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optimization > Rastrigin function

mathematical analysis > real analysis > real-valued function > function of several real variables > Rastrigin function

Preferred term

Rastrigin function

Definition(s)

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 as a 2-dimensional function and has been generalized by Rudolph. The generalized version was popularized by Hoffmeister & Bäck and 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.
On an ${\\displaystyle n}$ $n$ -dimensional domain it is defined by:

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

where ${\\displaystyle A=10}$ $A=10$ and ${\\displaystyle x_{i}\\in [-5.12,5.12]}$ $x_{i}\\in [-5.12,5.12]$ . There are many extrema:
- The global minimum is at ${\\displaystyle \\mathbf {x} =\\mathbf {0} }$ where ${\\displaystyle f(\\mathbf {x} )=0}$ .

Broader concept(s)

In other languages

fonction de Rastrigin

French

URI

http://data.loterre.fr/ark:/67375/PSR-QL0GMPR2-2

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