#include <itkCMAEvolutionStrategyOptimizer.h>

Detailed Description

A Covariance Matrix Adaptation Evolution Strategy Optimizer.

Based on the work by Hansen:

http://www.bionik.tu-berlin.de/user/niko/
Hansen and Ostermeier, "Completely Derandomized Self-Adaptation in Evolution Strategies", Evolutionary Computation, 9(2), pp. 159-195 (2001).
See also the Matlab code, cmaes.m, which you can download from the website mentioned above.

Definition at line 49 of file itkCMAEvolutionStrategyOptimizer.h.

Inheritance diagram for itk::CMAEvolutionStrategyOptimizer:

[legend]

Public Types
using	ConstPointer = SmartPointer< const Self >

using	Pointer = SmartPointer< Self >

using	ScaledCostFunctionType = ScaledSingleValuedCostFunction

using	ScalesType = NonLinearOptimizer::ScalesType

using	Self = CMAEvolutionStrategyOptimizer

enum	StopConditionType { MetricError , MaximumNumberOfIterations , PositionToleranceMin , PositionToleranceMax , ValueTolerance , ZeroStepLength , Unknown }

using	Superclass = ScaledSingleValuedNonLinearOptimizer

Public Types inherited from itk::ScaledSingleValuedNonLinearOptimizer
using	ConstPointer = SmartPointer< const Self >

using	Pointer = SmartPointer< Self >

using	ScaledCostFunctionPointer = ScaledCostFunctionType::Pointer

using	ScaledCostFunctionType = ScaledSingleValuedCostFunction

using	ScalesType = NonLinearOptimizer::ScalesType

using	Self = ScaledSingleValuedNonLinearOptimizer

using	Superclass = SingleValuedNonLinearOptimizer

Public Member Functions
virtual const char *	GetClassName () const

virtual unsigned long	GetCurrentIteration () const

virtual double	GetCurrentMaximumD () const

virtual double	GetCurrentMinimumD () const

virtual const ParametersType &	GetCurrentScaledStep ()

virtual double	GetCurrentSigma () const

virtual double	GetCurrentStepLength () const

virtual MeasureType	GetCurrentValue () const

virtual double	GetInitialSigma () const

virtual double	GetMaximumDeviation () const

virtual unsigned long	GetMaximumNumberOfIterations () const

virtual double	GetMinimumDeviation () const

virtual unsigned int	GetNumberOfParents () const

virtual unsigned int	GetPopulationSize () const

virtual double	GetPositionToleranceMax () const

virtual double	GetPositionToleranceMin () const

virtual const char *	GetRecombinationWeightsPreset () const

virtual double	GetSigmaDecayA () const

virtual double	GetSigmaDecayAlpha () const

virtual const StopConditionType &	GetStopCondition ()

virtual unsigned int	GetUpdateBDPeriod () const

virtual bool	GetUseCovarianceMatrixAdaptation () const

virtual bool	GetUseDecayingSigma () const

virtual double	GetValueTolerance () const

	ITK_DISALLOW_COPY_AND_MOVE (CMAEvolutionStrategyOptimizer)

virtual void	ResumeOptimization ()

virtual void	SetInitialSigma (double _arg)

virtual void	SetMaximumDeviation (double _arg)

virtual void	SetMaximumNumberOfIterations (unsigned long _arg)

virtual void	SetMinimumDeviation (double _arg)

virtual void	SetNumberOfParents (unsigned int _arg)

virtual void	SetPopulationSize (unsigned int _arg)

virtual void	SetPositionToleranceMax (double _arg)

virtual void	SetPositionToleranceMin (double _arg)

virtual void	SetRecombinationWeightsPreset (const char *_arg)

virtual void	SetSigmaDecayA (double _arg)

virtual void	SetSigmaDecayAlpha (double _arg)

virtual void	SetUpdateBDPeriod (unsigned int _arg)

virtual void	SetUseCovarianceMatrixAdaptation (bool _arg)

virtual void	SetUseDecayingSigma (bool _arg)

virtual void	SetValueTolerance (double _arg)

void	StartOptimization () override

virtual void	StopOptimization ()

Public Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
virtual const char *	GetClassName () const

const ParametersType &	GetCurrentPosition () const override

virtual bool	GetMaximize () const

virtual const ScaledCostFunctionType *	GetScaledCostFunction ()

virtual const ParametersType &	GetScaledCurrentPosition ()

bool	GetUseScales () const

virtual void	InitializeScales ()

	ITK_DISALLOW_COPY_AND_MOVE (ScaledSingleValuedNonLinearOptimizer)

virtual void	MaximizeOff ()

virtual void	MaximizeOn ()

void	SetCostFunction (CostFunctionType *costFunction) override

virtual void	SetMaximize (bool _arg)

virtual void	SetUseScales (bool arg)

Static Public Member Functions
static Pointer	New ()

Static Public Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
static Pointer	New ()

