Virtual Library of Simulation Experiments:

Optimization Test Problems

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Michalewicz Function

Description:

Dimensions: d

The Michalewicz function has d! local minima, and it is multimodal. The parameter m defines the steepness of they valleys and ridges; a larger m leads to a more difficult search. The recommended value of m is m = 10. The function's two-dimensional form is shown in the plot above.

Input Domain:

The function is usually evaluated on the hypercube x_i ∈ [0, π], for all i = 1, …, d.

Global Minima:

Code:

References:

Global Optimization Test Functions Index. Retrieved June 2013, from http://infinity77.net/global_optimization/test_functions.html#test-functions-index.

Global Optimization Test Problems. Retrieved June 2013, from
http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO.htm.

Molga, M., & Smutnicki, C. Test functions for optimization needs (2005). Retrieved June 2013, from http://www.zsd.ict.pwr.wroc.pl/files/docs/functions.pdf.

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For questions or comments, please email Derek Bingham at: dbingham@stat.sfu.ca.