Virtual Library of Simulation Experiments:

Optimization Test Problems

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Hartmann 4-Dimensional Function

Description:

Dimensions: 4

The 4-dimensional Hartmann function is multimodal. It is given here in the form of Picheny et al. (2012), having a mean of zero and a variance of one. The authors also add a small Gaussian error term to the output.

Input Domain:

The function is evaluated on the hypercube x_i ∈ [0, 1], for all i = 1, 2, 3, 4.

Code:

References:

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

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.