Protected Types
using	CovarianceMatrixType = Array2D< double >

using	EigenValueMatrixType = vnl_diag_matrix< double >

using	MeasureContainerType = std::vector< MeasureIndexPairType >

using	MeasureHistoryType = std::deque< MeasureType >

using	MeasureIndexPairType = std::pair< MeasureType, unsigned int >

using	ParameterContainerType = std::vector< ParametersType >

using	RandomGeneratorType = itk::Statistics::MersenneTwisterRandomVariateGenerator

using	RecombinationWeightsType = Array< double >

Protected Member Functions
virtual void	AdvanceOneStep ()

	CMAEvolutionStrategyOptimizer ()

virtual void	FixNumericalErrors ()

virtual void	GenerateOffspring ()

virtual void	InitializeBCD ()

virtual void	InitializeConstants ()

virtual void	InitializeProgressVariables ()

void	PrintSelf (std::ostream &os, Indent indent) const override

virtual void	SortCostFunctionValues ()

virtual bool	TestConvergence (bool firstCheck)

virtual void	UpdateBD ()

virtual void	UpdateC ()

virtual void	UpdateConjugateEvolutionPath ()

virtual void	UpdateEvolutionPath ()

virtual void	UpdateHeaviside ()

virtual void	UpdateSigma ()

	~CMAEvolutionStrategyOptimizer () override=default

Protected Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
virtual void	GetScaledDerivative (const ParametersType &parameters, DerivativeType &derivative) const

virtual MeasureType	GetScaledValue (const ParametersType &parameters) const

virtual void	GetScaledValueAndDerivative (const ParametersType &parameters, MeasureType &value, DerivativeType &derivative) const

void	PrintSelf (std::ostream &os, Indent indent) const override

	ScaledSingleValuedNonLinearOptimizer ()

void	SetCurrentPosition (const ParametersType &param) override

virtual void	SetScaledCurrentPosition (const ParametersType &parameters)

	~ScaledSingleValuedNonLinearOptimizer () override=default

Protected Attributes
CovarianceMatrixType	m_B

CovarianceMatrixType	m_C

ParametersType	m_ConjugateEvolutionPath

double	m_ConjugateEvolutionPathConstant { 0.0 }

MeasureContainerType	m_CostFunctionValues

double	m_CovarianceMatrixAdaptationConstant { 0.0 }

double	m_CovarianceMatrixAdaptationWeight { 0.0 }

unsigned long	m_CurrentIteration { 0 }

double	m_CurrentMaximumD { 1.0 }

double	m_CurrentMinimumD { 1.0 }

ParametersType	m_CurrentNormalizedStep

ParametersType	m_CurrentScaledStep

double	m_CurrentSigma { 0.0 }

MeasureType	m_CurrentValue { 0.0 }

EigenValueMatrixType	m_D

double	m_EffectiveMu { 0.0 }

ParametersType	m_EvolutionPath

double	m_EvolutionPathConstant { 0.0 }

double	m_ExpectationNormNormalDistribution { 0.0 }

bool	m_Heaviside { false }

unsigned long	m_HistoryLength { 0 }

MeasureHistoryType	m_MeasureHistory

ParameterContainerType	m_NormalizedSearchDirs

unsigned int	m_NumberOfParents { 0 }

unsigned int	m_PopulationSize { 0 }

RandomGeneratorType::Pointer	m_RandomGenerator { RandomGeneratorType::GetInstance() }

RecombinationWeightsType	m_RecombinationWeights

ParameterContainerType	m_SearchDirs

double	m_SigmaDampingConstant { 0.0 }

bool	m_Stop { false }

StopConditionType	m_StopCondition { Unknown }

unsigned int	m_UpdateBDPeriod { 1 }

bool	m_UseCovarianceMatrixAdaptation { true }

Protected Attributes inherited from itk::ScaledSingleValuedNonLinearOptimizer
ScaledCostFunctionPointer	m_ScaledCostFunction

ParametersType	m_ScaledCurrentPosition

Private Attributes
double	m_InitialSigma { 1.0 }

double	m_MaximumDeviation { std::numeric_limits<double>::max() }

unsigned long	m_MaximumNumberOfIterations { 100 }

double	m_MinimumDeviation { 0.0 }

double	m_PositionToleranceMax { 1e8 }

double	m_PositionToleranceMin { 1e-12 }

std::string	m_RecombinationWeightsPreset { "superlinear" }

double	m_SigmaDecayA { 50 }

double	m_SigmaDecayAlpha { 0.602 }

bool	m_UseDecayingSigma { false }

double	m_ValueTolerance { 1e-12 }

Member Typedef Documentation

◆ ConstPointer

using itk::CMAEvolutionStrategyOptimizer::ConstPointer = SmartPointer<const Self>

Definition at line 57 of file itkCMAEvolutionStrategyOptimizer.h.

◆ CovarianceMatrixType

using itk::CMAEvolutionStrategyOptimizer::CovarianceMatrixType = Array2D<double>

protected

Definition at line 230 of file itkCMAEvolutionStrategyOptimizer.h.

