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.

The mathematical form of a function in $$n$$ dimensions with $$m$$ maxima is:

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

or, similarly,

$$ f(x_1,x_2,...,x_{n-1},x_n) = \sum_{i = 1}^{m} \; \left( c_{i} + \sum\limits_{j = 1}^{n} (x_{j} - a_{ij})^2 \right)^{-1} $$

Global minima
Numerically certified global minima and the corresponding solutions were obtained using interval methods for up to $$n = 10$$.