benchmarkfcns.friedman1

benchmarkfcns.friedman1(x: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous'], rnd: bool = False) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, 1]']

Computes the value of the Friedman N. 1 benchmark function.

Properties:

  • Global minimum: In the domain [0, 1], the minimum is approximately 0.3954

  • Location of global minimum: x_1 * x_2 approx 0, x_3 = 0.5, x_4 = 0, and x_5 = 0.

  • Number of dimensions: 10 (though only 5 are active)

  • Recommended domain: [0, 1]^10

  • Number of local minima: Several, due to the sin term

  • Number of global minima: At least 1 within the [0, 1] unit hypercube

  • Convexity: Non-convex

  • Separability: Non-separable

  • Modality: Multimodal

  • Symmetry: Symmetric for x_1 and x_2

  • Differentiable: Yes

Inputs:

  • x: A matrix of size M-by-10.

  • rnd: An optional boolean flag that, if true, adds a small random noise to the

    function value to create a noisy version of the function. Default is false.

For more information, please visit: benchmarkfcns.info/doc/friedman1fcn

Mathematical Definition

Visualization

friedman1 landscape