Rastrigin function

Rastrigin function of two variables

In 3D

Contour

In mathematical optimization, the Rastrigin function is a non-convex function used as a performance test problem for optimization algorithms. It is a typical example of non-linear multimodal function. It was first proposed by Rastrigin as a 2-dimensional function and has been generalized by Rudolph. The generalized version was popularized by Hoffmeister & Bäck and Mühlenbein et al. Finding the minimum of this function is a fairly difficult problem due to its large search space and its large number of local minima.

On an n-dimensional domain it is defined by:

$f(\mathbf {x} )=An+\sum _{i=1}^{n}\left[x_{i}^{2}-A\cos(2\pi x_{i})\right]$

where $A=10$ and $x_{i}\in [-5.12,5.12]$. It has a global minimum at $\mathbf {x} =\mathbf {0}$ where $f(\mathbf {x} )=0$.

See also

• Test functions for optimization