Kowalik Function (F15)

Source: R/F15.R

A multimodal test function used for testing optimization algorithms, based on fitting experimental data. Fixed dimension of 4.

F15(x)

Arguments

x

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

Value

Numeric scalar representing the function value.

Details

Formula: $$f(x) = \sum_{i=1}^{11}\left(a_i - \frac{x_1(b_i^2 + b_i x_2)}{b_i^2 + b_i x_3 + x_4}\right)^2$$

where \(a_i\) and \(b_i\) are predefined constants from experimental data.

Global minimum: \(f(0.1928, 0.1908, 0.1231, 0.1358) \approx 0.0003075\)

Characteristics:

  • Type: Multimodal

  • Separable: No

  • Differentiable: Yes

  • Fixed dimension: 4

  • Default bounds: \([-5, 5]^4\)

This function is derived from a curve-fitting problem and has several local minima near the global minimum.

See also

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

Examples

F15(c(0.1928, 0.1908, 0.1231, 0.1358))  # Returns approximately 0.0003
#> [1] 0.0003074952
F15(c(0, 0, 0, 0))  # Returns a larger value
#> [1] 0.1484132