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.<ref>Template:Cite journal</ref>
The mathematical form of a function in <math>n</math> dimensions with <math>m</math> maxima is:
<math> f(\vec{x}) = \sum_{i = 1}^{m} \; \left( c_{i} + \sum\limits_{j = 1}^{n} (x_{j} - a_{ji})^2 \right)^{-1} </math>
or, similarly,
<math> 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} </math>
Global minimaEdit
Numerically certified global minima and the corresponding solutions were obtained using interval methods for up to <math>n = 10</math>.<ref name="vanaret2015hybridation">Vanaret C. (2015) Hybridization of interval methods and evolutionary algorithms for solving difficult optimization problems. PhD thesis. Ecole Nationale de l'Aviation Civile. Institut National Polytechnique de Toulouse, France.</ref>
See alsoEdit
ReferencesEdit
<references/>
Further readingEdit
Shekel, J. 1971. "Test Functions for Multimodal Search Techniques." Fifth Annual Princeton Conference on Information Science and Systems.