IHR3 Class Reference
multi-objective problem IHR3. More...
#include <MultiObjectiveFunctions.h>
Public Member Functions | |
| IHR3 (unsigned d=10) | |
| Constructor. | |
| ~IHR3 () | |
| Destructor. | |
| unsigned int | objectives () const |
| return the number of objectives to optimize | |
| void | result (double *const &point, std::vector< double > &value) |
| bool | ProposeStartingPoint (double *&point) const |
| 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 | h (double x, double n) |
| double | hf (double x, double y0, double ymax) |
| double | hg (double x) |
Protected Attributes | |
| Matrix | m_Transformation |
| transformation matrix | |
Detailed Description
multi-objective problem IHR3.The rotated variant of the ZDT3 problem:
![\[ f_{1}(x)= |y_1| \]](form_33.png)
![\[ f_{2}(x)=g(y)h_f( 1 - \sqrt{\frac{y_1}{ g(y) }} - \frac{h(y_1)}{g(y)}sin(10 \pi y_1)) \]](form_44.png)
![\[ g(y)=1+\frac{9 \sum_{i=2}^{n}h_g(y_i)}{(n-1)} \]](form_35.png)
with auxiliary functions:
![\[ h: \mathbf{R} \rightarrow [0,1], x \rightarrow (1+exp(\frac{-x}{ \sqrt{n} }))^{-1} \]](form_36.png)
![\[ h_f: \mathbf{R} \rightarrow \mathbf{R}, x \rightarrow \left\{\begin{array}{ll} x, & \mbox{if } |y_1|\leq y_{max} \\ 1+|y_1|, & \mbox{ otherwise} \end{array}\right. \]](form_37.png)
![\[ h_g: \mathbf{R} \rightarrow \mathbf{R}_{\leq 0}, x \rightarrow \frac{x^2}{|x|+0.1} \]](form_38.png)
where ![$ x\in [0,1]^n $](form_39.png)
, y is defined by 
where O is an arbitrary orthogonal rotation matrix and 
and usually 
Definition at line 592 of file MultiObjectiveFunctions.h.
Constructor & Destructor Documentation
| IHR3::IHR3 | ( | unsigned | d = 10 |
) |
Constructor.
Definition at line 875 of file MultiObjectiveFunctions.cpp.
References initRandomRotation(), and ObjectiveFunction::m_name.
| IHR3::~IHR3 | ( | ) |
Destructor.
Definition at line 881 of file MultiObjectiveFunctions.cpp.
References ObjectiveFunctionT< T * >::constrainthandler.
Member Function Documentation
| double IHR3::h | ( | double | x, | |
| double | n | |||
| ) | [protected] |
| double IHR3::hf | ( | double | x, | |
| double | y0, | |||
| double | ymax | |||
| ) | [protected] |
| double IHR3::hg | ( | double | x | ) | [protected] |
| void IHR3::initRandomRotation | ( | ) |
Create a random orthogonal transformation.
Definition at line 942 of file MultiObjectiveFunctions.cpp.
References ObjectiveFunctionVS< double >::m_dimension, and m_Transformation.
Referenced by IHR3().
| bool IHR3::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 934 of file MultiObjectiveFunctions.cpp.
| unsigned int IHR3::objectives | ( | ) | const [virtual] |
return the number of objectives to optimize
Implements ObjectiveFunction.
Definition at line 888 of file MultiObjectiveFunctions.cpp.
| bool IHR3::ProposeStartingPoint | ( | double *& | point | ) | const |
Definition at line 920 of file MultiObjectiveFunctions.cpp.
References ObjectiveFunctionVS< double >::m_dimension.
| void IHR3::result | ( | double *const & | point, | |
| std::vector< double > & | value | |||
| ) |
Definition at line 893 of file MultiObjectiveFunctions.cpp.
References h(), hf(), hg(), ObjectiveFunctionVS< double >::m_dimension, ObjectiveFunction::m_timesCalled, m_Transformation, and transform().
| void IHR3::transform | ( | const double * | in, | |
| std::vector< double > & | out | |||
| ) | const [protected] |
transform in, resulting in out
Definition at line 972 of file MultiObjectiveFunctions.cpp.
References ObjectiveFunctionVS< double >::m_dimension, and m_Transformation.
Referenced by result().
| bool IHR3::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
- Returns:
- true if an utopian point is known, false otherwise
Reimplemented from ObjectiveFunctionVS< double >.
Definition at line 929 of file MultiObjectiveFunctions.cpp.
Member Data Documentation
Matrix IHR3::m_Transformation [protected] |
transformation matrix
Definition at line 617 of file MultiObjectiveFunctions.h.
Referenced by initRandomRotation(), result(), and transform().
The documentation for this class was generated from the following files: