benchmarkfcns.multifidelity.forrester

benchmarkfcns.multifidelity.forrester(arg0: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]']

Computes the value of the Forrester function at different fidelity levels. SCORES = multifidelity.forrester(X) computes the value of the Forrester function at point X. multifidelity.forrester accepts a matrix of size M-by-1 and returns a vector SCORES of size M-by-4 in which each column contains the function value for each row of X and each column contains the function value for the corresponding fidelity level. Properties (High-fidelity):

  • Global Minimum: approx -6.021

  • Location of Global Minimum: approx 0.757

  • Local Minimum: approx 0.051 (a much shallower dip)

  • Recommended Domain: [0, 1]

  • Dimensions: 1

  • Convexity: Non-convex (it has a distinct “hump” and a deep valley)

  • Modality: Multimodal (one global and one local minimum)

  • Differentiable: Infinitely differentiable (it is smooth everywhere)

For more information, please visit: arxiv.org/pdf/2204.07867

Mathematical Definition

Visualization

forrester landscape