sot::Schoen Class Reference

Schoen function More...

#include <test_problems.h>

Inheritance diagram for sot::Schoen:

Public Member Functions
	Schoen (int dim)
	Constructor with k = max(2^dim, 500) More...
	Schoen (int dim, int k)
	Constructor for given k. More...
vec	lBounds () const
	Method for getting the lower variable bounds. More...
vec	uBounds () const
	Method for getting the upper variable bounds. More...
int	dim () const
	Method for getting the number of dimensions. More...
double	min () const
	Method for getting global minimum value. More...
vec	optimum () const
	Method for getting the global minimizer. More...
std::string	name () const
	Method for getting the name of the optimization problem. More...
double	eval (const vec &x) const
	Method for evaluating the objective function. More...
Public Member Functions inherited from sot::TestProblem
vec	evals (const mat &points) const
	Method for evaluating the objective function at multiple points. More...

Protected Attributes
int	mDim
vec	mxLow
vec	mxUp
vec	mOptimum
double	mMinimum = 0.0
std::string	mName
int	mk
vec	mf
vec	mAlpha
mat	mZ
double	mDistTol = 1e-10

Detailed Description

Schoen function

Function: \(f(x) = \displaystyle\frac{\displaystyle\sum_{i=1}^k f_i \displaystyle\prod_{j \neq i} \|x - z_j\|^{\alpha}}{ \displaystyle\sum_{i=1}^k \displaystyle\prod_{j \neq i} \|x - z_j\|^{\alpha}} \)
Domain: \( 0 \leq x_i \leq 1 \)
Minimum value: \(0\)
Minimizer: Randomly generated

Here \(z_j \in [0,1]^d\) for \(j=1,\dots,k\) are the locations of the stationary points and \(f_j \in \mathbf{R}\) are the values at these stationary points. The locations of \(z_j\) are generated uniformly and \(f_j\) are drawn from at \(U[0,100]\) distribution. We force \(f_1 = 0\) so the global minimum value is always 0 and is located at \(z_1\). The exponents \(\alpha\) are drawn from a \(U[2,3]\) distribution.

Author

David Eriksson, dme65.nosp@m.@cor.nosp@m.nell..nosp@m.edu

Constructor & Destructor Documentation

sot::Schoen::Schoen ( int  dim )

inline

Constructor with k = max(2^dim, 500)

Parameters

dim	Number of dimensions

sot::Schoen::Schoen ( int  dim, int  k  )

inline

Constructor for given k.

Parameters

dim	Number of dimensions
k	Number of stationary points

Member Function Documentation

int sot::Schoen::dim ( ) const

inlinevirtual

Method for getting the number of dimensions.

Returns

The number of dimensions

Implements sot::Problem.

double sot::Schoen::eval ( const vec &  point ) const

inlinevirtual

Method for evaluating the objective function.

Parameters

point

Is the next point for which to evaluate the objective function

Returns

The value of the objective function at the input

Implements sot::Problem.

vec sot::Schoen::lBounds ( ) const

inlinevirtual

Method for getting the lower variable bounds.

Returns

Upper variable bounds

Implements sot::Problem.

double sot::Schoen::min ( ) const

inlinevirtual

Method for getting global minimum value.

Returns

Value at the global minumum

Implements sot::Problem.

std::string sot::Schoen::name ( ) const

inlinevirtual

Method for getting the name of the optimization problem.

Returns

The optimization problem name

Implements sot::Problem.

vec sot::Schoen::optimum ( ) const

inlinevirtual

Method for getting the global minimizer.

Returns

The global minimizer

Implements sot::Problem.

vec sot::Schoen::uBounds ( ) const

inlinevirtual

Method for getting the upper variable bounds.

Returns

Upper variable bounds

Implements sot::Problem.

Member Data Documentation

vec sot::Schoen::mAlpha

protected

Exponents

int sot::Schoen::mDim

protected

Number of dimensions

double sot::Schoen::mDistTol = 1e-10

protected

Distance tolerance for distinguishing points

vec sot::Schoen::mf

protected

Values at the stationary points

int sot::Schoen::mk

protected

Number of stationary points

double sot::Schoen::mMinimum = 0.0

protected

Global minimum value

std::string sot::Schoen::mName

protected

Optimization problem name

vec sot::Schoen::mOptimum

protected

Global minimizer

vec sot::Schoen::mxLow

protected

Lower variable bounds

vec sot::Schoen::mxUp

protected

Upper variable bounds

mat sot::Schoen::mZ

protected

Locations of the stationary points

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

• include/sot_bits/test_problems.h