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 ^[1] as a 2-dimensional function and has been generalized by Mühlenbein et al.^[2] Finding the minimum of this function is a fairly difficult problem due to its large search space and its large number of local minima.

It is defined by:

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

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

Notes

1. ↑ Rastrigin, L. A. "Systems of extremal control." (1974).
2. ↑ H. Mühlenbein, D. Schomisch and J. Born. "The Parallel Genetic Algorithm as Function Optimizer ". Parallel Computing, 17, pages 619–632, 1991.