IHR2 Class Reference

multi-objective problem IHR2. More...

#include <MultiObjectiveFunctions.h>

Inheritance diagram for IHR2:

Public Member Functions
	IHR2 (unsigned d=10)
	Constructor.
	~IHR2 ()
	Destructor.
unsigned int	objectives () const
	return the number of objectives to optimize
void	result (double *const &point, std::vector< double > &value)
	objective function evaluation
bool	ProposeStartingPoint (double *&point) const
	For a BoxConstraintHandler we can automatically propose a starting point.
bool	utopianFitness (std::vector< double > &value) const
	If possible, this method returns (a bound on) the best possible fitness.
bool	nadirFitness (std::vector< double > &value) const
	If possible, this method returns (a bound on) the worst possible fitness.
void	initRandomRotation ()
	Create a random orthogonal transformation.
Protected Member Functions
void	transform (const double *in, std::vector< double > &out) const
	transform in, resulting in out
double	hf (double x, double y0, double ymax)
double	hg (double x)
Protected Attributes
Matrix	m_Transformation
	transformation matrix

Detailed Description

multi-objective problem IHR2.

The rotated variant of the ZDT2 problem:

$f_{1}(x)= |y_1|$

$f_{2}(x)=g(y)h_f( 1 - (\frac{y_1}{ g(y) } )^2 )$

$g(y)=1+\frac{9 \sum_{i=2}^{n}h_g(y_i)}{(n-1)}$

with auxiliary functions:

$h_f: \mathbf{R} \rightarrow \mathbf{R}, x \rightarrow \left\{\begin{array}{ll} x, & \mbox{if } |y_1|\leq y_{max} \\ 1+|y_1|, & \mbox{ otherwise} \end{array}\right.$

$h_g: \mathbf{R} \rightarrow \mathbf{R}_{\leq 0}, x \rightarrow \frac{x^2}{|x|+0.1}$

where $x\in [0,1]^n$ , y is defined by $ y= Ox $ where O is an arbitrary orthogonal rotation matrix and $y_{max} = 1/max_j (|o_{1j}|)$ and usually $ n=10 $

Definition at line 532 of file MultiObjectiveFunctions.h.

Constructor & Destructor Documentation

IHR2::IHR2 ( unsigned d = 10 )

Constructor.

Definition at line 750 of file MultiObjectiveFunctions.cpp.

References initRandomRotation(), and ObjectiveFunction::m_name.

IHR2::~IHR2 ( )

Destructor.

Definition at line 756 of file MultiObjectiveFunctions.cpp.

References ObjectiveFunctionT< double * >::constrainthandler.

Member Function Documentation

double IHR2::hf	(	double	x,
		double	y0,
		double	ymax
	)			`[protected]`

Definition at line 859 of file MultiObjectiveFunctions.cpp.

Referenced by result().

double IHR2::hg ( double x ) [protected]

Definition at line 866 of file MultiObjectiveFunctions.cpp.

Referenced by result().

void IHR2::initRandomRotation ( )

Create a random orthogonal transformation.

Definition at line 817 of file MultiObjectiveFunctions.cpp.

References ObjectiveFunctionVS< double >::m_dimension, and m_Transformation.

Referenced by IHR2().

bool IHR2::nadirFitness ( std::vector< double > & value ) const [virtual]

If possible, this method returns (a bound on) the worst possible fitness.

For single objective optimization this information is rarely of any use, while for multi objective optimization a so-called nadir point is important for the computation of standard quality indicators like the hypervolume.

Parameters:

fitness

component wise worst fitness

Returns:: true if a nadir point is known, false otherwise

Reimplemented from ObjectiveFunctionVS< double >.

Definition at line 809 of file MultiObjectiveFunctions.cpp.

unsigned int IHR2::objectives ( ) const [virtual]

return the number of objectives to optimize

Implements ObjectiveFunction.

Definition at line 763 of file MultiObjectiveFunctions.cpp.

bool IHR2::ProposeStartingPoint ( double *& point ) const [virtual]

For a BoxConstraintHandler we can automatically propose a starting point.

Reimplemented from ObjectiveFunctionVS< double >.

Definition at line 795 of file MultiObjectiveFunctions.cpp.

References ObjectiveFunctionVS< double >::m_dimension.

void IHR2::result	(	double *const &	point,
		std::vector< double > &	value
	)			`[virtual]`

objective function evaluation

Implements ObjectiveFunctionT< double * >.

Definition at line 768 of file MultiObjectiveFunctions.cpp.

References hf(), hg(), ObjectiveFunctionVS< double >::m_dimension, ObjectiveFunction::m_timesCalled, m_Transformation, and transform().

void IHR2::transform	(	const double *	in,
		std::vector< double > &	out
	)			const `[protected]`

transform in, resulting in out

Definition at line 847 of file MultiObjectiveFunctions.cpp.

References ObjectiveFunctionVS< double >::m_dimension, and m_Transformation.

Referenced by result().

bool IHR2::utopianFitness ( std::vector< double > & value ) const [virtual]

If possible, this method returns (a bound on) the best possible fitness.

For the single objective case the function should return the fitness in the global optimum. For the multi objective case this function should return a utopian point.

Parameters:

fitness

component wise utopian fitness