benchmarkfcns.forrester

benchmarkfcns.forrester(arg0: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, 1]']

Computes the value of the Forrester benchmark function. SCORES = forrester(X) computes the value of the Forrester function at point X. forrester accepts a matrix of size M-by-N and returns a vector SCORES of size M-by-1 in which each row contains the function value for the corresponding row of X. Properties:

  • 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)

  • Differentiability: Infinitely differentiable (it is smooth everywhere)

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

Mathematical Definition

Visualization

forrester landscape