Rastrigin function

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Rastrigin function of two variables
In 3D

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.

On an n-dimensional domain it is defined by:

where and . It has a global minimum at where .

See also[edit]


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