Six-Hump Camel Back Function (F16)

Source: R/F16.R

A multimodal test function with six local minima, two of which are global. Fixed dimension of 2.

F16(x)

Arguments

x

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

Value

Numeric scalar representing the function value.

Details

Formula: $$f(x) = 4x_1^2 - 2.1x_1^4 + \frac{x_1^6}{3} + x_1 x_2 - 4x_2^2 + 4x_2^4$$

Global minimum: \(f(\pm 0.0898, \mp 0.7126) \approx -1.0316\)

There are two global minima at approximately \((0.0898, -0.7126)\) and \((-0.0898, 0.7126)\).

Characteristics:

  • Type: Multimodal

  • Separable: No

  • Differentiable: Yes

  • Fixed dimension: 2

  • Number of local minima: 6

  • Number of global minima: 2

  • Default bounds: \([-5, 5]^2\)

The function has a shape resembling a camel's back with six humps (minima).

See also

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

Examples

F16(c(0.0898, -0.7126))   # Returns approximately -1.0316 (global minimum)
#> [1] -1.031628
F16(c(-0.0898, 0.7126))   # Returns approximately -1.0316 (global minimum)
#> [1] -1.031628
F16(c(0, 0))              # Returns 0
#> [1] 0