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Shekel function

From Wikipedia, the free encyclopedia
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 dimensions with maxima is:

or, similarly,

Global minima

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Numerically certified global minima and the corresponding solutions were obtained using interval methods for up to .[2]

See also

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References

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  1. ^ Molga, M.; Smutnicki, C. (2005). "Test functions for optimization needs. Test functions for optimization needs" (PDF). Test Functions for Optimization Needs. 101: 48.
  2. ^ 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.

Further reading

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