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marinepredator (version 0.0.1)

F20: Hartmann 6D Function (F20)

Description

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

Usage

F20(x)

Value

Numeric scalar representing the function value.

Arguments

x

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

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

Run this code
F20(c(0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573))
# Returns approximately -3.32237

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