sgpp::optimization::FuzzyExtensionPrincipleViaOptimization Class Reference

Zadeh's fuzzy extension principle by solving optimization problems for each \(\alpha\) level. More...

#include <FuzzyExtensionPrincipleViaOptimization.hpp>

Inheritance diagram for sgpp::optimization::FuzzyExtensionPrincipleViaOptimization:

Public Member Functions
void	clone (std::unique_ptr< FuzzyExtensionPrinciple > &clone) const override
	FuzzyExtensionPrincipleViaOptimization (const base::ScalarFunction &f, size_t numberOfAlphaSegments=DEFAULT_NUMBER_OF_ALPHA_SEGMENTS)
	Constructor.
	FuzzyExtensionPrincipleViaOptimization (const FuzzyExtensionPrincipleViaOptimization &other)
	Copy constructor.
	FuzzyExtensionPrincipleViaOptimization (const optimizer::UnconstrainedOptimizer &optimizer, size_t numberOfAlphaSegments=DEFAULT_NUMBER_OF_ALPHA_SEGMENTS)
	Constructor with custom optimization algorithm.
	~FuzzyExtensionPrincipleViaOptimization () override
	Destructor.
Public Member Functions inherited from sgpp::optimization::FuzzyExtensionPrinciple
FuzzyInterval *	apply (const std::vector< FuzzyInterval * > &xFuzzy)
	Apply the fuzzy extension principle to fuzzy input intervals.
	FuzzyExtensionPrinciple (const base::ScalarFunction &f, size_t numberOfAlphaSegments=DEFAULT_NUMBER_OF_ALPHA_SEGMENTS)
	Constructor.
	FuzzyExtensionPrinciple (const FuzzyExtensionPrinciple &other)
	Copy constructor.
const base::DataVector &	getAlphaLevels () const
const std::vector< base::DataVector > &	getMaximumPoints () const
const base::DataVector &	getMaximumValues () const
const std::vector< base::DataVector > &	getMinimumPoints () const
const base::DataVector &	getMinimumValues () const
size_t	getNumberOfAlphaSegments () const
const std::vector< base::DataVector > &	getOptimizationDomainsLowerBounds () const
const std::vector< base::DataVector > &	getOptimizationDomainsUpperBounds () const
void	setNumberOfAlphaSegments (size_t numberOfAlphaSegments)
virtual	~FuzzyExtensionPrinciple ()
	Destructor.

Protected Member Functions
void	optimizeForSingleAlphaLevel (size_t j, base::DataVector &minimumPoint, double &minimumValue, base::DataVector &maximumPoint, double &maximumValue) override
	Solve the minimization/maximization problem for a single \(\alpha\) level.
void	prepareApply () override
	Custom preparation method that is called before the parallelized optimizeForSingleAlphaLevel calls.

Protected Attributes
optimizer::MultiStart	defaultOptimizer
	default optimization algorithm
std::unique_ptr< base::ScalarFunctionGradient >	fGradient
	objective function gradient
std::unique_ptr< base::ScalarFunctionGradient >	fGradientScaled
	scaled objective gradient (confidence interval to unit hyper-cube)
std::unique_ptr< base::ScalarFunctionHessian >	fHessian
	objective function Hessian
std::unique_ptr< base::ScalarFunctionHessian >	fHessianScaled
	scaled objective Hessian (confidence interval to unit hyper-cube)
std::unique_ptr< base::ScalarFunction >	fScaled
	scaled objective function (confidence interval to unit hyper-cube)
std::unique_ptr< optimizer::UnconstrainedOptimizer >	optimizer
	optimization algorithm
Protected Attributes inherited from sgpp::optimization::FuzzyExtensionPrinciple
base::DataVector	alphaLevels
	number of \(\alpha\) segments
std::unique_ptr< base::ScalarFunction >	f
	function through which to propagate the uncertainties
size_t	m
	number of \(\alpha\) segments
std::vector< base::DataVector >	maximumPoints
	vector of maximum points (after apply call)
base::DataVector	maximumValues
	vector of maximum function values (after apply call)
std::vector< base::DataVector >	minimumPoints
	vector of minimum points (after apply call)
base::DataVector	minimumValues
	vector of minimum function values (after apply call)
std::vector< base::DataVector >	optimizationDomainsLowerBounds
	vector of lower bounds of input confidence intervals (after apply call)
std::vector< base::DataVector >	optimizationDomainsUpperBounds
	vector of upper bounds of input confidence intervals (after apply call)

