# Rastrigin#

struct rastrigin#

The Rastrigin problem.

This is a scalable box-constrained continuous single-objective problem. The objective function is the generalised n-dimensional Rastrigin function:

$F\left(x_1,\ldots,x_n\right) = 10 \cdot n + \sum_{i=1}^n x_i^2 - 10\cdot\cos\left( 2\pi \cdot x_i \right), \quad x_i \in \left[ -5.12,5.12 \right].$

Gradients (dense) are also provided as:

$G_i\left(x_1,\ldots,x_n\right) = 2 x_i + 10 \cdot 2\pi \cdot\sin\left( 2\pi \cdot x_i \right)$
And Hessians (sparse as only the diagonal is non-zero) are:
$H_{ii}\left(x_1,\ldots,x_n\right) = 2 + 10 \cdot 4\pi^2 \cdot\cos\left( 2\pi \cdot x_i \right)$
The global minimum is in the origin, where $$F\left( 0,\ldots,0 \right) = 0$$.

Public Functions

rastrigin(unsigned dim = 1u)#

Constructor from dimension.

Constructs a Rastrigin problem

Parameters

dim – the problem dimensions.

Throws

std::invalid_argument – if dim is < 1

vector_double fitness(const vector_double&) const#

Fitness computation.

Computes the fitness for this UDP

Parameters

x – the decision vector.

Returns

the fitness of x.

std::pair<vector_double, vector_double> get_bounds() const#

Box-bounds.

It returns the box-bounds for this UDP.

Returns

the lower and upper bounds for each of the decision vector components

It returns the fitness gradient for this UDP.

The gradient is represented in a sparse form as required by problem::gradient().

Parameters

x – the decision vector.

Returns

the gradient of the fitness function

std::vector<vector_double> hessians(const vector_double&) const#

Hessians.

It returns the hessians for this UDP.

The hessians are represented in a sparse form as required by problem::hessians().

Parameters

x – the decision vector.

Returns

the hessians of the fitness function

std::vector<sparsity_pattern> hessians_sparsity() const#

Hessians sparsity (only the diagonal elements are non zero)

It returns the hessian sparisty structure for this UDP.

The hessian sparisty is represented in the form required by problem::hessians_sparsity().

Returns

the hessians of the fitness function

inline std::string get_name() const#

Problem name.

Returns

a string containing the problem name

vector_double best_known() const#

Optimal solution.

Returns

the decision vector corresponding to the best solution for this problem.

Public Members

unsigned m_dim#

Problem dimensions.