Quartic Function with Noise (F07)

Source: R/F07.R

A unimodal test function with quartic terms and added uniform random noise. The noise makes this a stochastic function, useful for testing robustness.

F07(x)

Arguments

x

Numeric vector of input values.

Value

Numeric scalar representing the function value.

Details

Formula: $$f(x) = \sum_{i=1}^{n} i \cdot x_i^4 + \text{random}[0,1)$$

Global minimum: \(f(0, 0, ..., 0) \approx 0\) (stochastic, depends on noise)

Characteristics:

  • Type: Unimodal (with noise)

  • Separable: Yes (deterministic part)

  • Differentiable: Yes

  • Stochastic: Yes (random noise added)

  • Default bounds: \([-1.28, 1.28]^n\)

  • Default dimensions: 50

The random noise component makes function evaluations non-deterministic, testing an algorithm's ability to handle noisy objective functions.

See also

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

Examples

F07(c(0, 0, 0))  # Returns a value close to 0 (with some noise)
#> [1] 0.4023282
# Multiple calls may return different values due to noise:
replicate(5, F07(c(0, 0, 0)))
#> [1] 0.19566983 0.40353812 0.06366146 0.38870131 0.97554784