Shekel function

A Shekel function in 2 dimensions and with 10 maxima

The Shekel function or also Shekel's foxholes is a multidimensional, multimodal, continuous, deterministic function commonly used as a test function for testing optimization techniques.^[1]

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

${\displaystyle f(\overrightarrow{x})=\sum _{i=1}^m{(c_i+\sum _{j=1}^n(x_j-a_{ji}{)}^2)}^{-1}}$

or, similarly,

${\displaystyle f(x_1,x_2,...,x_{n-1},x_n)=\sum _{i=1}^m{(c_i+\sum _{j=1}^n(x_j-a_{ij}{)}^2)}^{-1}}$

Global minima

Numerically certified global minima and the corresponding solutions were obtained using interval methods for up to ${\displaystyle n=10}$.^[2]

See also

• Test functions for optimization

References

Further reading

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

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