benchmarkfcns.biggsexp03

benchmarkfcns.biggsexp03(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 Biggs EXP N. 03 benchmark function. SCORES = biggsexp03(X) computes the value of the Biggs EXP N. 03 function at point X. biggsexp03 accepts a matrix of size M-by-3 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: 0

  • Location of global minimum: (1, 10, 1)

  • Number of dimensions: 3

  • Recommended domain: [0, 20]^3

  • Number of local minima: 0

  • Number of global minima: 1

  • Convexity: non-convex

  • Separability: non-separable

  • Modality: unimodal in the standard domain, but can be multimodal in larger

domains

  • Symmetry: non-symmetric

  • Differentiable: yes

Mathematical Definition

\[\begin{split}f(\mathbf{x}) = \sum_{i=1}^{10} \left( x_3 e^{-t_i x_1} - 5 e^{-t_i x_2} - y_i \right)^2 \\\end{split}\]

t_i: 0.1i text{for} i = 1, dots, 10 \ y_i: e^{-t_i} - 5e^{-10t_i} text{for} i = 1, dots, 10

Visualization

../_images/biggsexp03fcn.png