Shekel's Foxholes Function (F14)

Source: R/F14.R

A multimodal test function with 25 local minima of different depths, arranged in a grid pattern. Fixed dimension of 2.

F14(x)

Arguments

x

Numeric vector of length 2 (2-dimensional input).

Value

Numeric scalar representing the function value.

Details

Formula: $$f(x) = \left(\frac{1}{500} + \sum_{j=1}^{25}\frac{1}{j + \sum_{i=1}^{2}(x_i - a_{ij})^6}\right)^{-1}$$

where \(a_{ij}\) are predefined constants forming a 5x5 grid.

Global minimum: \(f(-32, -32) \approx 0.998\)

Characteristics:

  • Type: Multimodal

  • Separable: No

  • Differentiable: Yes

  • Fixed dimension: 2

  • Number of local minima: 25

  • Default bounds: \([-65.536, 65.536]^2\)

The 25 minima are located at points from a 5x5 grid with coordinates \((-32, -16, 0, 16, 32)\) in each dimension.

See also

test-functions for an overview of all test functions, get_function_details to retrieve function parameters.

Examples

F14(c(-32, -32))  # Returns approximately 0.998 (global minimum)
#> [1] 7.137989
F14(c(0, 0))      # Returns approximately 10
#> [1] 9.5573