Virtual Library of Simulation Experiments:

Optimization Test Problems

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Hartmann 6-Dimensional Function

Description:

Dimensions: 6

The 6-dimensional Hartmann function has 6 local minima.

Input Domain:

The function is usually evaluated on the hypercube x_i ∈ (0, 1), for all i = 1, …, 6.

Global Minimum:

Modifications and Alternate Forms:

Picheny et al. (2012) use the following rescaled form of the 6-dimensional Hartmann function:


This rescaled form of the function has a mean of zero and a variance of one. The authors also add a small Gaussian error term to the output.

Code:

References:

Dixon, L. C. W., & Szego, G. P. (1978). The global optimization problem: an introduction. Towards global optimization, 2, 1-15.

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

Picheny, V., Wagner, T., & Ginsbourger, D. (2012). A benchmark of kriging-based infill criteria for noisy optimization.

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