benchmarkfcns.biggsexp05

benchmarkfcns.biggsexp05(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. 05 benchmark function. SCORES = biggsexp05(X) computes the value of the Biggs EXP N. 05 function at point X. biggsexp05 accepts a matrix of size M-by-5 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, 5, 4)

  • Number of dimensions: 5

  • Recommended domain: [0, 20]^5

  • Number of local minima: 0

  • Number of global minima: 1

  • Convexity: non-convex

  • Separability: non-separable

  • Modality: unimodal

  • Symmetry: non-symmetric

  • Differentiable: yes

For more information, please visit: benchmarkfcns.info/doc/biggsexp05fcn

Mathematical Definition

\[\begin{split}f_{\text{BiggsExp05}}(\mathbf{x}) = \sum_{i=1}^{10} \left( x_3 e^{-t_i x_1} - x_4 e^{-t_i x_2} + 3 e^{-t_i x_5} - y_i \right)^2 \\\end{split}\]

t_i = 0.1i text{for} i = 1, dots, 10 \ y_i = e^{-t_i} - 5e^{-10t_i} + 3e^{-4t_i}

Visualization

No visualization available for this function.