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 in 1974 by Rastrigin[1] as a 2-dimensional function and has been generalized by Rudolph.[2] The generalized version was popularized by Hoffmeister & Bäck[3] and Mühlenbein et al.[4] 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 -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. ^ G. Rudolph. "Globale Optimierung mit parallelen Evolutionsstrategien". Diplomarbeit. Department of Computer Science, University of Dortmund, July 1990.
  3. ^ F. Hoffmeister and T. Bäck. "Genetic Algorithms and Evolution Strategies: Similarities and Differences", pages 455–469 in: H.-P. Schwefel and R. Männer (eds.): Parallel Problem Solving from Nature, PPSN I, Proceedings, Springer, 1991.
  4. ^ H. Mühlenbein, D. Schomisch and J. Born. "The Parallel Genetic Algorithm as Function Optimizer ". Parallel Computing, 17, pages 619–632, 1991.