Rastrigin function

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 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.

It is defined by:

where A = 10 and x i ∈ [ − 5.12 , 5.12 ] . It has a global minimum at x = 0 where f ( x ) = 0 .