syn::deflected_corrugated_spring Class Reference

#include <synthetic.hpp>

Inheritance diagram for syn::deflected_corrugated_spring:

Public Member Functions
	deflected_corrugated_spring (int dims)
double	evaluate (inst::set x) override
Public Member Functions inherited from syn::synthetic
	synthetic (const std::string &n, u_int dims, double lb, double ub, double opt)
	synthetic (const std::string &n, u_int dims, double opt)
	~synthetic ()
sspace::sspace_t *	get_search_space ()
void	set_properties (std::vector< properties > p)
std::vector< properties >	get_properties ()
inst::set	get_opt_param ()
double	get_opt ()
void	update_opt (double opt)
u_int	get_dims ()
void	validate_param_set (inst::set x)
Public Member Functions inherited from optk::benchmark
	benchmark (const std::string &name)
std::string	get_name ()

Additional Inherited Members
Protected Member Functions inherited from syn::synthetic
void	set_opt_param (inst::set op)
Protected Attributes inherited from syn::synthetic
u_int	m_dims
double	m_lb
double	m_ub
double	m_opt
std::vector< properties >	m_properties
inst::set	opt_params
sspace::sspace_t	m_sspace
Protected Attributes inherited from optk::benchmark
std::string	m_name

Detailed Description

The (type III) Complex Deceptive Problem is given by

\[ f(\mathbf{x}) = -\left[ \frac{1}{n}\sum^n_{i=1}g_i(x_i)\right]^\beta, \]

where \(\beta\) is a non-linearity factor. Here we take \(\beta = 2\). Further

\[ g_i(x_i) = \begin{cases} x_i &\text{if } x_i < 0\\ -\frac{x_i}{\alpha_i} + \frac{4}{5} &\text{if } 0\le x_i \le \frac{4}{5}\alpha_i \\ \frac{5x_i}{\alpha_i} - 4 &\text{if } \frac{4}{5}\alpha_i \le x_i < \alpha_i \\ \frac{5(x_i - \alpha_i)}{\alpha_i - 1}+1 &\text{if } \alpha_i \le x+o < \frac{1 + 4\alpha_i}{5} \\ \frac{x_i - 1}{1-\alpha_i} + \frac{4}{5} &\text{otherwise.} \end{cases} \]

For each dimension, we select \(\alpha_i \in (0, 1)\). The parameters are constrained such that \(0\le x_i \le 1\). The global minimum arises at \(\mathbf{x}_i^* = \alpha_i\), with value f({x}^*) = -1. \(. */ class deceptive: public synthetic { public: deceptive (int dims); double evaluate (inst::set x) override; }; /** The deflected corrugated spring benchmark has the following formula: \f[ f(\mathbf{x}) = 0.1 \sum^n_{i=1}(x_i - \alpha)^2 - \cos \left( k \sqrt{\sum^n_{i=1}(x_i - \alpha)^2}\right), \f] where \) = k = 5 x_i 2$. The global minimum is located at \(x^*_i = \alpha\) with a value of \(f(\mathbf{x}^*) = -1\).

Member Function Documentation

evaluate()

double syn::deflected_corrugated_spring::evaluate ( inst::set  x )

overridevirtual

Evaluate the benchmark (i.e. calculate the value of the objective fuinction) on the provided values.

Parameters

x	A vector of double-precision values to evaluate the benchmark at.

Todo:

Verify that a vector of doubles does not constrict the range of benchmark functions which may be evaluated (i.e. as opposed to categorical variables such as strings).

Implements optk::benchmark.

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

• includes/benchmarks/synthetic.hpp
• src/benchmarks/synthetic.cpp