◆ EigenValueMatrixType

using itk::CMAEvolutionStrategyOptimizer::EigenValueMatrixType = vnl_diag_matrix<double>

protected

Definition at line 229 of file itkCMAEvolutionStrategyOptimizer.h.

◆ MeasureContainerType

using itk::CMAEvolutionStrategyOptimizer::MeasureContainerType = std::vector<MeasureIndexPairType>

protected

Definition at line 235 of file itkCMAEvolutionStrategyOptimizer.h.

◆ MeasureHistoryType

using itk::CMAEvolutionStrategyOptimizer::MeasureHistoryType = std::deque<MeasureType>

protected

Definition at line 232 of file itkCMAEvolutionStrategyOptimizer.h.

◆ MeasureIndexPairType

using itk::CMAEvolutionStrategyOptimizer::MeasureIndexPairType = std::pair<MeasureType, unsigned int>

protected

Definition at line 234 of file itkCMAEvolutionStrategyOptimizer.h.

◆ ParameterContainerType

using itk::CMAEvolutionStrategyOptimizer::ParameterContainerType = std::vector<ParametersType>

protected

Definition at line 231 of file itkCMAEvolutionStrategyOptimizer.h.

◆ Pointer

using itk::CMAEvolutionStrategyOptimizer::Pointer = SmartPointer<Self>

Definition at line 56 of file itkCMAEvolutionStrategyOptimizer.h.

◆ RandomGeneratorType

using itk::CMAEvolutionStrategyOptimizer::RandomGeneratorType = itk::Statistics::MersenneTwisterRandomVariateGenerator

protected

Definition at line 237 of file itkCMAEvolutionStrategyOptimizer.h.

◆ RecombinationWeightsType

using itk::CMAEvolutionStrategyOptimizer::RecombinationWeightsType = Array<double>

protected

Definition at line 228 of file itkCMAEvolutionStrategyOptimizer.h.

◆ ScaledCostFunctionType

using itk::ScaledSingleValuedNonLinearOptimizer::ScaledCostFunctionType = ScaledSingleValuedCostFunction

Definition at line 86 of file itkScaledSingleValuedNonLinearOptimizer.h.

◆ ScalesType

using itk::ScaledSingleValuedNonLinearOptimizer::ScalesType = NonLinearOptimizer::ScalesType

Definition at line 85 of file itkScaledSingleValuedNonLinearOptimizer.h.

◆ Self

using itk::CMAEvolutionStrategyOptimizer::Self = CMAEvolutionStrategyOptimizer

Definition at line 54 of file itkCMAEvolutionStrategyOptimizer.h.

◆ Superclass

using itk::CMAEvolutionStrategyOptimizer::Superclass = ScaledSingleValuedNonLinearOptimizer

Definition at line 55 of file itkCMAEvolutionStrategyOptimizer.h.

Member Enumeration Documentation

◆ StopConditionType

enum itk::CMAEvolutionStrategyOptimizer::StopConditionType

Enumerator
MetricError
MaximumNumberOfIterations
PositionToleranceMin
PositionToleranceMax
ValueTolerance
ZeroStepLength
Unknown

Definition at line 69 of file itkCMAEvolutionStrategyOptimizer.h.

Constructor & Destructor Documentation

◆ CMAEvolutionStrategyOptimizer()

itk::CMAEvolutionStrategyOptimizer::CMAEvolutionStrategyOptimizer ( )

protected

Constructor

◆ ~CMAEvolutionStrategyOptimizer()

itk::CMAEvolutionStrategyOptimizer::~CMAEvolutionStrategyOptimizer ( )

overrideprotecteddefault

Destructor

Member Function Documentation

◆ AdvanceOneStep()

virtual void itk::CMAEvolutionStrategyOptimizer::AdvanceOneStep ( )

protectedvirtual

Compute the m_CurrentPosition = m(g+1), m_CurrentValue, and m_CurrentScaledStep

◆ FixNumericalErrors()

virtual void itk::CMAEvolutionStrategyOptimizer::FixNumericalErrors ( )

protectedvirtual

Some checks, to be sure no numerical errors occur

Adjust too low/high deviation that otherwise would violate m_MinimumDeviation or m_MaximumDeviation.
Adjust too low deviations that otherwise would cause numerical problems (because of finite precision of the datatypes).
Check if "main axis standard deviation sigma*D(i,i) has effect" (?) (just another check whether the steps are not too small)
Adjust step size in case of equal function values (flat fitness)
Adjust step size in case of equal best function values over history

◆ GenerateOffspring()

virtual void itk::CMAEvolutionStrategyOptimizer::GenerateOffspring ( )

protectedvirtual

GenerateOffspring: Fill m_SearchDirs, m_NormalizedSearchDirs, and m_CostFunctionValues

◆ GetClassName()

virtual const char * itk::CMAEvolutionStrategyOptimizer::GetClassName ( ) const

virtual

Reimplemented from itk::ScaledSingleValuedNonLinearOptimizer.

