Shekel function

{{short description|Function used as a performance test problem for optimization algorithms}}

Image:Shekel_2D.jpg

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.{{cite journal|last1=Molga |first1=M. |last2=Smutnicki |first2=C. |title=Test functions for optimization needs. Test functions for optimization needs |journal=Test Functions for Optimization Needs|url=https://marksmannet.com/RobertMarks/Classes/ENGR5358/Papers/functions.pdf |date=2005 |volume=101 |page=48}}

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}