Implements the SMS-EMOA. More...

#include <shark/Algorithms/DirectSearch/SMS-EMOA.h>

Collaboration diagram for shark::detail::SMSEMOA:

Public Types
typedef std::vector< ResultSet < RealVector, RealVector > >	SolutionSetType
	The result type of the optimizer, a vector of tuples \(( \vec x, \vec{f}( \vec{x} )\). More...

Public Member Functions
	SMSEMOA ()
	Default c'tor. More...

std::string	name () const
	Returns the name of the algorithm. More...

template<typename Archive >
void	serialize (Archive &archive, const unsigned int version)
	Stores/loads the algorithm's state. More...

void	configure (const PropertyTree &node)
	Initializes the algorithm from a configuration-tree node. More...

void	init (unsigned int mu=this_type::DEFAULT_MU(), double pc=this_type::DEFAULT_PC(), double nc=this_type::DEFAULT_NC(), double nm=this_type::DEFAULT_NM(), bool useApproximatedHypervolume=this_type::DEFAULT_USE_APPROXIMATED_HYPERVOLUME(), double errorBound=this_type::DEFAULT_ERROR_BOUND(), double errorProbability=this_type::DEFAULT_ERROR_PROBABILITY())
	Initializes the algorithm. More...

template<typename Function >
void	init (const Function &f, const RealVector &sp)
	Initializes the algorithm for the supplied objective function. More...

template<typename Function >
SolutionSetType	step (const Function &f)
	Executes one iteration of the algorithm. More...

Static Public Member Functions
static unsigned int	DEFAULT_MU ()
	Default parent population size. More...

static double	DEFAULT_PC ()
	Default crossover probability. More...

static double	DEFAULT_NC ()
	Default value for nc. More...

static double	DEFAULT_NM ()
	Default value for nm. More...

static bool	DEFAULT_USE_APPROXIMATED_HYPERVOLUME ()
	Default choice whether to rely on the approximated hypervolume indicator. More...

static double	DEFAULT_ERROR_BOUND ()
	Default error bound for the approximated hypervolume indicator. More...

static double	DEFAULT_ERROR_PROBABILITY ()
	Default error probability for the approximated hypervolume indicator. More...

Protected Attributes
smsemoa::Population	m_pop
	Population of size \(\mu + 1\). More...

unsigned int	m_mu
	Population size \(\mu\). More...

bool	m_useApproximatedHypervolume
	Flag for deciding whether to use the approximated hypervolume. More...

shark::moo::PenalizingEvaluator	m_evaluator
	Evaluation operator. More...

RankShareComparator	rsc
	Comparator for individuals based on their multi-objective rank and share. More...

FastNonDominatedSort	m_fastNonDominatedSort
	Operator that provides Deb's fast non-dominated sort. More...

IndicatorBasedSelection < HypervolumeIndicator >	m_selection
	Selection operator relying on the (contributing) hypervolume indicator. More...

ApproximatedHypervolumeSelection	m_approximatedSelection
	Selection operator relying on the approximated (contributing) hypervolume indicator. More...

SimulatedBinaryCrossover < RealVector >	m_sbx
	Crossover operator. More...

PolynomialMutator	m_mutator
	Mutation operator. More...

double	m_crossoverProbability
	Crossover probability. More...

Detailed Description

Implements the SMS-EMOA.

Please see the following paper for further reference:

Beume, Naujoks, Emmerich. SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research.

Definition at line 90 of file SMS-EMOA.h.

Member Typedef Documentation

typedef std::vector< ResultSet< RealVector, RealVector > > shark::detail::SMSEMOA::SolutionSetType

The result type of the optimizer, a vector of tuples \(( \vec x, \vec{f}( \vec{x} )\).

Definition at line 110 of file SMS-EMOA.h.

Constructor & Destructor Documentation

shark::detail::SMSEMOA::SMSEMOA ( )

inline

Default c'tor.

Definition at line 166 of file SMS-EMOA.h.

References init().

Member Function Documentation

void shark::detail::SMSEMOA::configure ( const PropertyTree & node )

inline

Initializes the algorithm from a configuration-tree node.

The following sub keys are recognized:

Mu, type: unsigned int, default value: 100.
CrossoverProbability, type: double, default value: 0.9.
NC, type: double, default value: 20.
NM, type: double; default value: 20.
UseApproximatedHypervolume, type: bool, default value: false.
ErrorBound, type: double, default value: \(10^{-6}\).
ErrorProbability, type: double, default value: \(10^{-6}\).

