Rastrigine function

Plot of the Rastrigin function in two dimensions

The Rastrigin function is a non-convex function from the field of mathematical optimization . The rastrigin function was proposed as a two-dimensional function by Leonard A. Rastrigin in 1974 and generalized to higher dimensions by Günter Rudolph in 1990. The generalized version was published by Hoffmeister & Bäck and Mühlenbein et al. made popular.

definition

Contour plot of the Rastrigin function

The rastrigin function is through

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

defined, where is a constant, the dimension and with . ${\displaystyle A=10}$ ${\displaystyle n}$ ${\displaystyle {\mathbf {x} }=(x_{1},\ldots ,x_{n})}$ ${\displaystyle x_{i}\in [-5.12,5.12]}$

use

The rastrigin function is a typical example of a non-linear multimodal function . It is used for the performance analysis of optimization algorithms, and because of its large search space and the high number of local minima it represents a difficult problem. Your global minimum is at with . ${\displaystyle \mathbf {x} =\mathbf {0} }$ ${\displaystyle f(\mathbf {x} )=0}$

Web links

• Rastrigin function in programming (English)
• Brief Description of the Rastrigin function (English)

Individual evidence

1. ^ A. Törn and A. Zilinskas. "Global Optimization". Lecture Notes in Computer Science, Nº 350, Springer-Verlag, Berlin, 1989.
2. ↑ G. Rudolph. "Global optimization with parallel evolution strategies". Thesis. 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 (Ed.): 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.