benchmarkfcns.perm

benchmarkfcns.perm(x: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous'], beta: SupportsFloat | SupportsIndex = 0.5) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, 1]']

Computes the value of the Perm function. SCORES = perm(X) computes the value of the Perm function at point X. perm 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. SCORES = perm(X, beta=BETA) specifies the BETA parameter. Properties:

  • Global minimum: 0

  • Location of global minimum: (1, 2, …, n)

  • Number of dimensions: n

  • Recommended domain: [-n, n]^n

  • Number of local minima: many

  • Number of global minima: 1

  • Convexity: non-convex

  • Separability: non-separable

  • Modality: multimodal

Mathematical Definition

Visualization

perm landscape