Metric (mathematics): Difference between revisions
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The | |||
'''Shekel function''' is a multidimensional, multimodal, continuous, deterministic [[function (mathematics)|function]] commonly used as a test function for testing [[optimization (mathematics)|optimization]] techniques. | |||
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} \tfrac{1}{c_{i} + \sum\limits_{j = 1}^{n} (x_{j} - a_{ji})^2 } | |||
</math> | |||
or, similarly, | |||
<math> | |||
f(x_1,x_2,...,x_{n-1},x_n) = \sum_{i = 1}^{m} \tfrac{1}{c_{i} + \sum\limits_{j = 1}^{n} (x_{j} - a_{ij})^2 } | |||
</math> | |||
[[Image:Shekel_2D.jpg|right|thumb|400px|A Shekel function in 2 dimensions and with 10 maxima]] | |||
== References == | |||
Shekel, J. 1971. "Test Functions for Multimodal Search Techniques." ''Fifth Annual Princeton Conference on Information Science and Systems''. | |||
== See also == | |||
*[[Test functions for optimization]] | |||
[[Category:Mathematical optimization]] | |||
{{Mathanalysis-stub}} | |||
{{Mathapplied-stub}} | |||
Revision as of 03:37, 4 January 2014
Shekel function is a multidimensional, multimodal, continuous, deterministic function commonly used as a test function for testing optimization techniques.
The mathematical form of a function in dimensions with maxima is:
or, similarly,
References
Shekel, J. 1971. "Test Functions for Multimodal Search Techniques." Fifth Annual Princeton Conference on Information Science and Systems.