Reimplemented in elastix::CMAEvolutionStrategy< TElastix >.

◆ GetCurrentIteration()

virtual unsigned long itk::CMAEvolutionStrategyOptimizer::GetCurrentIteration ( ) const

virtual

Get the current iteration number:

◆ GetCurrentMaximumD()

virtual double itk::CMAEvolutionStrategyOptimizer::GetCurrentMaximumD ( ) const

virtual

The current maximum square root eigen value

◆ GetCurrentMinimumD()

virtual double itk::CMAEvolutionStrategyOptimizer::GetCurrentMinimumD ( ) const

virtual

The current minimum square root eigen value

◆ GetCurrentScaledStep()

virtual const ParametersType & itk::CMAEvolutionStrategyOptimizer::GetCurrentScaledStep ( )

virtual

Get the last step taken ( scaledPos_{k+1} - scaledPos_{k} ) If you want the step taken in the space of unscaled parameters, simply use: CMAESOptimizer->GetScaledCostFunction()->ConvertScaledToUnscaledParameters( ... ) To obtain the magnitude of the step, use ->GetCurretScaledStep().magnitude().

◆ GetCurrentSigma()

virtual double itk::CMAEvolutionStrategyOptimizer::GetCurrentSigma ( ) const

virtual

The current value of sigma

◆ GetCurrentStepLength()

virtual double itk::CMAEvolutionStrategyOptimizer::GetCurrentStepLength ( ) const

inlinevirtual

This function is just for convenience, since many optimizers have such a function. It return the current sigma times the current maximumD.

Definition at line 110 of file itkCMAEvolutionStrategyOptimizer.h.

◆ GetCurrentValue()

virtual MeasureType itk::CMAEvolutionStrategyOptimizer::GetCurrentValue ( ) const

virtual

Get the metric value at the current position

◆ GetInitialSigma()

virtual double itk::CMAEvolutionStrategyOptimizer::GetInitialSigma ( ) const

virtual

◆ GetMaximumDeviation()

virtual double itk::CMAEvolutionStrategyOptimizer::GetMaximumDeviation ( ) const

virtual

◆ GetMaximumNumberOfIterations()

virtual unsigned long itk::CMAEvolutionStrategyOptimizer::GetMaximumNumberOfIterations ( ) const

virtual

Setting: convergence condition: the maximum number of iterations. Default: 100

◆ GetMinimumDeviation()

virtual double itk::CMAEvolutionStrategyOptimizer::GetMinimumDeviation ( ) const

virtual

◆ GetNumberOfParents()

virtual unsigned int itk::CMAEvolutionStrategyOptimizer::GetNumberOfParents ( ) const

virtual

◆ GetPopulationSize()

virtual unsigned int itk::CMAEvolutionStrategyOptimizer::GetPopulationSize ( ) const

virtual

◆ GetPositionToleranceMax()

virtual double itk::CMAEvolutionStrategyOptimizer::GetPositionToleranceMax ( ) const

virtual

◆ GetPositionToleranceMin()

virtual double itk::CMAEvolutionStrategyOptimizer::GetPositionToleranceMin ( ) const

virtual

◆ GetRecombinationWeightsPreset()

virtual const char * itk::CMAEvolutionStrategyOptimizer::GetRecombinationWeightsPreset ( ) const

virtual

◆ GetSigmaDecayA()

virtual double itk::CMAEvolutionStrategyOptimizer::GetSigmaDecayA ( ) const

virtual

◆ GetSigmaDecayAlpha()

virtual double itk::CMAEvolutionStrategyOptimizer::GetSigmaDecayAlpha ( ) const

virtual

◆ GetStopCondition()

virtual const StopConditionType & itk::CMAEvolutionStrategyOptimizer::GetStopCondition ( )

virtual

Get the stop condition of the last run

◆ GetUpdateBDPeriod()

virtual unsigned int itk::CMAEvolutionStrategyOptimizer::GetUpdateBDPeriod ( ) const

virtual

◆ GetUseCovarianceMatrixAdaptation()

virtual bool itk::CMAEvolutionStrategyOptimizer::GetUseCovarianceMatrixAdaptation ( ) const

virtual

◆ GetUseDecayingSigma()

virtual bool itk::CMAEvolutionStrategyOptimizer::GetUseDecayingSigma ( ) const

virtual

◆ GetValueTolerance()

virtual double itk::CMAEvolutionStrategyOptimizer::GetValueTolerance ( ) const

virtual

◆ InitializeBCD()

virtual void itk::CMAEvolutionStrategyOptimizer::InitializeBCD ( )

protectedvirtual

Initialize the covariance matrix and its eigen decomposition

◆ InitializeConstants()

virtual void itk::CMAEvolutionStrategyOptimizer::InitializeConstants ( )

protectedvirtual

Compute the following constant variables:

m_PopulationSize (if not provided by the user)
m_NumberOfParents (if not provided by the user)
m_RecombinationWeights
m_EffectiveMu
m_ConjugateEvolutionPathConstant
m_SigmaDampingConstant
m_CovarianceMatrixAdaptationWeight
m_CovarianceMatrixAdaptationConstant
m_UpdateBDPeriod;
m_UseCovarianceMatrixAdaptation;
m_EvolutionPathConstant
m_ExpectationNormNormalDistribution
m_HistoryLength

◆ InitializeProgressVariables()

virtual void itk::CMAEvolutionStrategyOptimizer::InitializeProgressVariables ( )

protectedvirtual

Initialize the following 'progress' variables:

m_CurrentSigma
m_Heaviside
m_SearchDirs
m_NormalizedSearchDirs
m_CostFunctionValues
m_CurrentScaledStep
m_CurrentNormalizedStep
m_EvolutionPath
m_ConjugateEvolutionPath
m_MeasureHistory
m_CurrentMaximumD, m_CurrentMinimumD

Reimplemented in elastix::CMAEvolutionStrategy< TElastix >.

◆ ITK_DISALLOW_COPY_AND_MOVE()

itk::CMAEvolutionStrategyOptimizer::ITK_DISALLOW_COPY_AND_MOVE ( CMAEvolutionStrategyOptimizer )

◆ New()

static Pointer itk::CMAEvolutionStrategyOptimizer::New ( )

static

◆ PrintSelf()

void itk::CMAEvolutionStrategyOptimizer::PrintSelf	(	std::ostream &	os,
		Indent	indent
	)		const

overrideprotected

PrintSelf

◆ ResumeOptimization()

virtual void itk::CMAEvolutionStrategyOptimizer::ResumeOptimization ( )

virtual

◆ SetInitialSigma()

virtual void itk::CMAEvolutionStrategyOptimizer::SetInitialSigma ( double _arg )

virtual

Setting: the initial standard deviation used to generate offspring Recommended value: 1/3 * the expected range of the parameters Default: 1.0;

◆ SetMaximumDeviation()

virtual void itk::CMAEvolutionStrategyOptimizer::SetMaximumDeviation ( double _arg )

virtual

Setting: the maximum deviation. It is ensured that: max_i( sigma*sqrt(C[i,i]) ) < MaximumDeviation Default: +infinity

◆ SetMaximumNumberOfIterations()

virtual void itk::CMAEvolutionStrategyOptimizer::SetMaximumNumberOfIterations ( unsigned long _arg )

virtual

◆ SetMinimumDeviation()

virtual void itk::CMAEvolutionStrategyOptimizer::SetMinimumDeviation ( double _arg )

virtual

Setting: the minimum deviation. It is ensured that: min_i( sigma*sqrt(C[i,i]) ) > MinimumDeviation Default: 0.0

◆ SetNumberOfParents()

virtual void itk::CMAEvolutionStrategyOptimizer::SetNumberOfParents ( unsigned int _arg )

virtual

Setting: the number of parents (points for recombination, $\mu$ ) if set to 0, a default value is chosen: floor( populationSize / 2 ), which can be inspected after having started the optimisation. Default: 0

◆ SetPopulationSize()

virtual void itk::CMAEvolutionStrategyOptimizer::SetPopulationSize ( unsigned int _arg )

virtual

Setting: the population size ( $\lambda$ ); if set to 0, a default value is chosen: 4 + floor( 3 ln(NumberOfParameters) ), which can be inspected after having started the optimisation. Default: 0

◆ SetPositionToleranceMax()

virtual void itk::CMAEvolutionStrategyOptimizer::SetPositionToleranceMax ( double _arg )

virtual

Setting: convergence condition: the maximum step size. 'convergence' is declared if: if ( sigma * sqrt(C[i,i]) > PositionToleranceMax*sigma0 for any i ) Default: 1e8

◆ SetPositionToleranceMin()

virtual void itk::CMAEvolutionStrategyOptimizer::SetPositionToleranceMin ( double _arg )

virtual

Setting: convergence condition: the minimum step size. convergence is declared if: if ( sigma * max( abs(p_c[i]), sqrt(C[i,i]) ) < PositionToleranceMin*sigma0 for all i ) where p_c is the evolution path Default: 1e-12

◆ SetRecombinationWeightsPreset()

virtual void itk::CMAEvolutionStrategyOptimizer::SetRecombinationWeightsPreset ( const char * _arg )

virtual

Setting: how the recombination weights are chosen: "equal", "linear" or "superlinear" are supported equal: weights = ones(mu,1); linear: weights = mu+1-(1:mu)'; superlinear: weights = log(mu+1)-log(1:mu)'; Default: "superlinear"

◆ SetSigmaDecayA()

virtual void itk::CMAEvolutionStrategyOptimizer::SetSigmaDecayA ( double _arg )

virtual

Setting: the A parameter for the decaying sigma sequence. Default: 50

◆ SetSigmaDecayAlpha()

virtual void itk::CMAEvolutionStrategyOptimizer::SetSigmaDecayAlpha ( double _arg )

virtual

Setting: the alpha parameter for the decaying sigma sequence. Default: 0.602

◆ SetUpdateBDPeriod()

virtual void itk::CMAEvolutionStrategyOptimizer::SetUpdateBDPeriod ( unsigned int _arg )

virtual

Setting: the number of iterations after which B and D are updated. If 0: a default value is computed: floor( 1.0 / c_cov / Nd / 10.0 ) This value can be inspected after calling StartOptimization

