Virtual Library of Simulation Experiments:

Test Functions and Datasets

Hartmann 6-Dimensional Function


Dimensions: 6

The 6-dimensional Hartmann function has 6 local minima.

Input Domain:

The function is usually evaluated on the hypercube xi ∈ (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.



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

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

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