The problems are used to evaluate the performance of the surrogate models. Now, we are implementing a set of problems, they are used for modeling, unconstrained optimization, constrained optimization, and multi-objective optimization.

Note

Till now, we only implement problems for unconstrained single-objective optimization, unconstrained multi-fidelity single-objective optimization, constrained single-objective optimization.

Problems class structure

Now, we want to introduce the basic Functions class:

class Functions(ABC):
 @staticmethod
 def f(x: np.ndarray) -> np.ndarray:
   ...

 @staticmethod
 def f_der(x: np.ndarray) -> np.ndarray:
   ...
 @staticmethod
 def hf(x: np.ndarray) -> np.ndarray:
   ...

 @staticmethod
 def lf(x: np.ndarray, factor: float) -> np.ndarray:
   ...
 @staticmethod
 def hf_der(x: np.ndarray) -> np.ndarray:
   ...
 @staticmethod
 def lf_der(x: np.ndarray) -> np.ndarray:
   ...
 @staticmethod
 def f_cons(x: np.ndarray) -> np.ndarray:
   ...

 @staticmethod
 def hf_cons(x: np.ndarray) -> np.ndarray:
   ...

 @staticmethod
 def lf_cons(x: np.ndarray) -> np.ndarray:
   ...

Single fidelity problems

Example for single fidelity function

Here, an example of using function sf_functions is given. The Forrester function Forrester is used to illustrate:

import numpy as np
from mfpml.problems.sf_functions import Forrester
from mfpml.design_of_experiment.sf_samplers import LatinHyperCube

# Initialize the single-fidelity function
function = Forrester()
print("Input domain:", function.input_domain)

# Sample input space using Latin Hypercube Sampling
sampler = LatinHyperCube(design_space=function.input_domain)
sample_x = sampler.get_samples(num_samples=2, seed=1)
print("Sampled inputs:", sample_x)

# Evaluate the function
sample_y = function.f(sample_x)
print("Function outputs:", sample_y)

Implemented single fidelity Functions

Methods	API of sampling methods
Forrester	Forrester
Branin	Branin
Hartmann3	Hartmann3
Hartmann6	Hartmann6
Sixhump	Sixhump
GoldPrice	GoldPrice
Sasena	Sasena
Ackley	Ackley
AckleyN2	AckleyN2
Thevenot	Thevenot

Multi fidelity problems

Example for multi fidelity function

Here, an example of using function mf_functions is given. The Forrester_1a function is used to illustrate:

import numpy as np
from mfpml.problems.mf_functions import Forrester_1b
from mfpml.design_of_experiment.mf_samplers import MFSobolSequence

# Initialize the multi-fidelity function
function = Forrester_1b()
design_space = function.input_domain
print("Input domain:", design_space)

# Sample input space using Multi-Fidelity Sobol Sequence
sampler = MFSobolSequence(design_space=design_space, num_fidelity=2, nested=True)
samples = sampler.get_samples(num_samples=[4, 11])
print("Sampled inputs at two fidelities:", samples)

# Evaluate the function
sample_y = function(samples)
print("Function outputs:", sample_y)

Implemented multi fidelity Functions

Methods	API of sampling methods
Forrester_1a	Forrester_1a
Forrester_1b	Forrester_1b
Forrester_1c	Forrester_1c
mf_Hartmann3	mf_Hartmann3
mf_Hartmann6	mf_Hartmann6
mf_Sixhump	mf_Sixhump
mf_Discontinuous	mf_Discontinuous
PhaseShiftedOscillations	PhaseShiftedOscillations
ContinuousNonlinearCorrelation1D	ContinuousNonlinearCorrelation1D