Shekel function

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({\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}}

Numerically certified global minima and the corresponding solutions were obtained using interval methods for up to

[2] Shekel, J.

"Test Functions for Multimodal Search Techniques."

Fifth Annual Princeton Conference on Information Science and Systems.

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