Shekel 10 Function (F23)

Source: R/F23.R

A multimodal test function from the Shekel family with 10 local minima. Fixed dimension of 4.

F23(x)

Arguments

x

Numeric vector of length 4 (4-dimensional input).

Value

Numeric scalar representing the function value.

Details

Formula: $$f(x) = -\sum_{i=1}^{10} \frac{1}{(x - a_i)^T(x - a_i) + c_i}$$

where \(a_i\) are 4-dimensional vectors and \(c_i\) are scalars.

Global minimum: \(f(4, 4, 4, 4) \approx -10.5364\)

Characteristics:

  • Type: Multimodal

  • Separable: No

  • Differentiable: Yes

  • Fixed dimension: 4

  • Number of local minima: 10

  • Default bounds: \([0, 10]^4\)

The Shekel 10 function is the most challenging of the Shekel family due to having the most local minima.

See also

test-functions for an overview of all test functions, get_function_details to retrieve function parameters, F21 for Shekel 5, F22 for Shekel 7.

Examples

F23(c(4, 4, 4, 4))  # Returns approximately -10.54 (near global minimum)
#>           [,1]
#> [1,] -10.53628
F23(c(0, 0, 0, 0))  # Returns a value close to 0
#>            [,1]
#> [1,] -0.3217291