benchmarkfcns.debn1

benchmarkfcns.debn1(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 Deb N. 1 benchmark function. SCORES = deb1(X) computes the value of the Deb N. 1 function at point X. deb1 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: -1

  • Location of global minimum: x_i = 0.1 + 0.2k for k in {0, 1, 2, 3, 4} (within [0, 1])

  • Number of dimensions: n

  • Recommended domain: [0, 1]^n

  • Number of local minima: many

  • Number of global minima: 5^n

  • Convexity: non-convex

  • Separability: separable

  • Modality: multimodal

  • Symmetry: symmetric

  • Differentiable: Yes

Mathematical Definition

Visualization

debn1 landscape