Parameters

[in] node The configuration tree node.

Definition at line 213 of file SMS-EMOA.h.

References init().

static double shark::detail::SMSEMOA::DEFAULT_ERROR_BOUND ( )

inlinestatic

Default error bound for the approximated hypervolume indicator.

Definition at line 152 of file SMS-EMOA.h.

static double shark::detail::SMSEMOA::DEFAULT_ERROR_PROBABILITY ( )

inlinestatic

Default error probability for the approximated hypervolume indicator.

Definition at line 159 of file SMS-EMOA.h.

static unsigned int shark::detail::SMSEMOA::DEFAULT_MU ( )

inlinestatic

Default parent population size.

Definition at line 117 of file SMS-EMOA.h.

static double shark::detail::SMSEMOA::DEFAULT_NC ( )

inlinestatic

Default value for nc.

Definition at line 131 of file SMS-EMOA.h.

static double shark::detail::SMSEMOA::DEFAULT_NM ( )

inlinestatic

Default value for nm.

Definition at line 138 of file SMS-EMOA.h.

static double shark::detail::SMSEMOA::DEFAULT_PC ( )

inlinestatic

Default crossover probability.

Definition at line 124 of file SMS-EMOA.h.

static bool shark::detail::SMSEMOA::DEFAULT_USE_APPROXIMATED_HYPERVOLUME ( )

inlinestatic

Default choice whether to rely on the approximated hypervolume indicator.

Definition at line 145 of file SMS-EMOA.h.

void shark::detail::SMSEMOA::init	(	unsigned int	mu = `this_type::DEFAULT_MU()`,
		double	pc = `this_type::DEFAULT_PC()`,
		double	nc = `this_type::DEFAULT_NC()`,
		double	nm = `this_type::DEFAULT_NM()`,
		bool	useApproximatedHypervolume = `this_type::DEFAULT_USE_APPROXIMATED_HYPERVOLUME()`,
		double	errorBound = `this_type::DEFAULT_ERROR_BOUND()`,
		double	errorProbability = `this_type::DEFAULT_ERROR_PROBABILITY()`
	)

inline

Initializes the algorithm.

Parameters

[in]	mu	The population size.
[in]	pc	Crossover probability, default value: 0.8.
[in]	nc	Parameter of the simulated binary crossover operator, default value: 20.0.
[in]	nm	Parameter of the mutation operator, default value: 20.0.
[in]	useApproximatedHypervolume	Flag to determine whether to use the approximated hypervolume.
[in]	errorBound	The error bound \( \epsilon \) for the approximated hypervolume selection.
[in]	errorProbability	The error prob. \( \delta \) for the approximated hypervolume selection.

Definition at line 235 of file SMS-EMOA.h.

References m_approximatedSelection, m_crossoverProbability, m_mu, m_mutator, shark::SimulatedBinaryCrossover< PointType >::m_nc, shark::PolynomialMutator::m_nm, shark::SimulatedBinaryCrossover< PointType >::m_prob, m_sbx, m_selection, m_useApproximatedHypervolume, and shark::ApproximatedHypervolumeSelection::setMu().

Referenced by configure(), and SMSEMOA().

template<typename Function >

void shark::detail::SMSEMOA::init	(	const Function &	f,
		const RealVector &	sp
	)

inline

Initializes the algorithm for the supplied objective function.

Template Parameters

ObjectiveFunction The type of the objective function, needs to adhere to the concept of an AbstractObjectiveFunction.

Parameters

[in]	f	The objective function.
[in]	sp	An initial search point.

Definition at line 265 of file SMS-EMOA.h.

References shark::TypedIndividual< SearchSpaceType, ChromosomeType1, ChromosomeType2, ChromosomeType3, ChromosomeType4, ChromosomeType5, ChromosomeType6, ChromosomeType7, ChromosomeType8, ChromosomeType9, ChromosomeType10 >::age(), shark::TypedIndividual< SearchSpaceType, ChromosomeType1, ChromosomeType2, ChromosomeType3, ChromosomeType4, ChromosomeType5, ChromosomeType6, ChromosomeType7, ChromosomeType8, ChromosomeType9, ChromosomeType10 >::fitness(), shark::PolynomialMutator::init(), shark::BoxConstraintHandler< Vector >::lower(), m_approximatedSelection, m_evaluator, shark::SimulatedBinaryCrossover< PointType >::m_lower, m_mu, m_mutator, shark::moo::PenalizingEvaluator::m_penaltyFactor, m_pop, shark::SimulatedBinaryCrossover< PointType >::m_prob, m_sbx, m_selection, shark::SimulatedBinaryCrossover< PointType >::m_upper, shark::blas::max(), shark::repeat(), shark::ApproximatedHypervolumeSelection::setNoObjectives(), shark::TypedIndividual< SearchSpaceType, ChromosomeType1, ChromosomeType2, ChromosomeType3, ChromosomeType4, ChromosomeType5, ChromosomeType6, ChromosomeType7, ChromosomeType8, ChromosomeType9, ChromosomeType10 >::setNoObjectives(), SHARKEXCEPTION, and shark::BoxConstraintHandler< Vector >::upper().