◆ SetUseCovarianceMatrixAdaptation()

virtual void itk::CMAEvolutionStrategyOptimizer::SetUseCovarianceMatrixAdaptation ( bool _arg )

virtual

Setting: whether the covariance matrix adaptation scheme should be used. Default: true. If false: CovMatrix = Identity. This parameter may be changed by the optimiser, if it sees that the adaptation rate is nearly 0 (UpdateBDPeriod >= MaxNrOfIterations). This can be inspected calling StartOptimization()

◆ SetUseDecayingSigma()

virtual void itk::CMAEvolutionStrategyOptimizer::SetUseDecayingSigma ( bool _arg )

virtual

Setting: Use a sigma that decays according to a predefined function, instead of the adaptive scheme proposed by Hansen et al. if true: currentsigma(k+1) = currentsigma(k) * (A+k)^alpha / (A+k+1)^alpha where: k = the current iteration A, alpha = user-specified parameters (see below)

Default: false

◆ SetValueTolerance()

virtual void itk::CMAEvolutionStrategyOptimizer::SetValueTolerance ( double _arg )

virtual

Setting: convergence condition: the minimum change of the cost function value over time. convergence is declared if: the range of the best cost function value measured over a period of M iterations was not greater than the valueTolerance, where: M = m_HistoryLength = min( maxnrofit, 10+ceil(3*10*N/lambda) ). Default: 1e-12

◆ SortCostFunctionValues()

virtual void itk::CMAEvolutionStrategyOptimizer::SortCostFunctionValues ( )

protectedvirtual

Sort the m_CostFunctionValues vector and update m_MeasureHistory

◆ StartOptimization()

void itk::CMAEvolutionStrategyOptimizer::StartOptimization ( )

override

◆ StopOptimization()

virtual void itk::CMAEvolutionStrategyOptimizer::StopOptimization ( )

virtual

◆ TestConvergence()

virtual bool itk::CMAEvolutionStrategyOptimizer::TestConvergence ( bool firstCheck )

protectedvirtual

Check if convergence has occurred:

Check if the maximum number of iterations will not be exceeded in the following iteration
Check if the step was not too large: if ( sigma * sqrt(C[i,i]) > PositionToleranceMax*sigma0 for any i )
Check for zero steplength (should never happen): if ( sigma * D[i] <= 0 for all i )
if firstCheck==true -> quit function
Check if the step was not too small: if ( sigma * max( abs(p_c[i]), sqrt(C[i,i]) ) < PositionToleranceMin*sigma0 for all i )
Check if the value tolerance is satisfied.

◆ UpdateBD()

virtual void itk::CMAEvolutionStrategyOptimizer::UpdateBD ( )

protectedvirtual

Update the eigen decomposition and m_CurrentMaximumD/m_CurrentMinimumD

◆ UpdateC()

virtual void itk::CMAEvolutionStrategyOptimizer::UpdateC ( )

protectedvirtual

Update the covariance matrix C

◆ UpdateConjugateEvolutionPath()

virtual void itk::CMAEvolutionStrategyOptimizer::UpdateConjugateEvolutionPath ( )

protectedvirtual

Update m_ConjugateEvolutionPath

◆ UpdateEvolutionPath()

virtual void itk::CMAEvolutionStrategyOptimizer::UpdateEvolutionPath ( )

protectedvirtual

Update m_EvolutionPath

◆ UpdateHeaviside()

virtual void itk::CMAEvolutionStrategyOptimizer::UpdateHeaviside ( )

protectedvirtual

Update m_Heaviside

◆ UpdateSigma()

virtual void itk::CMAEvolutionStrategyOptimizer::UpdateSigma ( )

protectedvirtual

Update the Sigma either by adaptation or using the predefined function

Field Documentation

◆ m_B

CovarianceMatrixType itk::CMAEvolutionStrategyOptimizer::m_B

protected

B: eigen vector matrix

Definition at line 314 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_C

CovarianceMatrixType itk::CMAEvolutionStrategyOptimizer::m_C

protected

C: covariance matrix

Definition at line 312 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_ConjugateEvolutionPath

ParametersType itk::CMAEvolutionStrategyOptimizer::m_ConjugateEvolutionPath

protected

$p_\sigma$

Definition at line 306 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_ConjugateEvolutionPathConstant

double itk::CMAEvolutionStrategyOptimizer::m_ConjugateEvolutionPathConstant { 0.0 }

protected

$c_{\sigma}$

Definition at line 266 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_CostFunctionValues

