A multimodal test function with 6 local minima in 6 dimensions. Fixed dimension of 6.

F20(x)

Arguments

x

Numeric vector of length 6 (6-dimensional input).

Value

Numeric scalar representing the function value.

Details

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.

See also

test-functions for an overview of all test functions, get_function_details to retrieve function parameters, F19 for the 3D version.

Examples

F20(c(0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573))
#> [1] -3.321877
# Returns approximately -3.32237