marinepredator (version 0.0.1)

F22: Shekel 7 Function (F22)

Description

A multimodal test function from the Shekel family with 7 local minima. Fixed dimension of 4.

Usage

F22(x)

Value

Numeric scalar representing the function value.

Arguments

x

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

Details

Formula: $$f(x) = -\sum_{i=1}^{7} \frac{1}{(x - a_i)^T(x - a_i) + c_i}$$

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

Global minimum: \(f(4, 4, 4, 4) \approx -10.4029\)

Characteristics:

• Type: Multimodal

• Separable: No

• Differentiable: Yes

• Fixed dimension: 4

• Number of local minima: 7

• Default bounds: \([0, 10]^4\)

The Shekel 7 function has more local minima than Shekel 5, making it slightly more challenging.

See Also

test-functions for an overview of all test functions, get_function_details to retrieve function parameters, F21 for Shekel 5, F23 for Shekel 10.

Examples

F22(c(4, 4, 4, 4))  # Returns approximately -10.40 (near global minimum)
F22(c(0, 0, 0, 0))  # Returns a value close to 0