MeasureContainerType itk::CMAEvolutionStrategyOptimizer::m_CostFunctionValues

protected

cost function values for each $x_i = m + d_i$

Definition at line 298 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_CovarianceMatrixAdaptationConstant

double itk::CMAEvolutionStrategyOptimizer::m_CovarianceMatrixAdaptationConstant { 0.0 }

protected

$c_{cov}$

Definition at line 270 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_CovarianceMatrixAdaptationWeight

double itk::CMAEvolutionStrategyOptimizer::m_CovarianceMatrixAdaptationWeight { 0.0 }

protected

$\mu_{cov} = \mu_{eff}$

Definition at line 274 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_CurrentIteration

unsigned long itk::CMAEvolutionStrategyOptimizer::m_CurrentIteration { 0 }

protected

The current iteration number

Definition at line 246 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_CurrentMaximumD

double itk::CMAEvolutionStrategyOptimizer::m_CurrentMaximumD { 1.0 }

protected

The current maximum square root eigen value:

Definition at line 288 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_CurrentMinimumD

double itk::CMAEvolutionStrategyOptimizer::m_CurrentMinimumD { 1.0 }

protected

The current minimum square root eigen value:

Definition at line 286 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_CurrentNormalizedStep

ParametersType itk::CMAEvolutionStrategyOptimizer::m_CurrentNormalizedStep

protected

$1/\sigma * D^{-1} * B' * m_CurrentScaledStep, needed for p_{\sigma}$

Definition at line 302 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_CurrentScaledStep

ParametersType itk::CMAEvolutionStrategyOptimizer::m_CurrentScaledStep

protected

$m(g+1) - m(g)$

Definition at line 300 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_CurrentSigma

double itk::CMAEvolutionStrategyOptimizer::m_CurrentSigma { 0.0 }

protected

The current value of Sigma

Definition at line 283 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_CurrentValue

MeasureType itk::CMAEvolutionStrategyOptimizer::m_CurrentValue { 0.0 }

protected

The value of the cost function at the current position

Definition at line 243 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_D

EigenValueMatrixType itk::CMAEvolutionStrategyOptimizer::m_D

protected

D: sqrt(eigen values)

Definition at line 316 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_EffectiveMu

double itk::CMAEvolutionStrategyOptimizer::m_EffectiveMu { 0.0 }

protected

Some other constants, without set/get methods These settings have default values. $\mu_{eff}$

Definition at line 264 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_EvolutionPath

ParametersType itk::CMAEvolutionStrategyOptimizer::m_EvolutionPath

protected

$p_c$

Definition at line 304 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_EvolutionPathConstant

double itk::CMAEvolutionStrategyOptimizer::m_EvolutionPathConstant { 0.0 }

protected

$c_c$

Definition at line 272 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_ExpectationNormNormalDistribution

double itk::CMAEvolutionStrategyOptimizer::m_ExpectationNormNormalDistribution { 0.0 }

protected

$chiN = E( \|N(0,I)\|$

Definition at line 276 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_Heaviside

bool itk::CMAEvolutionStrategyOptimizer::m_Heaviside { false }

protected

$h_{\sigma}$

Definition at line 291 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_HistoryLength

unsigned long itk::CMAEvolutionStrategyOptimizer::m_HistoryLength { 0 }

protected

Length of the MeasureHistory deque

Definition at line 280 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_InitialSigma

double itk::CMAEvolutionStrategyOptimizer::m_InitialSigma { 1.0 }

private

Definition at line 430 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_MaximumDeviation

double itk::CMAEvolutionStrategyOptimizer::m_MaximumDeviation { std::numeric_limits<double>::max() }

private

Definition at line 434 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_MaximumNumberOfIterations

unsigned long itk::CMAEvolutionStrategyOptimizer::m_MaximumNumberOfIterations { 100 }

private

Settings that are only inspected/changed by the associated get/set member functions.

Definition at line 428 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_MeasureHistory

MeasureHistoryType itk::CMAEvolutionStrategyOptimizer::m_MeasureHistory

protected

History of best measure values

Definition at line 309 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_MinimumDeviation

double itk::CMAEvolutionStrategyOptimizer::m_MinimumDeviation { 0.0 }

private

Definition at line 435 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_NormalizedSearchDirs

ParameterContainerType itk::CMAEvolutionStrategyOptimizer::m_NormalizedSearchDirs

protected

realisations of $N(0,I)$

Definition at line 296 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_NumberOfParents

unsigned int itk::CMAEvolutionStrategyOptimizer::m_NumberOfParents { 0 }

protected

Definition at line 257 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_PopulationSize

unsigned int itk::CMAEvolutionStrategyOptimizer::m_PopulationSize { 0 }

protected

Definition at line 256 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_PositionToleranceMax

double itk::CMAEvolutionStrategyOptimizer::m_PositionToleranceMax { 1e8 }

private

Definition at line 436 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_PositionToleranceMin

double itk::CMAEvolutionStrategyOptimizer::m_PositionToleranceMin { 1e-12 }

private

Definition at line 437 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_RandomGenerator

RandomGeneratorType::Pointer itk::CMAEvolutionStrategyOptimizer::m_RandomGenerator { RandomGeneratorType::GetInstance() }

protected

The random number generator used to generate the offspring.