Additional Inherited Members
Static Public Attributes inherited from sgpp::optimization::FuzzyExtensionPrinciple
static const size_t	DEFAULT_NUMBER_OF_ALPHA_SEGMENTS = 10
	default number of \(\alpha\) segments

Detailed Description

Zadeh's fuzzy extension principle by solving optimization problems for each \(\alpha\) level.

Constructor & Destructor Documentation

FuzzyExtensionPrincipleViaOptimization() [1/3]

sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::FuzzyExtensionPrincipleViaOptimization ( const base::ScalarFunction &  f, size_t  numberOfAlphaSegments = DEFAULT_NUMBER_OF_ALPHA_SEGMENTS  )

explicit

Constructor.

By default, MultiStart is used as optimization algorithm.

Parameters

f	function through which to propagate the uncertainties
numberOfAlphaSegments	number of \(\alpha\) segments

References sgpp::optimization::optimizer::MultiStart::clone(), defaultOptimizer, and optimizer.

FuzzyExtensionPrincipleViaOptimization() [2/3]

sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::FuzzyExtensionPrincipleViaOptimization ( const optimizer::UnconstrainedOptimizer &  optimizer, size_t  numberOfAlphaSegments = DEFAULT_NUMBER_OF_ALPHA_SEGMENTS  )

explicit

Constructor with custom optimization algorithm.

Parameters

optimizer	optimization algorithm and function through which to propagate the uncertainties
numberOfAlphaSegments	number of \(\alpha\) segments

References sgpp::optimization::FuzzyExtensionPrinciple::clone(), fGradient, fHessian, and optimizer.

FuzzyExtensionPrincipleViaOptimization() [3/3]

sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::FuzzyExtensionPrincipleViaOptimization

(

const FuzzyExtensionPrincipleViaOptimization &

other

)

Copy constructor.

Parameters

other

other fuzzy extension principle

References fGradient, fGradientScaled, fHessian, fHessianScaled, fScaled, and optimizer.

~FuzzyExtensionPrincipleViaOptimization()

sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::~FuzzyExtensionPrincipleViaOptimization ( )

override

Destructor.

Member Function Documentation

clone()

void sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::clone ( std::unique_ptr< FuzzyExtensionPrinciple > &  clone ) const

overridevirtual

Parameters

[out]

clone

pointer to cloned object

Implements sgpp::optimization::FuzzyExtensionPrinciple.

Reimplemented in sgpp::optimization::FuzzyExtensionPrincipleViaTransformation, and sgpp::optimization::FuzzyExtensionPrincipleViaVertexMethod.

References clone().

Referenced by clone().

optimizeForSingleAlphaLevel()

void sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::optimizeForSingleAlphaLevel ( size_t  j, base::DataVector &  minimumPoint, double &  minimumValue, base::DataVector &  maximumPoint, double &  maximumValue  )

overrideprotectedvirtual

Solve the minimization/maximization problem for a single \(\alpha\) level.

Parameters

[in]	j	index of \(\alpha\) level
[out]	minimumPoint	minimum point
[out]	minimumValue	minimum function value
[out]	maximumPoint	maximum point
[out]	maximumValue	maximum function value

Implements sgpp::optimization::FuzzyExtensionPrinciple.

Reimplemented in sgpp::optimization::FuzzyExtensionPrincipleViaTransformation, and sgpp::optimization::FuzzyExtensionPrincipleViaVertexMethod.

