Shekel function

Short description: Function used as a performance test problem for optimization algorithms

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 n dimensions with m maxima is:

f(x→)=∑i=1m(ci+∑j=1n(xj−aji)2)−1

or, similarly,

f(x1,x2,...,xn−1,xn)=∑i=1m(ci+∑j=1n(xj−aij)2)−1

## Contents

* 1 Global minima
* 2 See also
* 3 References
* 4 Further reading

## Global minima

Numerically certified global minima and the corresponding solutions were obtained using interval methods for up to n=10.[2]

## See also

* Test functions for optimization

## References

1. ↑ Molga, M.; Smutnicki, C. (2005). "Test functions for optimization needs. Test functions for optimization needs". Test Functions for Optimization Needs 101: 48. https://marksmannet.com/RobertMarks/Classes/ENGR5358/Papers/functions.pdf.
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

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

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/Shekel function. Read more

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Shekel_function&oldid=194384"