Definition at line 240 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_RecombinationWeights

RecombinationWeightsType itk::CMAEvolutionStrategyOptimizer::m_RecombinationWeights

protected

array of $w_i$

Definition at line 278 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_RecombinationWeightsPreset

std::string itk::CMAEvolutionStrategyOptimizer::m_RecombinationWeightsPreset { "superlinear" }

private

Definition at line 433 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_SearchDirs

ParameterContainerType itk::CMAEvolutionStrategyOptimizer::m_SearchDirs

protected

$d_i = x_i - m$

Definition at line 294 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_SigmaDampingConstant

double itk::CMAEvolutionStrategyOptimizer::m_SigmaDampingConstant { 0.0 }

protected

$d_{\sigma}$

Definition at line 268 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_SigmaDecayA

double itk::CMAEvolutionStrategyOptimizer::m_SigmaDecayA { 50 }

private

Definition at line 431 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_SigmaDecayAlpha

double itk::CMAEvolutionStrategyOptimizer::m_SigmaDecayAlpha { 0.602 }

private

Definition at line 432 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_Stop

bool itk::CMAEvolutionStrategyOptimizer::m_Stop { false }

protected

Boolean that indicates whether the optimizer should stop

Definition at line 252 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_StopCondition

StopConditionType itk::CMAEvolutionStrategyOptimizer::m_StopCondition { Unknown }

protected

The stop condition

Definition at line 249 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_UpdateBDPeriod

unsigned int itk::CMAEvolutionStrategyOptimizer::m_UpdateBDPeriod { 1 }

protected

Definition at line 258 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_UseCovarianceMatrixAdaptation

bool itk::CMAEvolutionStrategyOptimizer::m_UseCovarianceMatrixAdaptation { true }

protected

Settings that may be changed by the optimizer:

Definition at line 255 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_UseDecayingSigma

bool itk::CMAEvolutionStrategyOptimizer::m_UseDecayingSigma { false }

private

Definition at line 429 of file itkCMAEvolutionStrategyOptimizer.h.

◆ m_ValueTolerance

double itk::CMAEvolutionStrategyOptimizer::m_ValueTolerance { 1e-12 }

private

Definition at line 438 of file itkCMAEvolutionStrategyOptimizer.h.

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Private Attributes

Member Typedef Documentation

◆ ConstPointer

◆ CovarianceMatrixType

◆ EigenValueMatrixType

◆ MeasureContainerType

◆ MeasureHistoryType

◆ MeasureIndexPairType

◆ ParameterContainerType

◆ Pointer

◆ RandomGeneratorType

◆ RecombinationWeightsType

◆ ScaledCostFunctionType

◆ ScalesType

◆ Self

◆ Superclass

Member Enumeration Documentation

◆ StopConditionType

Constructor & Destructor Documentation

◆ CMAEvolutionStrategyOptimizer()

◆ ~CMAEvolutionStrategyOptimizer()

Member Function Documentation

◆ AdvanceOneStep()

◆ FixNumericalErrors()

◆ GenerateOffspring()

◆ GetClassName()

◆ GetCurrentIteration()

◆ GetCurrentMaximumD()

◆ GetCurrentMinimumD()

◆ GetCurrentScaledStep()

◆ GetCurrentSigma()

◆ GetCurrentStepLength()

◆ GetCurrentValue()

◆ GetInitialSigma()

◆ GetMaximumDeviation()

◆ GetMaximumNumberOfIterations()

◆ GetMinimumDeviation()

◆ GetNumberOfParents()

◆ GetPopulationSize()

◆ GetPositionToleranceMax()

◆ GetPositionToleranceMin()

◆ GetRecombinationWeightsPreset()

◆ GetSigmaDecayA()

◆ GetSigmaDecayAlpha()

◆ GetStopCondition()

◆ GetUpdateBDPeriod()

◆ GetUseCovarianceMatrixAdaptation()

◆ GetUseDecayingSigma()

◆ GetValueTolerance()

◆ InitializeBCD()

◆ InitializeConstants()

◆ InitializeProgressVariables()

◆ ITK_DISALLOW_COPY_AND_MOVE()

◆ New()

◆ PrintSelf()

◆ ResumeOptimization()

◆ SetInitialSigma()

◆ SetMaximumDeviation()

◆ SetMaximumNumberOfIterations()

◆ SetMinimumDeviation()

◆ SetNumberOfParents()

◆ SetPopulationSize()

◆ SetPositionToleranceMax()

◆ SetPositionToleranceMin()

◆ SetRecombinationWeightsPreset()

◆ SetSigmaDecayA()

◆ SetSigmaDecayAlpha()

◆ SetUpdateBDPeriod()

◆ SetUseCovarianceMatrixAdaptation()

◆ SetUseDecayingSigma()

◆ SetValueTolerance()

◆ SortCostFunctionValues()

◆ StartOptimization()