Shekel function

Shekel function is a multidimensional, multimodal, continuous, deterministic function commonly used as a test function for testing optimization techniques.

The mathematical form of a function in ${\displaystyle n}$ dimensions with ${\displaystyle m}$ maxima is:

${\displaystyle f({\vec {x}})=\sum _{i=1}^{m}\;\left(c_{i}+\sum \limits _{j=1}^{n}(x_{j}-a_{ji})^{2}\right)^{-1}}$

or, similarly,

${\displaystyle f(x_{1},x_{2},...,x_{n-1},x_{n})=\sum _{i=1}^{m}\;\left(c_{i}+\sum \limits _{j=1}^{n}(x_{j}-a_{ij})^{2}\right)^{-1}}$

A Shekel function in 2 dimensions and with 10 maxima

Global minima[]

Numerically certified global minima and the corresponding solutions were obtained using interval methods for up to ${\displaystyle n=10}$.^[1]

References[]

Shekel, J. 1971. "Test Functions for Multimodal Search Techniques." Fifth Annual Princeton Conference on Information Science and Systems.

See also[]

• Test functions for optimization

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