc._abc_data object>

static f(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y – responses from single fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = array([[-3.,  3.],        [-2.,  2.]])

classmethod is_dim_compatible(num_dim)

low_fidelity: List = None

num_cons: int = 0

num_dim: int = 2

num_obj: int = 1

optimum: float = -1.0316

optimum_scheme: List = [[0.0898, -0.7126], [-0.0898, 0.7126]]

class Thevenot(num_dim, m=5.0, beta=15)

Bases: Functions

Parameters:

• num_dim (int) – dimension of Thevenot function

• m (float)

• beta (float)

__init__(num_dim, m=5.0, beta=15)

Parameters:

• num_dim (int) – dimension of Thevenot function

• m (float)

• beta (float)

__update_parameters()

_abc_impl = <_abc._abc_data object>

f(x)

Parameters:

x (np.ndarray) – design scheme that needs to be evaluated

Returns:

y – responses from single fidelity functions

Return type:

np.ndarray

Raises:

NotImplementedError – Raised when not implemented.

input_domain: ndarray = None

classmethod is_dim_compatible(d)

Return type:

Any

low_fidelity: list = None

num_cons: int = 0

num_dim: int = None

num_obj: int = 1

optimum: float = None

optimum_scheme: list = None