References sgpp::optimization::FuzzyExtensionPrinciple::f, fGradientScaled, fHessianScaled, fScaled, sgpp::optimization::FuzzyExtensionPrinciple::m, sgpp::optimization::FuzzyExtensionPrinciple::maximumPoints, sgpp::optimization::FuzzyExtensionPrinciple::minimumPoints, sgpp::optimization::FuzzyExtensionPrinciple::optimizationDomainsLowerBounds, sgpp::optimization::FuzzyExtensionPrinciple::optimizationDomainsUpperBounds, optimizer, sgpp::base::ScaledScalarFunction::setLowerBounds(), sgpp::base::ScaledScalarFunctionGradient::setLowerBounds(), sgpp::base::ScaledScalarFunctionHessian::setLowerBounds(), sgpp::base::ScaledScalarFunction::setUpperBounds(), sgpp::base::ScaledScalarFunctionGradient::setUpperBounds(), sgpp::base::ScaledScalarFunctionHessian::setUpperBounds(), sgpp::base::ScaledScalarFunction::setValueFactor(), sgpp::base::ScaledScalarFunctionGradient::setValueFactor(), and sgpp::base::ScaledScalarFunctionHessian::setValueFactor().

prepareApply()

void sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::prepareApply ( )

overrideprotectedvirtual

Custom preparation method that is called before the parallelized optimizeForSingleAlphaLevel calls.

Reimplemented from sgpp::optimization::FuzzyExtensionPrinciple.

Reimplemented in sgpp::optimization::FuzzyExtensionPrincipleViaTransformation, and sgpp::optimization::FuzzyExtensionPrincipleViaVertexMethod.

References sgpp::optimization::FuzzyExtensionPrinciple::f, fGradient, fGradientScaled, fHessian, fHessianScaled, and fScaled.

Member Data Documentation

defaultOptimizer

optimizer::MultiStart sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::defaultOptimizer

protected

default optimization algorithm

Referenced by FuzzyExtensionPrincipleViaOptimization().

fGradient

std::unique_ptr<base::ScalarFunctionGradient> sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::fGradient

protected

objective function gradient

Referenced by FuzzyExtensionPrincipleViaOptimization(), FuzzyExtensionPrincipleViaOptimization(), and prepareApply().

fGradientScaled

std::unique_ptr<base::ScalarFunctionGradient> sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::fGradientScaled

protected

scaled objective gradient (confidence interval to unit hyper-cube)

Referenced by FuzzyExtensionPrincipleViaOptimization(), optimizeForSingleAlphaLevel(), and prepareApply().

fHessian

std::unique_ptr<base::ScalarFunctionHessian> sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::fHessian

protected

objective function Hessian

Referenced by FuzzyExtensionPrincipleViaOptimization(), FuzzyExtensionPrincipleViaOptimization(), and prepareApply().

fHessianScaled

std::unique_ptr<base::ScalarFunctionHessian> sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::fHessianScaled

protected

scaled objective Hessian (confidence interval to unit hyper-cube)

Referenced by FuzzyExtensionPrincipleViaOptimization(), optimizeForSingleAlphaLevel(), and prepareApply().

fScaled

std::unique_ptr<base::ScalarFunction> sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::fScaled

protected

scaled objective function (confidence interval to unit hyper-cube)

Referenced by FuzzyExtensionPrincipleViaOptimization(), optimizeForSingleAlphaLevel(), and prepareApply().

optimizer

std::unique_ptr<optimizer::UnconstrainedOptimizer> sgpp::optimization::FuzzyExtensionPrincipleViaOptimization::optimizer

protected

optimization algorithm

Referenced by FuzzyExtensionPrincipleViaOptimization(), FuzzyExtensionPrincipleViaOptimization(), FuzzyExtensionPrincipleViaOptimization(), and optimizeForSingleAlphaLevel().

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The documentation for this class was generated from the following files:

• optimization/src/sgpp/optimization/fuzzy/FuzzyExtensionPrincipleViaOptimization.hpp
• optimization/src/sgpp/optimization/fuzzy/FuzzyExtensionPrincipleViaOptimization.cpp