A multimodal test function with 6 local minima in 6 dimensions. Fixed dimension of 6.
F20(x)Numeric scalar representing the function value.
Formula: $$f(x) = -\sum_{i=1}^{4} c_i \exp\left(-\sum_{j=1}^{6} a_{ij}(x_j - p_{ij})^2\right)$$
where \(a_{ij}\), \(c_i\), and \(p_{ij}\) are predefined constants.
Global minimum: \(f(0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573) \approx -3.32237\)
Characteristics:
Type: Multimodal
Separable: No
Differentiable: Yes
Fixed dimension: 6
Number of local minima: 6
Default bounds: \([0, 1]^6\)
The Hartmann 6D function is more challenging than the 3D version due to the higher dimensionality.
test-functions for an overview of all test functions,
get_function_details to retrieve function parameters,
F19 for the 3D version.
F20(c(0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573))
#> [1] -3.321877
# Returns approximately -3.32237