std::string shark::detail::SMSEMOA::name ( ) const

inline

Returns the name of the algorithm.

Definition at line 173 of file SMS-EMOA.h.

template<typename Archive >

void shark::detail::SMSEMOA::serialize	(	Archive &	archive,
		const unsigned int	version
	)

inline

Stores/loads the algorithm's state.

Template Parameters

Archive The type of the archive.

Parameters

[in,out]	archive	The archive to use for loading/storing.
[in]	version	Currently unused.

Definition at line 184 of file SMS-EMOA.h.

References m_approximatedSelection, m_crossoverProbability, m_evaluator, m_fastNonDominatedSort, m_mu, m_mutator, m_pop, m_sbx, m_selection, and rsc.

template<typename Function >

SolutionSetType shark::detail::SMSEMOA::step ( const Function & f )

inline

Executes one iteration of the algorithm.

Template Parameters

The	type of the objective to iterate upon.

Parameters

[in] f The function to iterate upon.

Returns: The Pareto-set/-front approximation after the iteration.

Definition at line 317 of file SMS-EMOA.h.

References m_approximatedSelection, m_crossoverProbability, m_evaluator, m_fastNonDominatedSort, m_mu, m_mutator, m_pop, m_sbx, m_selection, m_useApproximatedHypervolume, and shark::makeResultSet().

Member Data Documentation

ApproximatedHypervolumeSelection shark::detail::SMSEMOA::m_approximatedSelection

protected

Selection operator relying on the approximated (contributing) hypervolume indicator.

Definition at line 100 of file SMS-EMOA.h.

Referenced by init(), serialize(), and step().

double shark::detail::SMSEMOA::m_crossoverProbability

protected

Crossover probability.

Definition at line 104 of file SMS-EMOA.h.

Referenced by init(), serialize(), and step().

shark::moo::PenalizingEvaluator shark::detail::SMSEMOA::m_evaluator

protected

Evaluation operator.

Definition at line 96 of file SMS-EMOA.h.

Referenced by init(), serialize(), and step().

FastNonDominatedSort shark::detail::SMSEMOA::m_fastNonDominatedSort

protected

Operator that provides Deb's fast non-dominated sort.

Definition at line 98 of file SMS-EMOA.h.

Referenced by serialize(), and step().

unsigned int shark::detail::SMSEMOA::m_mu

protected

Population size \(\mu\).

Definition at line 93 of file SMS-EMOA.h.

Referenced by init(), serialize(), and step().

PolynomialMutator shark::detail::SMSEMOA::m_mutator

protected

Mutation operator.

Definition at line 102 of file SMS-EMOA.h.

Referenced by init(), serialize(), and step().

smsemoa::Population shark::detail::SMSEMOA::m_pop

protected

Population of size \(\mu + 1\).

Definition at line 92 of file SMS-EMOA.h.

Referenced by init(), serialize(), and step().

SimulatedBinaryCrossover< RealVector > shark::detail::SMSEMOA::m_sbx

protected

Crossover operator.

Definition at line 101 of file SMS-EMOA.h.

Referenced by init(), serialize(), and step().

IndicatorBasedSelection<HypervolumeIndicator> shark::detail::SMSEMOA::m_selection

protected

Selection operator relying on the (contributing) hypervolume indicator.

Definition at line 99 of file SMS-EMOA.h.

Referenced by init(), serialize(), and step().

bool shark::detail::SMSEMOA::m_useApproximatedHypervolume

protected

Flag for deciding whether to use the approximated hypervolume.

Definition at line 94 of file SMS-EMOA.h.

Referenced by init(), and step().

RankShareComparator shark::detail::SMSEMOA::rsc

protected

Comparator for individuals based on their multi-objective rank and share.

Definition at line 97 of file SMS-EMOA.h.

Referenced by serialize().

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

include/shark/Algorithms/DirectSearch/SMS-EMOA.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation